{"id":475955,"date":"2023-08-09T07:24:43","date_gmt":"2023-08-09T07:24:43","guid":{"rendered":""},"modified":"2024-06-11T19:24:00","modified_gmt":"2024-06-11T19:24:00","slug":"auto-regressive-models","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/vn\/wiki\/auto-regressive-models\/","title":{"rendered":"M\u00f4 h\u00ecnh t\u1ef1 h\u1ed3i quy"},"content":{"rendered":"<p>M\u00f4 h\u00ecnh h\u1ed3i quy t\u1ef1 \u0111\u1ed9ng l\u00e0 m\u1ed9t lo\u1ea1i m\u00f4 h\u00ecnh th\u1ed1ng k\u00ea \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau, bao g\u1ed3m x\u1eed l\u00fd ng\u00f4n ng\u1eef t\u1ef1 nhi\u00ean, ph\u00e2n t\u00edch chu\u1ed7i th\u1eddi gian v\u00e0 t\u1ea1o h\u00ecnh \u1ea3nh. C\u00e1c m\u00f4 h\u00ecnh n\u00e0y d\u1ef1 \u0111o\u00e1n m\u1ed9t chu\u1ed7i c\u00e1c gi\u00e1 tr\u1ecb d\u1ef1a tr\u00ean c\u00e1c gi\u00e1 tr\u1ecb \u0111\u01b0\u1ee3c quan s\u00e1t tr\u01b0\u1edbc \u0111\u00f3, khi\u1ebfn ch\u00fang r\u1ea5t ph\u00f9 h\u1ee3p cho c\u00e1c t\u00e1c v\u1ee5 li\u00ean quan \u0111\u1ebfn d\u1eef li\u1ec7u tu\u1ea7n t\u1ef1. C\u00e1c m\u00f4 h\u00ecnh t\u1ef1 h\u1ed3i quy \u0111\u00e3 \u0111\u01b0\u1ee3c ch\u1ee9ng minh l\u00e0 c\u00f3 hi\u1ec7u qu\u1ea3 cao trong vi\u1ec7c t\u1ea1o ra d\u1eef li\u1ec7u th\u1ef1c t\u1ebf v\u00e0 d\u1ef1 \u0111o\u00e1n k\u1ebft qu\u1ea3 trong t\u01b0\u01a1ng lai.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">L\u1ecbch s\u1eed ngu\u1ed3n g\u1ed1c c\u1ee7a c\u00e1c m\u00f4 h\u00ecnh T\u1ef1 h\u1ed3i quy v\u00e0 l\u1ea7n \u0111\u1ea7u ti\u00ean \u0111\u1ec1 c\u1eadp \u0111\u1ebfn n\u00f3<\/h2>\n\n\n\n<p>Kh\u00e1i ni\u1ec7m t\u1ef1 h\u1ed3i quy c\u00f3 t\u1eeb \u0111\u1ea7u th\u1ebf k\u1ef7 20, v\u1edbi c\u00f4ng tr\u00ecnh ti\u00ean phong \u0111\u01b0\u1ee3c th\u1ef1c hi\u1ec7n b\u1edfi nh\u00e0 th\u1ed1ng k\u00ea ng\u01b0\u1eddi Anh Yule v\u00e0o n\u0103m 1927. Tuy nhi\u00ean, ch\u00ednh c\u00f4ng tr\u00ecnh c\u1ee7a nh\u00e0 to\u00e1n h\u1ecdc Norbert Wiener v\u00e0o nh\u1eefng n\u0103m 1940 \u0111\u00e3 \u0111\u1eb7t n\u1ec1n m\u00f3ng cho c\u00e1c m\u00f4 h\u00ecnh t\u1ef1 h\u1ed3i quy hi\u1ec7n \u0111\u1ea1i. Nghi\u00ean c\u1ee9u c\u1ee7a Wiener v\u1ec1 c\u00e1c qu\u00e1 tr\u00ecnh v\u00e0 d\u1ef1 \u0111o\u00e1n ng\u1eabu nhi\u00ean \u0111\u00e3 \u0111\u1eb7t n\u1ec1n m\u00f3ng cho s\u1ef1 ph\u00e1t tri\u1ec3n c\u1ee7a c\u00e1c m\u00f4 h\u00ecnh h\u1ed3i quy t\u1ef1 \u0111\u1ed9ng nh\u01b0 ch\u00fang ta bi\u1ebft ng\u00e0y nay.<\/p>\n\n\n\n<p>Thu\u1eadt ng\u1eef \u201ct\u1ef1 h\u1ed3i quy\u201d \u0111\u01b0\u1ee3c Ragnar Frisch \u0111\u01b0a ra l\u1ea7n \u0111\u1ea7u ti\u00ean trong l\u0129nh v\u1ef1c kinh t\u1ebf v\u00e0o cu\u1ed1i nh\u1eefng n\u0103m 1920. Frisch \u0111\u00e3 s\u1eed d\u1ee5ng thu\u1eadt ng\u1eef n\u00e0y \u0111\u1ec3 m\u00f4 t\u1ea3 m\u1ed9t m\u00f4 h\u00ecnh h\u1ed3i quy m\u1ed9t bi\u1ebfn theo c\u00e1c gi\u00e1 tr\u1ecb tr\u1ec5 c\u1ee7a ch\u00ednh n\u00f3, t\u1eeb \u0111\u00f3 n\u1eafm b\u1eaft \u0111\u01b0\u1ee3c s\u1ef1 ph\u1ee5 thu\u1ed9c c\u1ee7a m\u1ed9t bi\u1ebfn v\u00e0o qu\u00e1 kh\u1ee9 c\u1ee7a ch\u00ednh n\u00f3.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">M\u00f4 h\u00ecnh t\u1ef1 h\u1ed3i quy: Th\u00f4ng tin chi ti\u1ebft<\/h2>\n\n\n\n<p>M\u00f4 h\u00ecnh t\u1ef1 \u0111\u1ed9ng h\u1ed3i quy (AR) l\u00e0 c\u00f4ng c\u1ee5 thi\u1ebft y\u1ebfu trong ph\u00e2n t\u00edch chu\u1ed7i th\u1eddi gian, \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 d\u1ef1 b\u00e1o c\u00e1c gi\u00e1 tr\u1ecb trong t\u01b0\u01a1ng lai d\u1ef1a tr\u00ean d\u1eef li\u1ec7u l\u1ecbch s\u1eed. Nh\u1eefng m\u00f4 h\u00ecnh n\u00e0y gi\u1ea3 \u0111\u1ecbnh r\u1eb1ng c\u00e1c gi\u00e1 tr\u1ecb trong qu\u00e1 kh\u1ee9 \u1ea3nh h\u01b0\u1edfng \u0111\u1ebfn c\u00e1c gi\u00e1 tr\u1ecb hi\u1ec7n t\u1ea1i v\u00e0 t\u01b0\u01a1ng lai theo c\u00e1ch tuy\u1ebfn t\u00ednh. Ch\u00fang \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong kinh t\u1ebf, t\u00e0i ch\u00ednh, d\u1ef1 b\u00e1o th\u1eddi ti\u1ebft v\u00e0 nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c n\u01a1i ph\u1ed5 bi\u1ebfn d\u1eef li\u1ec7u chu\u1ed7i th\u1eddi gian.<\/p><h3>Bi\u1ec3u di\u1ec5n to\u00e1n h\u1ecdc<\/h3><p>M\u00f4 h\u00ecnh tr\u1eadt t\u1ef1 t\u1ef1 h\u1ed3i quy <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">P<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.1944em;\"><\/span><span class=\"mord mathnormal\">P<\/span><\/span><\/span><\/span> (AR(p)) \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n d\u01b0\u1edbi d\u1ea1ng to\u00e1n h\u1ecdc nh\u01b0 sau:\n<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>Y<\/mi><mi>t<\/mi><\/msub><mo>=<\/mo><msub><mi>\u03d5<\/mi><mn>1<\/mn><\/msub><msub><mi>Y<\/mi><mrow><mi>t<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msub><mo>+<\/mo><msub><mi>\u03d5<\/mi><mn>2<\/mn><\/msub><msub><mi>Y<\/mi><mrow><mi>t<\/mi><mo>\u2212<\/mo><mn>2<\/mn><\/mrow><\/msub><mo>+<\/mo><mo>\u22ef<\/mo><mo>+<\/mo><msub><mi>\u03d5<\/mi><mi>P<\/mi><\/msub><msub><mi>Y<\/mi><mrow><mi>t<\/mi><mo>\u2212<\/mo><mi>P<\/mi><\/mrow><\/msub><mo>+<\/mo><msub><mi>\u03f5<\/mi><mi>t<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">Y_t = \\phi_1 Y_{t-1} + \\phi_2 Y_{t-2} + \\cdots + \\phi_p Y_{tp} + \\epsilon_t<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em;\"><span style=\"top: -2.55em; margin-left: -0.2222em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9028em; vertical-align: -0.2083em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03d5<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em;\"><span style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em;\"><span style=\"top: -2.55em; margin-left: -0.2222em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9028em; vertical-align: -0.2083em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03d5<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em;\"><span style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em;\"><span style=\"top: -2.55em; margin-left: -0.2222em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em; vertical-align: -0.0833em;\"><\/span><span class=\"minner\">\u22ef<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9805em; vertical-align: -0.2861em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03d5<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em;\"><span style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">P<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em;\"><span style=\"top: -2.55em; margin-left: -0.2222em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mathnormal mtight\">P<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03f5<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em;\"><span style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p><p>\u1ede \u0111\u00e2u:<\/p><ul><li><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>Y<\/mi><mi>t<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">Y_t<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em;\"><span style=\"top: -2.55em; margin-left: -0.2222em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> l\u00e0 gi\u00e1 tr\u1ecb c\u1ee7a chu\u1ed7i t\u1ea1i th\u1eddi \u0111i\u1ec3m <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>t<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">t<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6151em;\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span>.<\/li><li><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03d5<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>\u03d5<\/mi><mn>2<\/mn><\/msub><mo separator=\"true\">,<\/mo><mo>\u2026<\/mo><mo separator=\"true\">,<\/mo><msub><mi>\u03d5<\/mi><mi>P<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\phi_1, \\phi_2, \\ldots, \\phi_p<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9805em; vertical-align: -0.2861em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03d5<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em;\"><span style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03d5<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em;\"><span style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em;\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03d5<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em;\"><span style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">P<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> l\u00e0 c\u00e1c h\u1ec7 s\u1ed1 c\u1ee7a m\u00f4 h\u00ecnh.<\/li><li><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>Y<\/mi><mrow><mi>t<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msub><mo separator=\"true\">,<\/mo><msub><mi>Y<\/mi><mrow><mi>t<\/mi><mo>\u2212<\/mo><mn>2<\/mn><\/mrow><\/msub><mo separator=\"true\">,<\/mo><mo>\u2026<\/mo><mo separator=\"true\">,<\/mo><msub><mi>Y<\/mi><mrow><mi>t<\/mi><mo>\u2212<\/mo><mi>P<\/mi><\/mrow><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">Y_{t-1}, Y_{t-2}, \\ldots, Y_{tp}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em; vertical-align: -0.2861em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em;\"><span style=\"top: -2.55em; margin-left: -0.2222em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em;\"><span style=\"top: -2.55em; margin-left: -0.2222em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em;\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em;\"><span style=\"top: -2.55em; margin-left: -0.2222em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mathnormal mtight\">P<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> l\u00e0 c\u00e1c gi\u00e1 tr\u1ecb qu\u00e1 kh\u1ee9 c\u1ee7a chu\u1ed7i.<\/li><li><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03f5<\/mi><mi>t<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\epsilon_t<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03f5<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em;\"><span style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> l\u00e0 thu\u1eadt ng\u1eef l\u1ed7i t\u1ea1i th\u1eddi \u0111i\u1ec3m <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>t<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">t<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6151em;\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span>, th\u01b0\u1eddng \u0111\u01b0\u1ee3c coi l\u00e0 nhi\u1ec5u tr\u1eafng v\u1edbi gi\u00e1 tr\u1ecb trung b\u00ecnh b\u1eb1ng 0 v\u00e0 ph\u01b0\u01a1ng sai kh\u00f4ng \u0111\u1ed5i.<\/li><\/ul><h3>X\u00e1c \u0111\u1ecbnh th\u1ee9 t\u1ef1 (p)<\/h3><p>M\u1ec7nh l\u1ec7nh <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">P<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.1944em;\"><\/span><span class=\"mord mathnormal\">P<\/span><\/span><\/span><\/span> c\u1ee7a m\u00f4 h\u00ecnh AR l\u00e0 r\u1ea5t quan tr\u1ecdng v\u00ec n\u00f3 x\u00e1c \u0111\u1ecbnh s\u1ed1 l\u01b0\u1ee3ng quan s\u00e1t trong qu\u00e1 kh\u1ee9 s\u1ebd \u0111\u01b0\u1ee3c \u0111\u01b0a v\u00e0o m\u00f4 h\u00ecnh. S\u1ef1 l\u1ef1a ch\u1ecdn c\u1ee7a <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">P<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.1944em;\"><\/span><span class=\"mord mathnormal\">P<\/span><\/span><\/span><\/span> bao g\u1ed3m m\u1ed9t s\u1ef1 \u0111\u00e1nh \u0111\u1ed5i:<\/p><ul><li><strong>B\u1eadc th\u1ea5p<\/strong> m\u00f4 h\u00ecnh (nh\u1ecf <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">P<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.1944em;\"><\/span><span class=\"mord mathnormal\">P<\/span><\/span><\/span><\/span>) c\u00f3 th\u1ec3 kh\u00f4ng n\u1eafm b\u1eaft \u0111\u01b0\u1ee3c t\u1ea5t c\u1ea3 c\u00e1c m\u1eabu c\u00f3 li\u00ean quan trong d\u1eef li\u1ec7u, d\u1eabn \u0111\u1ebfn t\u00ecnh tr\u1ea1ng kh\u00f4ng ph\u00f9 h\u1ee3p.<\/li><li><strong>Th\u1ee9 t\u1ef1 cao h\u01a1n<\/strong> m\u00f4 h\u00ecnh (l\u1edbn <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">P<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.1944em;\"><\/span><span class=\"mord mathnormal\">P<\/span><\/span><\/span><\/span>) c\u00f3 th\u1ec3 n\u1eafm b\u1eaft \u0111\u01b0\u1ee3c c\u00e1c m\u1eabu ph\u1ee9c t\u1ea1p h\u01a1n nh\u01b0ng c\u00f3 nguy c\u01a1 b\u1ecb trang b\u1ecb qu\u00e1 m\u1ee9c, trong \u0111\u00f3 m\u00f4 h\u00ecnh m\u00f4 t\u1ea3 nhi\u1ec5u ng\u1eabu nhi\u00ean thay v\u00ec quy tr\u00ecnh c\u01a1 b\u1ea3n.<\/li><\/ul><p>C\u00e1c ph\u01b0\u01a1ng ph\u00e1p ph\u1ed5 bi\u1ebfn \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh th\u1ee9 t\u1ef1 t\u1ed1i \u01b0u <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">P<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.1944em;\"><\/span><span class=\"mord mathnormal\">P<\/span><\/span><\/span><\/span> bao g\u1ed3m:<\/p><ul><li><strong>H\u00e0m t\u1ef1 t\u01b0\u01a1ng quan m\u1ed9t ph\u1ea7n (PACF)<\/strong>: X\u00e1c \u0111\u1ecbnh \u0111\u1ed9 tr\u1ec5 \u0111\u00e1ng k\u1ec3 c\u1ea7n \u0111\u01b0\u1ee3c \u0111\u01b0a v\u00e0o.<\/li><li><strong>Ti\u00eau ch\u00ed th\u00f4ng tin<\/strong>: C\u00e1c ti\u00eau ch\u00ed nh\u01b0 Ti\u00eau ch\u00ed Th\u00f4ng tin Akaike (AIC) v\u00e0 m\u00f4 h\u00ecnh c\u00e2n b\u1eb1ng Ti\u00eau ch\u00ed Th\u00f4ng tin Bayesian (BIC) ph\u00f9 h\u1ee3p v\u00e0 ph\u1ee9c t\u1ea1p \u0111\u1ec3 l\u1ef1a ch\u1ecdn m\u1ed9t ti\u00eau ch\u00ed ph\u00f9 h\u1ee3p <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">P<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.1944em;\"><\/span><span class=\"mord mathnormal\">P<\/span><\/span><\/span><\/span>.<\/li><\/ul><h3>\u01af\u1edbc t\u00ednh m\u00f4 h\u00ecnh<\/h3><p>\u01af\u1edbc t\u00ednh c\u00e1c th\u00f4ng s\u1ed1 <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03d5<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>\u03d5<\/mi><mn>2<\/mn><\/msub><mo separator=\"true\">,<\/mo><mo>\u2026<\/mo><mo separator=\"true\">,<\/mo><msub><mi>\u03d5<\/mi><mi>P<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\phi_1, \\phi_2, \\ldots, \\phi_p<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9805em; vertical-align: -0.2861em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03d5<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em;\"><span style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03d5<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em;\"><span style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em;\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03d5<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em;\"><span style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">P<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> li\u00ean quan \u0111\u1ebfn vi\u1ec7c \u0111i\u1ec1u ch\u1ec9nh m\u00f4 h\u00ecnh cho ph\u00f9 h\u1ee3p v\u1edbi d\u1eef li\u1ec7u l\u1ecbch s\u1eed. \u0110i\u1ec1u n\u00e0y c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c th\u1ef1c hi\u1ec7n b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng c\u00e1c k\u1ef9 thu\u1eadt nh\u01b0:<\/p><ul><li><strong>\u01af\u1edbc t\u00ednh b\u00ecnh ph\u01b0\u01a1ng nh\u1ecf nh\u1ea5t<\/strong>: Gi\u1ea3m thi\u1ec3u t\u1ed5ng sai s\u1ed1 b\u00ecnh ph\u01b0\u01a1ng gi\u1eefa gi\u00e1 tr\u1ecb \u0111\u01b0\u1ee3c quan s\u00e1t v\u00e0 gi\u00e1 tr\u1ecb d\u1ef1 \u0111o\u00e1n.<\/li><li><strong>\u01af\u1edbc l\u01b0\u1ee3ng kh\u1ea3 n\u0103ng t\u1ed1i \u0111a<\/strong>: T\u00ecm c\u00e1c tham s\u1ed1 t\u1ed1i \u0111a h\u00f3a kh\u1ea3 n\u0103ng quan s\u00e1t d\u1eef li\u1ec7u \u0111\u00e3 cho.<\/li><\/ul><h3>Ch\u1ea9n \u0111o\u00e1n m\u00f4 h\u00ecnh<\/h3><p>Sau khi l\u1eafp m\u00f4 h\u00ecnh AR, vi\u1ec7c \u0111\u00e1nh gi\u00e1 t\u00ednh ph\u00f9 h\u1ee3p c\u1ee7a n\u00f3 l\u00e0 \u0111i\u1ec1u c\u1ea7n thi\u1ebft. Ki\u1ec3m tra ch\u1ea9n \u0111o\u00e1n ch\u00ednh bao g\u1ed3m:<\/p><ul><li><strong>Ph\u00e2n t\u00edch d\u01b0 l\u01b0\u1ee3ng<\/strong>: \u0110\u1ea3m b\u1ea3o r\u1eb1ng ph\u1ea7n d\u01b0 (l\u1ed7i) gi\u1ed1ng v\u1edbi nhi\u1ec5u tr\u1eafng, bi\u1ec3u th\u1ecb kh\u00f4ng c\u00f3 m\u1eabu n\u00e0o m\u00e0 m\u00f4 h\u00ecnh kh\u00f4ng gi\u1ea3i th\u00edch \u0111\u01b0\u1ee3c.<\/li><li><strong>Ki\u1ec3m tra h\u1ed9p Ljung<\/strong>: \u0110\u00e1nh gi\u00e1 li\u1ec7u c\u00f3 b\u1ea5t k\u1ef3 s\u1ef1 t\u1ef1 t\u01b0\u01a1ng quan n\u00e0o c\u1ee7a ph\u1ea7n d\u01b0 kh\u00e1c bi\u1ec7t \u0111\u00e1ng k\u1ec3 so v\u1edbi 0 hay kh\u00f4ng.<\/li><\/ul><h3>C\u00e1c \u1ee9ng d\u1ee5ng<\/h3><p>C\u00e1c m\u00f4 h\u00ecnh AR r\u1ea5t linh ho\u1ea1t v\u00e0 c\u00f3 th\u1ec3 t\u00ecm th\u1ea5y \u1ee9ng d\u1ee5ng trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau:<\/p><ul><li><strong>Kinh t\u1ebf v\u00e0 t\u00e0i ch\u00ednh<\/strong>: D\u1ef1 b\u00e1o gi\u00e1 c\u1ed5 phi\u1ebfu, l\u00e3i su\u1ea5t v\u00e0 c\u00e1c ch\u1ec9 s\u1ed1 kinh t\u1ebf.<\/li><li><strong>D\u1ef1 b\u00e1o th\u1eddi ti\u1ebft<\/strong>: D\u1ef1 \u0111o\u00e1n m\u00f4 h\u00ecnh nhi\u1ec7t \u0111\u1ed9 v\u00e0 l\u01b0\u1ee3ng m\u01b0a.<\/li><li><strong>K\u1ef9 thu\u1eadt<\/strong>: H\u1ec7 th\u1ed1ng x\u1eed l\u00fd v\u00e0 \u0111i\u1ec1u khi\u1ec3n t\u00edn hi\u1ec7u.<\/li><li><strong>Th\u1ed1ng k\u00ea sinh h\u1ecdc<\/strong>: M\u00f4 h\u00ecnh h\u00f3a d\u1eef li\u1ec7u chu\u1ed7i th\u1eddi gian sinh h\u1ecdc.<\/li><\/ul><h3>\u01afu \u0111i\u1ec3m v\u00e0 h\u1ea1n ch\u1ebf<\/h3><p><strong>Thu\u1eadn l\u1ee3i:<\/strong><\/p><ul><li>\u0110\u01a1n gi\u1ea3n v\u00e0 d\u1ec5 th\u1ef1c hi\u1ec7n.<\/li><li>Gi\u1ea3i th\u00edch r\u00f5 r\u00e0ng c\u00e1c th\u00f4ng s\u1ed1.<\/li><li>Hi\u1ec7u qu\u1ea3 cho vi\u1ec7c d\u1ef1 b\u00e1o ng\u1eafn h\u1ea1n.<\/li><\/ul><p><strong>H\u1ea1n ch\u1ebf:<\/strong><\/p><ul><li>Gi\u1ea3 s\u1eed c\u00e1c m\u1ed1i quan h\u1ec7 tuy\u1ebfn t\u00ednh.<\/li><li>C\u00f3 th\u1ec3 kh\u00f4ng ph\u00f9 h\u1ee3p v\u1edbi d\u1eef li\u1ec7u c\u00f3 t\u00ednh th\u1eddi v\u1ee5 m\u1ea1nh ho\u1eb7c c\u00e1c m\u1eabu phi tuy\u1ebfn t\u00ednh.<\/li><li>Nh\u1ea1y c\u1ea3m trong vi\u1ec7c l\u1ef1a ch\u1ecdn th\u1ee9 t\u1ef1 <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">P<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.1944em;\"><\/span><span class=\"mord mathnormal\">P<\/span><\/span><\/span><\/span>.<\/li><\/ul><h3>V\u00ed d\u1ee5<\/h3><p>H\u00e3y xem x\u00e9t m\u00f4 h\u00ecnh AR(2) (b\u1eadc 2) cho d\u1eef li\u1ec7u chu\u1ed7i th\u1eddi gian:\n<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>Y<\/mi><mi>t<\/mi><\/msub><mo>=<\/mo><mn>0.5<\/mn><msub><mi>Y<\/mi><mrow><mi>t<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msub><mo>+<\/mo><mn>0.2<\/mn><msub><mi>Y<\/mi><mrow><mi>t<\/mi><mo>\u2212<\/mo><mn>2<\/mn><\/mrow><\/msub><mo>+<\/mo><msub><mi>\u03f5<\/mi><mi>t<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">Y_t = 0,5 Y_{t-1} + 0,2 Y_{t-2} + \\epsilon_t<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em;\"><span style=\"top: -2.55em; margin-left: -0.2222em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8917em; vertical-align: -0.2083em;\"><\/span><span class=\"mord\">0.5<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em;\"><span style=\"top: -2.55em; margin-left: -0.2222em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8917em; vertical-align: -0.2083em;\"><\/span><span class=\"mord\">0.2<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em;\"><span style=\"top: -2.55em; margin-left: -0.2222em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03f5<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em;\"><span style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\n\u1ede \u0111\u00e2y, gi\u00e1 tr\u1ecb t\u1ea1i th\u1eddi \u0111i\u1ec3m <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>t<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">t<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6151em;\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span> ph\u1ee5 thu\u1ed9c v\u00e0o gi\u00e1 tr\u1ecb t\u1ea1i hai th\u1eddi \u0111i\u1ec3m tr\u01b0\u1edbc \u0111\u00f3, v\u1edbi h\u1ec7 s\u1ed1 l\u1ea7n l\u01b0\u1ee3t l\u00e0 0,5 v\u00e0 0,2.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Ph\u00e2n t\u00edch c\u00e1c \u0111\u1eb7c \u0111i\u1ec3m ch\u00ednh c\u1ee7a m\u00f4 h\u00ecnh T\u1ef1 h\u1ed3i quy<\/h2>\n\n\n\n<p>C\u00e1c m\u00f4 h\u00ecnh t\u1ef1 h\u1ed3i quy cung c\u1ea5p m\u1ed9t s\u1ed1 t\u00ednh n\u0103ng ch\u00ednh khi\u1ebfn ch\u00fang c\u00f3 gi\u00e1 tr\u1ecb cho c\u00e1c \u1ee9ng d\u1ee5ng kh\u00e1c nhau:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>D\u1ef1 \u0111o\u00e1n tr\u00ecnh t\u1ef1<\/strong>: C\u00e1c m\u00f4 h\u00ecnh t\u1ef1 \u0111\u1ed9ng h\u1ed3i quy v\u01b0\u1ee3t tr\u1ed9i trong vi\u1ec7c d\u1ef1 \u0111o\u00e1n c\u00e1c gi\u00e1 tr\u1ecb trong t\u01b0\u01a1ng lai theo tr\u00ecnh t\u1ef1 th\u1eddi gian, khi\u1ebfn ch\u00fang tr\u1edf n\u00ean l\u00fd t\u01b0\u1edfng cho vi\u1ec7c d\u1ef1 b\u00e1o chu\u1ed7i th\u1eddi gian.<\/li>\n\n\n\n<li><strong>Kh\u1ea3 n\u0103ng s\u00e1ng t\u1ea1o<\/strong>: C\u00e1c m\u00f4 h\u00ecnh n\u00e0y c\u00f3 th\u1ec3 t\u1ea1o c\u00e1c m\u1eabu d\u1eef li\u1ec7u m\u1edbi gi\u1ed1ng v\u1edbi d\u1eef li\u1ec7u hu\u1ea5n luy\u1ec7n, khi\u1ebfn ch\u00fang tr\u1edf n\u00ean h\u1eefu \u00edch cho vi\u1ec7c t\u0103ng c\u01b0\u1eddng d\u1eef li\u1ec7u v\u00e0 c\u00e1c t\u00e1c v\u1ee5 s\u00e1ng t\u1ea1o nh\u01b0 t\u1ea1o v\u0103n b\u1ea3n v\u00e0 h\u00ecnh \u1ea3nh.<\/li>\n\n\n\n<li><strong>Uy\u1ec3n chuy\u1ec3n<\/strong>: C\u00e1c m\u00f4 h\u00ecnh t\u1ef1 \u0111\u1ed9ng h\u1ed3i quy c\u00f3 th\u1ec3 ch\u1ee9a c\u00e1c lo\u1ea1i d\u1eef li\u1ec7u kh\u00e1c nhau v\u00e0 kh\u00f4ng b\u1ecb gi\u1edbi h\u1ea1n trong m\u1ed9t mi\u1ec1n c\u1ee5 th\u1ec3, cho ph\u00e9p \u1ee9ng d\u1ee5ng ch\u00fang trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau.<\/li>\n\n\n\n<li><strong>Kh\u1ea3 n\u0103ng gi\u1ea3i th\u00edch<\/strong>: S\u1ef1 \u0111\u01a1n gi\u1ea3n trong c\u1ea5u tr\u00fac c\u1ee7a m\u00f4 h\u00ecnh cho ph\u00e9p d\u1ec5 d\u00e0ng di\u1ec5n gi\u1ea3i c\u00e1c tham s\u1ed1 v\u00e0 d\u1ef1 \u0111o\u00e1n c\u1ee7a m\u00f4 h\u00ecnh.<\/li>\n\n\n\n<li><strong>Kh\u1ea3 n\u0103ng th\u00edch \u1ee9ng<\/strong>: C\u00e1c m\u00f4 h\u00ecnh h\u1ed3i quy t\u1ef1 \u0111\u1ed9ng c\u00f3 th\u1ec3 th\u00edch \u1ee9ng v\u1edbi vi\u1ec7c thay \u0111\u1ed5i m\u1eabu d\u1eef li\u1ec7u v\u00e0 k\u1ebft h\u1ee3p th\u00f4ng tin m\u1edbi theo th\u1eddi gian.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">C\u00e1c lo\u1ea1i m\u00f4 h\u00ecnh t\u1ef1 h\u1ed3i quy<\/h2>\n\n\n\n<p>C\u00e1c m\u00f4 h\u00ecnh t\u1ef1 h\u1ed3i quy c\u00f3 nhi\u1ec1u d\u1ea1ng kh\u00e1c nhau, m\u1ed7i d\u1ea1ng c\u00f3 nh\u1eefng \u0111\u1eb7c \u0111i\u1ec3m ri\u00eang. C\u00e1c lo\u1ea1i m\u00f4 h\u00ecnh t\u1ef1 h\u1ed3i quy ch\u00ednh bao g\u1ed3m:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>M\u00f4 h\u00ecnh trung b\u00ecnh \u0111\u1ed9ng h\u1ed3i quy (ARMA)<\/strong>: K\u1ebft h\u1ee3p c\u00e1c th\u00e0nh ph\u1ea7n t\u1ef1 \u0111\u1ed9ng h\u1ed3i quy v\u00e0 trung b\u00ecnh \u0111\u1ed9ng \u0111\u1ec3 t\u00ednh c\u1ea3 l\u1ed7i hi\u1ec7n t\u1ea1i v\u00e0 l\u1ed7i qu\u00e1 kh\u1ee9.<\/li>\n\n\n\n<li><strong>C\u00e1c m\u00f4 h\u00ecnh Trung b\u00ecnh tr\u01b0\u1ee3t T\u00edch h\u1ee3p t\u1ef1 \u0111\u1ed9ng h\u1ed3i quy (ARIMA)<\/strong>: M\u1edf r\u1ed9ng ARMA b\u1eb1ng c\u00e1ch k\u1ebft h\u1ee3p ph\u01b0\u01a1ng ph\u00e1p sai ph\u00e2n \u0111\u1ec3 \u0111\u1ea1t \u0111\u01b0\u1ee3c t\u00ednh d\u1eebng trong d\u1eef li\u1ec7u chu\u1ed7i th\u1eddi gian kh\u00f4ng c\u1ed1 \u0111\u1ecbnh.<\/li>\n\n\n\n<li><strong>C\u00e1c m\u00f4 h\u00ecnh Trung b\u00ecnh tr\u01b0\u1ee3t t\u00edch h\u1ee3p t\u1ef1 \u0111\u1ed9ng h\u1ed3i quy theo m\u00f9a (SARIMA)<\/strong>: Phi\u00ean b\u1ea3n theo m\u00f9a c\u1ee7a ARIMA, ph\u00f9 h\u1ee3p v\u1edbi d\u1eef li\u1ec7u chu\u1ed7i th\u1eddi gian c\u00f3 m\u00f4 h\u00ecnh theo m\u00f9a.<\/li>\n\n\n\n<li><strong>M\u00f4 h\u00ecnh h\u1ed3i quy t\u1ef1 \u0111\u1ed9ng Vector (VAR)<\/strong>: Ph\u1ea7n m\u1edf r\u1ed9ng \u0111a bi\u1ebfn c\u1ee7a m\u00f4 h\u00ecnh h\u1ed3i quy t\u1ef1 \u0111\u1ed9ng, \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng khi nhi\u1ec1u bi\u1ebfn \u1ea3nh h\u01b0\u1edfng l\u1eabn nhau.<\/li>\n\n\n\n<li><strong>M\u1ea1ng b\u1ed9 nh\u1edb ng\u1eafn h\u1ea1n d\u00e0i (LSTM)<\/strong>: M\u1ed9t lo\u1ea1i m\u1ea1ng th\u1ea7n kinh t\u00e1i ph\u00e1t c\u00f3 th\u1ec3 n\u1eafm b\u1eaft c\u00e1c ph\u1ea7n ph\u1ee5 thu\u1ed9c t\u1ea7m xa trong d\u1eef li\u1ec7u tu\u1ea7n t\u1ef1, th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong c\u00e1c t\u00e1c v\u1ee5 x\u1eed l\u00fd ng\u00f4n ng\u1eef t\u1ef1 nhi\u00ean v\u00e0 nh\u1eadn d\u1ea1ng gi\u1ecdng n\u00f3i.<\/li>\n\n\n\n<li><strong>Model m\u00e1y bi\u1ebfn \u00e1p<\/strong>: M\u1ed9t lo\u1ea1i ki\u1ebfn tr\u00fac m\u1ea1ng th\u1ea7n kinh s\u1eed d\u1ee5ng c\u01a1 ch\u1ebf ch\u00fa \u00fd \u0111\u1ec3 x\u1eed l\u00fd d\u1eef li\u1ec7u tu\u1ea7n t\u1ef1, \u0111\u01b0\u1ee3c bi\u1ebft \u0111\u1ebfn v\u1edbi th\u00e0nh c\u00f4ng trong d\u1ecbch ng\u00f4n ng\u1eef v\u00e0 t\u1ea1o v\u0103n b\u1ea3n.<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1061\" height=\"440\" src=\"https:\/\/oneproxy.pro\/wp-content\/uploads\/2024\/06\/auto-egressive-model.png\" alt=\"M\u00f4 h\u00ecnh t\u1ef1 h\u1ed3i quy \u0111\u1ec3 x\u1eed l\u00fd ng\u00f4n ng\u1eef t\u1ef1 nhi\u00ean\" class=\"wp-image-505503\" title=\"M\u00f4 h\u00ecnh t\u1ef1 h\u1ed3i quy \u0111\u1ec3 x\u1eed l\u00fd ng\u00f4n ng\u1eef t\u1ef1 nhi\u00ean\" srcset=\"https:\/\/oneproxy.pro\/wp-content\/uploads\/2024\/06\/auto-egressive-model.png 1061w, https:\/\/oneproxy.pro\/wp-content\/uploads\/2024\/06\/auto-egressive-model-150x62.png 150w, https:\/\/oneproxy.pro\/wp-content\/uploads\/2024\/06\/auto-egressive-model-768x318.png 768w, https:\/\/oneproxy.pro\/wp-content\/uploads\/2024\/06\/auto-egressive-model-18x7.png 18w\" sizes=\"auto, (max-width: 1061px) 100vw, 1061px\" \/><figcaption class=\"wp-element-caption\">M\u00f4 h\u00ecnh t\u1ef1 h\u1ed3i quy \u0111\u1ec3 x\u1eed l\u00fd ng\u00f4n ng\u1eef t\u1ef1 nhi\u00ean<\/figcaption><\/figure>\n\n\n\n<p>D\u01b0\u1edbi \u0111\u00e2y l\u00e0 b\u1ea3ng so s\u00e1nh t\u00f3m t\u1eaft c\u00e1c \u0111\u1eb7c \u0111i\u1ec3m ch\u00ednh c\u1ee7a c\u00e1c m\u00f4 h\u00ecnh t\u1ef1 h\u1ed3i quy n\u00e0y:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Ng\u01b0\u1eddi m\u1eabu<\/th><th>C\u00e1c t\u00ednh n\u0103ng ch\u00ednh<\/th><th>\u1ee8ng d\u1ee5ng<\/th><\/tr><\/thead><tbody><tr><td>ARMA<\/td><td>T\u1ef1 \u0111\u1ed9ng h\u1ed3i quy, Trung b\u00ecnh tr\u01b0\u1ee3t<\/td><td>D\u1ef1 b\u00e1o chu\u1ed7i th\u1eddi gian<\/td><\/tr><tr><td>ARIMA<\/td><td>T\u1ef1 \u0111\u1ed9ng h\u1ed3i quy, T\u00edch h\u1ee3p, Trung b\u00ecnh \u0111\u1ed9ng<\/td><td>D\u1eef li\u1ec7u t\u00e0i ch\u00ednh, xu h\u01b0\u1edbng kinh t\u1ebf<\/td><\/tr><tr><td>SARIMA<\/td><td>T\u1ef1 \u0111\u1ed9ng h\u1ed3i quy theo m\u00f9a, T\u00edch h\u1ee3p, Trung b\u00ecnh tr\u01b0\u1ee3t<\/td><td>D\u1eef li\u1ec7u kh\u00ed h\u1eadu, m\u00f4 h\u00ecnh theo m\u00f9a<\/td><\/tr><tr><td>VAR<\/td><td>\u0110a bi\u1ebfn, t\u1ef1 \u0111\u1ed9ng h\u1ed3i quy<\/td><td>M\u00f4 h\u00ecnh kinh t\u1ebf v\u0129 m\u00f4<\/td><\/tr><tr><td>LSTM<\/td><td>M\u1ea1ng th\u1ea7n kinh t\u00e1i ph\u00e1t<\/td><td>X\u1eed l\u00fd ng\u00f4n ng\u1eef t\u1ef1 nhi\u00ean<\/td><\/tr><tr><td>M\u00e1y bi\u1ebfn \u00e1p<\/td><td>C\u01a1 ch\u1ebf ch\u00fa \u00fd, x\u1eed l\u00fd song song<\/td><td>T\u1ea1o v\u0103n b\u1ea3n, d\u1ecbch thu\u1eadt<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">C\u00e1ch s\u1eed d\u1ee5ng m\u00f4 h\u00ecnh Auto-regression, c\u00e1c v\u1ea5n \u0111\u1ec1 v\u00e0 gi\u1ea3i ph\u00e1p li\u00ean quan \u0111\u1ebfn vi\u1ec7c s\u1eed d\u1ee5ng<\/h2>\n\n\n\n<p>C\u00e1c m\u00f4 h\u00ecnh t\u1ef1 h\u1ed3i quy t\u00ecm th\u1ea5y \u1ee9ng d\u1ee5ng trong nhi\u1ec1u l\u0129nh v\u1ef1c:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>D\u1ef1 b\u00e1o chu\u1ed7i th\u1eddi gian<\/strong>: D\u1ef1 \u0111o\u00e1n gi\u00e1 c\u1ed5 phi\u1ebfu, ki\u1ec3u th\u1eddi ti\u1ebft ho\u1eb7c l\u01b0u l\u01b0\u1ee3ng truy c\u1eadp trang web.<\/li>\n\n\n\n<li><strong>X\u1eed l\u00fd ng\u00f4n ng\u1eef t\u1ef1 nhi\u00ean<\/strong>: T\u1ea1o v\u0103n b\u1ea3n, d\u1ecbch ng\u00f4n ng\u1eef, ph\u00e2n t\u00edch t\u00ecnh c\u1ea3m.<\/li>\n\n\n\n<li><strong>T\u1ea1o h\u00ecnh \u1ea3nh<\/strong>: T\u1ea1o h\u00ecnh \u1ea3nh th\u1ef1c t\u1ebf b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng M\u1ea1ng \u0111\u1ed1i th\u1ee7 s\u00e1ng t\u1ea1o (GAN).<\/li>\n\n\n\n<li><strong>S\u00e1ng t\u00e1c nh\u1ea1c<\/strong>: T\u1ea1o ra c\u00e1c chu\u1ed7i v\u00e0 t\u00e1c ph\u1ea9m \u00e2m nh\u1ea1c m\u1edbi.<\/li>\n\n\n\n<li><strong>Ph\u00e1t hi\u1ec7n b\u1ea5t th\u01b0\u1eddng<\/strong>: X\u00e1c \u0111\u1ecbnh c\u00e1c ngo\u1ea1i l\u1ec7 trong d\u1eef li\u1ec7u chu\u1ed7i th\u1eddi gian.<\/li>\n<\/ol>\n\n\n\n<p>M\u1eb7c d\u00f9 c\u00f3 nh\u1eefng \u0111i\u1ec3m m\u1ea1nh nh\u01b0ng c\u00e1c m\u00f4 h\u00ecnh t\u1ef1 h\u1ed3i quy v\u1eabn c\u00f3 m\u1ed9t s\u1ed1 h\u1ea1n ch\u1ebf:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Tr\u00ed nh\u1edb ng\u1eafn h\u1ea1n<\/strong>: H\u1ecd c\u00f3 th\u1ec3 g\u1eb7p kh\u00f3 kh\u0103n trong vi\u1ec7c n\u1eafm b\u1eaft c\u00e1c y\u1ebfu t\u1ed1 ph\u1ee5 thu\u1ed9c l\u00e2u d\u00e0i trong d\u1eef li\u1ec7u.<\/li>\n\n\n\n<li><strong>Trang b\u1ecb qu\u00e1 m\u1ee9c<\/strong>: C\u00e1c m\u00f4 h\u00ecnh t\u1ef1 h\u1ed3i quy b\u1eadc cao c\u00f3 th\u1ec3 ph\u00f9 h\u1ee3p qu\u00e1 m\u1ee9c v\u1edbi nhi\u1ec5u trong d\u1eef li\u1ec7u.<\/li>\n\n\n\n<li><strong>T\u00ednh c\u1ed1 \u0111\u1ecbnh c\u1ee7a d\u1eef li\u1ec7u<\/strong>: C\u00e1c m\u00f4 h\u00ecnh lo\u1ea1i ARIMA y\u00eau c\u1ea7u d\u1eef li\u1ec7u c\u1ed1 \u0111\u1ecbnh, \u0111i\u1ec1u n\u00e0y c\u00f3 th\u1ec3 kh\u00f3 \u0111\u1ea1t \u0111\u01b0\u1ee3c trong th\u1ef1c t\u1ebf.<\/li>\n<\/ol>\n\n\n\n<p>\u0110\u1ec3 gi\u1ea3i quy\u1ebft nh\u1eefng th\u00e1ch th\u1ee9c n\u00e0y, c\u00e1c nh\u00e0 nghi\u00ean c\u1ee9u \u0111\u00e3 \u0111\u1ec1 xu\u1ea5t nhi\u1ec1u gi\u1ea3i ph\u00e1p kh\u00e1c nhau:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>M\u1ea1ng th\u1ea7n kinh t\u00e1i ph\u00e1t (RNN)<\/strong>: Ch\u00fang cung c\u1ea5p kh\u1ea3 n\u0103ng ghi nh\u1edb d\u00e0i h\u1ea1n t\u1ed1t h\u01a1n.<\/li>\n\n\n\n<li><strong>K\u1ef9 thu\u1eadt ch\u00ednh quy h\u00f3a<\/strong>: \u0110\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 ng\u0103n ch\u1eb7n vi\u1ec7c trang b\u1ecb qu\u00e1 m\u1ee9c trong c\u00e1c m\u00f4 h\u00ecnh b\u1eadc cao.<\/li>\n\n\n\n<li><strong>S\u1ef1 kh\u00e1c bi\u1ec7t theo m\u00f9a<\/strong>: \u0110\u1ec3 \u0111\u1ea1t \u0111\u01b0\u1ee3c t\u00ednh \u1ed5n \u0111\u1ecbnh c\u1ee7a d\u1eef li\u1ec7u trong d\u1eef li\u1ec7u theo m\u00f9a.<\/li>\n\n\n\n<li><strong>C\u01a1 ch\u1ebf ch\u00fa \u00fd<\/strong>: C\u1ea3i thi\u1ec7n kh\u1ea3 n\u0103ng x\u1eed l\u00fd ph\u1ee5 thu\u1ed9c t\u1ea7m xa trong c\u00e1c m\u00f4 h\u00ecnh Transformer.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">C\u00e1c \u0111\u1eb7c \u0111i\u1ec3m ch\u00ednh v\u00e0 so s\u00e1nh kh\u00e1c v\u1edbi c\u00e1c thu\u1eadt ng\u1eef t\u01b0\u01a1ng t\u1ef1<\/h2>\n\n\n\n<p>C\u00e1c m\u00f4 h\u00ecnh h\u1ed3i quy t\u1ef1 \u0111\u1ed9ng th\u01b0\u1eddng \u0111\u01b0\u1ee3c so s\u00e1nh v\u1edbi c\u00e1c m\u00f4 h\u00ecnh chu\u1ed7i th\u1eddi gian kh\u00e1c, ch\u1eb3ng h\u1ea1n nh\u01b0:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>M\u00f4 h\u00ecnh Trung b\u00ecnh \u0110\u1ed9ng (MA)<\/strong>: Ch\u1ec9 t\u1eadp trung v\u00e0o m\u1ed1i quan h\u1ec7 gi\u1eefa gi\u00e1 tr\u1ecb hi\u1ec7n t\u1ea1i v\u00e0 sai s\u1ed1 trong qu\u00e1 kh\u1ee9, trong khi c\u00e1c m\u00f4 h\u00ecnh h\u1ed3i quy t\u1ef1 \u0111\u1ed9ng xem x\u00e9t c\u00e1c gi\u00e1 tr\u1ecb trong qu\u00e1 kh\u1ee9 c\u1ee7a bi\u1ebfn.<\/li>\n\n\n\n<li><strong>C\u00e1c m\u00f4 h\u00ecnh Trung b\u00ecnh tr\u01b0\u1ee3t t\u1ef1 \u0111\u1ed9ng h\u1ed3i quy (ARMA)<\/strong>: K\u1ebft h\u1ee3p c\u00e1c th\u00e0nh ph\u1ea7n trung b\u00ecnh \u0111\u1ed9ng v\u00e0 h\u1ed3i quy t\u1ef1 \u0111\u1ed9ng, mang l\u1ea1i c\u00e1ch ti\u1ebfp c\u1eadn to\u00e0n di\u1ec7n h\u01a1n \u0111\u1ec3 l\u1eadp m\u00f4 h\u00ecnh d\u1eef li\u1ec7u chu\u1ed7i th\u1eddi gian.<\/li>\n\n\n\n<li><strong>C\u00e1c m\u00f4 h\u00ecnh Trung b\u00ecnh tr\u01b0\u1ee3t t\u00edch h\u1ee3p t\u1ef1 \u0111\u1ed9ng h\u1ed3i quy (ARIMA)<\/strong>: K\u1ebft h\u1ee3p ph\u01b0\u01a1ng ph\u00e1p sai ph\u00e2n \u0111\u1ec3 \u0111\u1ea1t \u0111\u01b0\u1ee3c t\u00ednh d\u1eebng trong d\u1eef li\u1ec7u chu\u1ed7i th\u1eddi gian kh\u00f4ng c\u1ed1 \u0111\u1ecbnh.<\/li>\n<\/ol>\n\n\n\n<p>D\u01b0\u1edbi \u0111\u00e2y l\u00e0 b\u1ea3ng so s\u00e1nh n\u00eau b\u1eadt nh\u1eefng kh\u00e1c bi\u1ec7t ch\u00ednh gi\u1eefa c\u00e1c m\u00f4 h\u00ecnh chu\u1ed7i th\u1eddi gian n\u00e0y:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Ng\u01b0\u1eddi m\u1eabu<\/th><th>C\u00e1c t\u00ednh n\u0103ng ch\u00ednh<\/th><th>\u1ee8ng d\u1ee5ng<\/th><\/tr><\/thead><tbody><tr><td>T\u1ef1 \u0111\u1ed9ng h\u1ed3i quy (AR)<\/td><td>H\u1ed3i quy so v\u1edbi c\u00e1c gi\u00e1 tr\u1ecb trong qu\u00e1 kh\u1ee9<\/td><td>D\u1ef1 b\u00e1o chu\u1ed7i th\u1eddi gian<\/td><\/tr><tr><td>\u0110\u01b0\u1eddng trung b\u00ecnh \u0111\u1ed9ng (MA)<\/td><td>H\u1ed3i quy c\u00e1c l\u1ed7i trong qu\u00e1 kh\u1ee9<\/td><td>L\u1ecdc ti\u1ebfng \u1ed3n<\/td><\/tr><tr><td>\u0110\u01b0\u1eddng trung b\u00ecnh \u0111\u1ed9ng h\u1ed3i quy t\u1ef1 \u0111\u1ed9ng (ARMA)<\/td><td>S\u1ef1 k\u1ebft h\u1ee3p c\u1ee7a c\u00e1c th\u00e0nh ph\u1ea7n AR v\u00e0 MA<\/td><td>D\u1ef1 b\u00e1o chu\u1ed7i th\u1eddi gian, L\u1ecdc ti\u1ebfng \u1ed3n<\/td><\/tr><tr><td>\u0110\u01b0\u1eddng trung b\u00ecnh \u0111\u1ed9ng t\u00edch h\u1ee3p t\u1ef1 \u0111\u1ed9ng h\u1ed3i quy (ARIMA)<\/td><td>Vi ph\u00e2n v\u1ec1 t\u00ednh d\u1eebng<\/td><td>D\u1eef li\u1ec7u t\u00e0i ch\u00ednh, xu h\u01b0\u1edbng kinh t\u1ebf<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Vi\u1ec5n c\u1ea3nh v\u00e0 c\u00f4ng ngh\u1ec7 c\u1ee7a t\u01b0\u01a1ng lai li\u00ean quan \u0111\u1ebfn m\u00f4 h\u00ecnh Auto-regression<\/h2>\n\n\n\n<p>C\u00e1c m\u00f4 h\u00ecnh t\u1ef1 h\u1ed3i quy ti\u1ebfp t\u1ee5c ph\u00e1t tri\u1ec3n, \u0111\u01b0\u1ee3c th\u00fac \u0111\u1ea9y b\u1edfi nh\u1eefng ti\u1ebfn b\u1ed9 trong h\u1ecdc s\u00e2u v\u00e0 x\u1eed l\u00fd ng\u00f4n ng\u1eef t\u1ef1 nhi\u00ean. T\u01b0\u01a1ng lai c\u1ee7a c\u00e1c m\u00f4 h\u00ecnh t\u1ef1 h\u1ed3i quy c\u00f3 th\u1ec3 s\u1ebd li\u00ean quan \u0111\u1ebfn:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Ki\u1ebfn tr\u00fac ph\u1ee9c t\u1ea1p h\u01a1n<\/strong>: C\u00e1c nh\u00e0 nghi\u00ean c\u1ee9u s\u1ebd kh\u00e1m ph\u00e1 c\u00e1c c\u1ea5u tr\u00fac m\u1ea1ng ph\u1ee9c t\u1ea1p h\u01a1n v\u00e0 s\u1ef1 k\u1ebft h\u1ee3p c\u1ee7a c\u00e1c m\u00f4 h\u00ecnh h\u1ed3i quy t\u1ef1 \u0111\u1ed9ng v\u1edbi c\u00e1c ki\u1ebfn tr\u00fac kh\u00e1c nh\u01b0 Transformers v\u00e0 LSTM.<\/li>\n\n\n\n<li><strong>C\u01a1 ch\u1ebf ch\u00fa \u00fd<\/strong>: C\u01a1 ch\u1ebf ch\u00fa \u00fd s\u1ebd \u0111\u01b0\u1ee3c c\u1ea3i ti\u1ebfn \u0111\u1ec3 t\u0103ng c\u01b0\u1eddng s\u1ef1 ph\u1ee5 thu\u1ed9c l\u00e2u d\u00e0i trong d\u1eef li\u1ec7u tu\u1ea7n t\u1ef1.<\/li>\n\n\n\n<li><strong>\u0110\u00e0o t\u1ea1o hi\u1ec7u qu\u1ea3<\/strong>: Nh\u1eefng n\u1ed7 l\u1ef1c s\u1ebd \u0111\u01b0\u1ee3c th\u1ef1c hi\u1ec7n \u0111\u1ec3 gi\u1ea3m c\u00e1c y\u00eau c\u1ea7u t\u00ednh to\u00e1n \u0111\u1ec3 \u0111\u00e0o t\u1ea1o c\u00e1c m\u00f4 h\u00ecnh t\u1ef1 h\u1ed3i quy quy m\u00f4 l\u1edbn.<\/li>\n\n\n\n<li><strong>H\u1ecdc kh\u00f4ng gi\u00e1m s\u00e1t<\/strong>: C\u00e1c m\u00f4 h\u00ecnh h\u1ed3i quy t\u1ef1 \u0111\u1ed9ng s\u1ebd \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng cho c\u00e1c nhi\u1ec7m v\u1ee5 h\u1ecdc t\u1eadp kh\u00f4ng gi\u00e1m s\u00e1t, ch\u1eb3ng h\u1ea1n nh\u01b0 ph\u00e1t hi\u1ec7n s\u1ef1 b\u1ea5t th\u01b0\u1eddng v\u00e0 h\u1ecdc bi\u1ec3u di\u1ec5n.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">C\u00e1ch s\u1eed d\u1ee5ng ho\u1eb7c li\u00ean k\u1ebft m\u00e1y ch\u1ee7 proxy v\u1edbi c\u00e1c m\u00f4 h\u00ecnh T\u1ef1 \u0111\u1ed9ng h\u1ed3i quy<\/h2>\n\n\n\n<p>M\u00e1y ch\u1ee7 proxy c\u00f3 th\u1ec3 \u0111\u00f3ng m\u1ed9t vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c c\u1ea3i thi\u1ec7n hi\u1ec7u su\u1ea5t c\u1ee7a c\u00e1c m\u00f4 h\u00ecnh t\u1ef1 \u0111\u1ed9ng h\u1ed3i quy, \u0111\u1eb7c bi\u1ec7t trong m\u1ed9t s\u1ed1 \u1ee9ng d\u1ee5ng nh\u1ea5t \u0111\u1ecbnh:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Thu th\u1eadp d\u1eef li\u1ec7u<\/strong>: Khi thu th\u1eadp d\u1eef li\u1ec7u \u0111\u00e0o t\u1ea1o cho c\u00e1c m\u00f4 h\u00ecnh h\u1ed3i quy t\u1ef1 \u0111\u1ed9ng, m\u00e1y ch\u1ee7 proxy c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 \u1ea9n danh v\u00e0 \u0111a d\u1ea1ng h\u00f3a ngu\u1ed3n d\u1eef li\u1ec7u, \u0111\u1ea3m b\u1ea3o th\u1ec3 hi\u1ec7n ph\u00e2n ph\u1ed1i d\u1eef li\u1ec7u to\u00e0n di\u1ec7n h\u01a1n.<\/li>\n\n\n\n<li><strong>T\u0103ng c\u01b0\u1eddng d\u1eef li\u1ec7u<\/strong>: M\u00e1y ch\u1ee7 proxy cho ph\u00e9p t\u1ea1o c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u b\u1ed5 sung b\u1eb1ng c\u00e1ch truy c\u1eadp c\u00e1c ngu\u1ed3n tr\u1ef1c tuy\u1ebfn kh\u00e1c nhau v\u00e0 m\u00f4 ph\u1ecfng c\u00e1c t\u01b0\u01a1ng t\u00e1c kh\u00e1c nhau c\u1ee7a ng\u01b0\u1eddi d\u00f9ng, gi\u00fap c\u1ea3i thi\u1ec7n t\u00ednh kh\u00e1i qu\u00e1t c\u1ee7a m\u00f4 h\u00ecnh.<\/li>\n\n\n\n<li><strong>C\u00e2n b\u1eb1ng t\u1ea3i<\/strong>: Trong c\u00e1c \u1ee9ng d\u1ee5ng quy m\u00f4 l\u1edbn, m\u00e1y ch\u1ee7 proxy c\u00f3 th\u1ec3 ph\u00e2n ph\u1ed1i t\u1ea3i suy lu\u1eadn tr\u00ean nhi\u1ec1u m\u00e1y ch\u1ee7, \u0111\u1ea3m b\u1ea3o tri\u1ec3n khai hi\u1ec7u qu\u1ea3 v\u00e0 c\u00f3 th\u1ec3 m\u1edf r\u1ed9ng c\u00e1c m\u00f4 h\u00ecnh t\u1ef1 \u0111\u1ed9ng h\u1ed3i quy.<\/li>\n\n\n\n<li><strong>Quy\u1ec1n ri\u00eang t\u01b0 v\u00e0 b\u1ea3o m\u1eadt<\/strong>: M\u00e1y ch\u1ee7 proxy \u0111\u00f3ng vai tr\u00f2 trung gian gi\u1eefa m\u00e1y kh\u00e1ch v\u00e0 m\u00e1y ch\u1ee7, cung c\u1ea5p th\u00eam l\u1edbp b\u1ea3o m\u1eadt v\u00e0 quy\u1ec1n ri\u00eang t\u01b0 cho c\u00e1c \u1ee9ng d\u1ee5ng nh\u1ea1y c\u1ea3m s\u1eed d\u1ee5ng m\u00f4 h\u00ecnh t\u1ef1 \u0111\u1ed9ng h\u1ed3i quy.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">Li\u00ean k\u1ebft li\u00ean quan<\/h2>\n\n\n\n<p>\u0110\u1ec3 bi\u1ebft th\u00eam th\u00f4ng tin v\u1ec1 c\u00e1c m\u00f4 h\u00ecnh T\u1ef1 \u0111\u1ed9ng h\u1ed3i quy, b\u1ea1n c\u00f3 th\u1ec3 kh\u00e1m ph\u00e1 c\u00e1c t\u00e0i nguy\u00ean sau:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.wiley.com\/en-us\/Time+Series+Analysis%3A+Forecasting+and+Control%2C+5th+Edition-p-9781118675021\" target=\"_new\" rel=\"noopener nofollow\">Ph\u00e2n t\u00edch chu\u1ed7i th\u1eddi gian: D\u1ef1 b\u00e1o v\u00e0 ki\u1ec3m so\u00e1t c\u1ee7a George Box v\u00e0 Gwilym Jenkins<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/neco.1997.9.8.1735\" target=\"_new\" rel=\"noopener nofollow\">M\u1ea1ng b\u1ed9 nh\u1edb ng\u1eafn h\u1ea1n d\u00e0i (LSTM)<\/a><\/li>\n\n\n\n<li><a href=\"http:\/\/jalammar.github.io\/illustrated-transformer\/\" target=\"_new\" rel=\"noopener nofollow\">M\u00e1y bi\u1ebfn \u00e1p minh h\u1ecda c\u1ee7a Jay Alammar<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/towardsdatascience.com\/an-introduction-to-time-series-analysis-and-forecasting-in-python-af7eeb238a64\" target=\"_new\" rel=\"noopener nofollow\">Gi\u1edbi thi\u1ec7u v\u1ec1 Ph\u00e2n t\u00edch v\u00e0 D\u1ef1 b\u00e1o Chu\u1ed7i Th\u1eddi gian trong Python<\/a><\/li>\n<\/ol>\n\n\n\n<p>C\u00e1c m\u00f4 h\u00ecnh h\u1ed3i quy t\u1ef1 \u0111\u1ed9ng \u0111\u00e3 tr\u1edf th\u00e0nh c\u00f4ng c\u1ee5 c\u01a1 b\u1ea3n cho nhi\u1ec1u t\u00e1c v\u1ee5 li\u00ean quan \u0111\u1ebfn d\u1eef li\u1ec7u, cho ph\u00e9p d\u1ef1 \u0111o\u00e1n ch\u00ednh x\u00e1c v\u00e0 t\u1ea1o d\u1eef li\u1ec7u th\u1ef1c t\u1ebf. Khi nghi\u00ean c\u1ee9u trong l\u0129nh v\u1ef1c n\u00e0y ti\u1ebfn tri\u1ec3n, ch\u00fang ta c\u00f3 th\u1ec3 mong \u0111\u1ee3i c\u00e1c m\u00f4 h\u00ecnh ti\u00ean ti\u1ebfn v\u00e0 hi\u1ec7u qu\u1ea3 h\u01a1n n\u1eefa s\u1ebd xu\u1ea5t hi\u1ec7n, c\u00e1ch m\u1ea1ng h\u00f3a c\u00e1ch ch\u00fang ta x\u1eed l\u00fd d\u1eef li\u1ec7u tu\u1ea7n t\u1ef1 trong t\u01b0\u01a1ng lai.<\/p>","protected":false},"featured_media":497623,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-475955","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about <mark>Auto-regressive models: A Comprehensive Overview<\/mark>","faq_items":[{"question":"Question 1: What are Auto-regressive models?","answer":"Answer 1: Auto-regressive models are statistical models used to predict future values based on past observations. They are particularly effective for tasks involving sequential data, such as time-series analysis, natural language processing, and image generation. These models regress a variable against its own lagged values to capture dependencies and patterns in the data."},{"question":"Question 2: How did Auto-regressive models originate?","answer":"Answer 2: The concept of auto-regression dates back to the early 20th century, with contributions from statisticians such as Yule and economist Ragnar Frisch. The term \"auto-regressive\" was first introduced by Norbert Wiener in the 1940s, who laid the foundation for modern auto-regressive models through his work on stochastic processes and prediction."},{"question":"Question 3: How do Auto-regressive models work?","answer":"Answer 3: Auto-regressive models use past values of a variable to predict its current value. The model is trained using the method of least squares to estimate its parameters. Once trained, it can generate future values by recursively predicting based on its own past predictions."},{"question":"Question 4: What are the key features of Auto-regressive models?","answer":"Answer 4: Auto-regressive models offer sequence prediction, generative capabilities, flexibility, interpretability, and adaptability. They excel at forecasting future values in a time-ordered sequence and can generate new data samples resembling the training data. Their simplicity allows for easy interpretation, making them valuable in various applications."},{"question":"Question 5: What types of Auto-regressive models exist?","answer":"Answer 5: There are various types of Auto-regressive models, including Moving Average Auto-regressive (ARMA), Auto-regressive Integrated Moving Average (ARIMA), Seasonal Auto-regressive Integrated Moving Average (SARIMA), Vector Auto-regressive (VAR), Long Short-Term Memory (LSTM) networks, and Transformer models. Each type has specific characteristics suitable for different applications."},{"question":"Question 6: How can Auto-regressive models be used, and what challenges do they face?","answer":"Answer 6: Auto-regressive models are used in time-series forecasting, natural language processing, image generation, music composition, and anomaly detection. However, they may struggle with long-term memory, overfitting, and the need for data stationarity in ARIMA-type models. Solutions include using RNNs for better long-term memory and regularization techniques to prevent overfitting."},{"question":"Question 7: How do Auto-regressive models compare to other time-series models?","answer":"Answer 7: Auto-regressive models are compared with Moving Average (MA) models, Auto-regressive Moving Average (ARMA) models, and Auto-regressive Integrated Moving Average (ARIMA) models. Each model has distinct characteristics, with ARIMA incorporating differencing for stationarity in non-stationary time-series data."},{"question":"Question 8: What are the perspectives and future technologies related to Auto-regressive models?","answer":"Answer 8: The future of Auto-regressive models involves more complex architectures, improved attention mechanisms for better long-range dependencies, and efforts to reduce training computational requirements. They will likely find applications in unsupervised learning, anomaly detection, and representation learning."},{"question":"Question 9: How are proxy servers associated with Auto-regressive models?","answer":"Answer 9: Proxy servers can enhance the performance of Auto-regressive models by anonymizing and diversifying data sources during data collection. They enable data augmentation, load balancing, and add an extra layer of privacy and security for sensitive applications using Auto-regressive models."},{"question":"Question 10: Where can I find more information about Auto-regressive models?","answer":"Answer 10: For further information, you can explore the book \"Time Series Analysis: Forecasting and Control\" by George Box and Gwilym Jenkins, or learn more about Long Short-Term Memory (LSTM) networks from the article \"The Illustrated Transformer\" by Jay Alammar. Additionally, you can find resources on time series analysis and forecasting in Python for practical insights."}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/475955","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":4,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/475955\/revisions"}],"predecessor-version":[{"id":505505,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/475955\/revisions\/505505"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media\/497623"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media?parent=475955"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}