{"id":475954,"date":"2023-08-09T07:24:43","date_gmt":"2023-08-09T07:24:43","guid":{"rendered":""},"modified":"2023-09-05T11:11:41","modified_gmt":"2023-09-05T11:11:41","slug":"autoregressive-integrated-moving-average-arima","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/vn\/wiki\/autoregressive-integrated-moving-average-arima\/","title":{"rendered":"\u0110\u01b0\u1eddng trung b\u00ecnh \u0111\u1ed9ng t\u00edch h\u1ee3p t\u1ef1 h\u1ed3i quy (ARIMA)"},"content":{"rendered":"<p>Trung b\u00ecnh tr\u01b0\u1ee3t t\u00edch h\u1ee3p t\u1ef1 h\u1ed3i quy (ARIMA), l\u00e0 m\u1ed9t m\u00f4 h\u00ecnh th\u1ed1ng k\u00ea c\u01a1 b\u1ea3n, gi\u1eef m\u1ed9t vai tr\u00f2 quan tr\u1ecdng trong d\u1ef1 b\u00e1o chu\u1ed7i th\u1eddi gian. B\u1eaft ngu\u1ed3n t\u1eeb to\u00e1n h\u1ecdc \u01b0\u1edbc l\u01b0\u1ee3ng th\u1ed1ng k\u00ea, ARIMA \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau \u0111\u1ec3 d\u1ef1 b\u00e1o c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u trong t\u01b0\u01a1ng lai d\u1ef1a tr\u00ean c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u tr\u01b0\u1edbc \u0111\u00f3 trong chu\u1ed7i.<\/p>\n<h2>Ngu\u1ed3n g\u1ed1c c\u1ee7a ARIMA<\/h2>\n<p>ARIMA \u0111\u01b0\u1ee3c gi\u1edbi thi\u1ec7u l\u1ea7n \u0111\u1ea7u ti\u00ean v\u00e0o \u0111\u1ea7u nh\u1eefng n\u0103m 1970 b\u1edfi c\u00e1c nh\u00e0 th\u1ed1ng k\u00ea George Box v\u00e0 Gwilym Jenkins. S\u1ef1 ph\u00e1t tri\u1ec3n n\u00e0y d\u1ef1a tr\u00ean nghi\u00ean c\u1ee9u tr\u01b0\u1edbc \u0111\u00f3 v\u1ec1 c\u00e1c m\u00f4 h\u00ecnh t\u1ef1 h\u1ed3i quy (AR) v\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh \u0111\u1ed9ng (MA). B\u1eb1ng c\u00e1ch t\u00edch h\u1ee3p kh\u00e1i ni\u1ec7m sai ph\u00e2n, Box v\u00e0 Jenkins c\u00f3 th\u1ec3 x\u1eed l\u00fd chu\u1ed7i th\u1eddi gian kh\u00f4ng c\u1ed1 \u0111\u1ecbnh, t\u1eeb \u0111\u00f3 t\u1ea1o ra m\u00f4 h\u00ecnh ARIMA.<\/p>\n<h2>T\u00ecm hi\u1ec3u ARIMA<\/h2>\n<p>ARIMA l\u00e0 s\u1ef1 k\u1ebft h\u1ee3p c\u1ee7a ba ph\u01b0\u01a1ng ph\u00e1p c\u01a1 b\u1ea3n: T\u1ef1 h\u1ed3i quy (AR), T\u00edch h\u1ee3p (I) v\u00e0 Trung b\u00ecnh tr\u01b0\u1ee3t (MA). Nh\u1eefng ph\u01b0\u01a1ng ph\u00e1p n\u00e0y \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 ph\u00e2n t\u00edch v\u00e0 d\u1ef1 b\u00e1o d\u1eef li\u1ec7u chu\u1ed7i th\u1eddi gian.<\/p>\n<ul>\n<li>\n<p><strong>T\u1ef1 h\u1ed3i quy (AR)<\/strong>: Ph\u01b0\u01a1ng ph\u00e1p n\u00e0y s\u1eed d\u1ee5ng m\u1ed1i quan h\u1ec7 ph\u1ee5 thu\u1ed9c gi\u1eefa m\u1ed9t quan s\u00e1t v\u00e0 m\u1ed9t s\u1ed1 quan s\u00e1t b\u1ecb tr\u1ec5 (c\u00e1c giai \u0111o\u1ea1n tr\u01b0\u1edbc \u0111\u00f3).<\/p>\n<\/li>\n<li>\n<p><strong>T\u00edch h\u1ee3p (I)<\/strong>: C\u00e1ch ti\u1ebfp c\u1eadn n\u00e0y li\u00ean quan \u0111\u1ebfn vi\u1ec7c l\u1ea5y sai ph\u00e2n c\u00e1c quan s\u00e1t \u0111\u1ec3 l\u00e0m cho chu\u1ed7i th\u1eddi gian c\u00f3 t\u00ednh d\u1eebng.<\/p>\n<\/li>\n<li>\n<p><strong>\u0110\u01b0\u1eddng trung b\u00ecnh \u0111\u1ed9ng (MA)<\/strong>: K\u1ef9 thu\u1eadt n\u00e0y s\u1eed d\u1ee5ng s\u1ef1 ph\u1ee5 thu\u1ed9c gi\u1eefa m\u1ed9t quan s\u00e1t v\u00e0 sai s\u1ed1 d\u01b0 t\u1eeb m\u00f4 h\u00ecnh trung b\u00ecnh \u0111\u1ed9ng \u00e1p d\u1ee5ng cho c\u00e1c quan s\u00e1t c\u00f3 \u0111\u1ed9 tr\u1ec5.<\/p>\n<\/li>\n<\/ul>\n<p>C\u00e1c m\u00f4 h\u00ecnh ARIMA th\u01b0\u1eddng \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 ARIMA(p, d, q), trong \u0111\u00f3 &#039;p&#039; l\u00e0 th\u1ee9 t\u1ef1 c\u1ee7a ph\u1ea7n AR, &#039;d&#039; l\u00e0 th\u1ee9 t\u1ef1 sai ph\u00e2n c\u1ea7n thi\u1ebft \u0111\u1ec3 l\u00e0m cho chu\u1ed7i th\u1eddi gian \u0111\u1ee9ng y\u00ean v\u00e0 &#039;q&#039; l\u00e0 th\u1ee9 t\u1ef1 c\u1ee7a ph\u1ea7n MA.<\/p>\n<h2>C\u1ea5u tr\u00fac b\u00ean trong v\u00e0 ho\u1ea1t \u0111\u1ed9ng c\u1ee7a ARIMA<\/h2>\n<p>C\u1ea5u tr\u00fac c\u1ee7a ARIMA bao g\u1ed3m ba ph\u1ea7n: AR, I v\u00e0 MA. M\u1ed7i ph\u1ea7n \u0111\u00f3ng m\u1ed9t vai tr\u00f2 c\u1ee5 th\u1ec3 trong vi\u1ec7c ph\u00e2n t\u00edch d\u1eef li\u1ec7u:<\/p>\n<ul>\n<li><strong>ph\u1ea7n AR<\/strong> \u0111o l\u01b0\u1eddng \u1ea3nh h\u01b0\u1edfng c\u1ee7a gi\u00e1 tr\u1ecb c\u1ee7a c\u00e1c th\u1eddi k\u1ef3 tr\u01b0\u1edbc t\u1edbi th\u1eddi k\u1ef3 hi\u1ec7n t\u1ea1i.<\/li>\n<li><strong>m\u1ed9t ph\u1ea7n c\u1ee7a t\u00f4i<\/strong> \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 l\u00e0m cho d\u1eef li\u1ec7u \u1ed5n \u0111\u1ecbnh, ngh\u0129a l\u00e0 lo\u1ea1i b\u1ecf xu h\u01b0\u1edbng kh\u1ecfi d\u1eef li\u1ec7u.<\/li>\n<li><strong>ph\u1ea7n MA<\/strong> k\u1ebft h\u1ee3p s\u1ef1 ph\u1ee5 thu\u1ed9c gi\u1eefa m\u1ed9t quan s\u00e1t v\u00e0 sai s\u1ed1 d\u01b0 t\u1eeb m\u00f4 h\u00ecnh trung b\u00ecnh \u0111\u1ed9ng \u00e1p d\u1ee5ng cho c\u00e1c quan s\u00e1t c\u00f3 \u0111\u1ed9 tr\u1ec5.<\/li>\n<\/ul>\n<p>M\u00f4 h\u00ecnh ARIMA \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng cho chu\u1ed7i th\u1eddi gian theo ba giai \u0111o\u1ea1n:<\/p>\n<ol>\n<li><strong>Nh\u1eadn bi\u1ebft<\/strong>: X\u00e1c \u0111\u1ecbnh th\u1ee9 t\u1ef1 sai ph\u00e2n \u2018d\u2019 v\u00e0 th\u1ee9 t\u1ef1 c\u1ee7a c\u00e1c th\u00e0nh ph\u1ea7n AR ho\u1eb7c MA.<\/li>\n<li><strong>\u01af\u1edbc l\u01b0\u1ee3ng<\/strong>: Sau khi x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c m\u00f4 h\u00ecnh, d\u1eef li\u1ec7u ph\u00f9 h\u1ee3p v\u1edbi m\u00f4 h\u00ecnh \u0111\u1ec3 \u01b0\u1edbc l\u01b0\u1ee3ng c\u00e1c h\u1ec7 s\u1ed1.<\/li>\n<li><strong>x\u00e1c minh<\/strong>: M\u00f4 h\u00ecnh \u0111\u01b0\u1ee3c trang b\u1ecb \u0111\u01b0\u1ee3c ki\u1ec3m tra \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o n\u00f3 ph\u00f9 h\u1ee3p t\u1ed1t v\u1edbi d\u1eef li\u1ec7u.<\/li>\n<\/ol>\n<h2>C\u00e1c t\u00ednh n\u0103ng ch\u00ednh c\u1ee7a ARIMA<\/h2>\n<ul>\n<li>C\u00e1c m\u00f4 h\u00ecnh ARIMA c\u00f3 th\u1ec3 d\u1ef1 b\u00e1o c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u trong t\u01b0\u01a1ng lai d\u1ef1a tr\u00ean d\u1eef li\u1ec7u trong qu\u00e1 kh\u1ee9 v\u00e0 hi\u1ec7n t\u1ea1i.<\/li>\n<li>N\u00f3 c\u00f3 th\u1ec3 x\u1eed l\u00fd d\u1eef li\u1ec7u chu\u1ed7i th\u1eddi gian kh\u00f4ng c\u1ed1 \u0111\u1ecbnh.<\/li>\n<li>N\u00f3 \u0111\u1eb7c bi\u1ec7t hi\u1ec7u qu\u1ea3 khi d\u1eef li\u1ec7u cho th\u1ea5y xu h\u01b0\u1edbng r\u00f5 r\u00e0ng ho\u1eb7c m\u00f4 h\u00ecnh theo m\u00f9a.<\/li>\n<li>ARIMA y\u00eau c\u1ea7u m\u1ed9t l\u01b0\u1ee3ng l\u1edbn d\u1eef li\u1ec7u \u0111\u1ec3 mang l\u1ea1i k\u1ebft qu\u1ea3 ch\u00ednh x\u00e1c.<\/li>\n<\/ul>\n<h2>C\u00e1c lo\u1ea1i ARIMA<\/h2>\n<p>C\u00f3 hai lo\u1ea1i m\u00f4 h\u00ecnh ARIMA ch\u00ednh:<\/p>\n<ol>\n<li>\n<p><strong>ARIMA kh\u00f4ng theo m\u00f9a<\/strong>: \u0110\u00e2y l\u00e0 d\u1ea1ng \u0111\u01a1n gi\u1ea3n nh\u1ea5t c\u1ee7a ARIMA. N\u00f3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng cho d\u1eef li\u1ec7u kh\u00f4ng theo m\u00f9a khi kh\u00f4ng c\u00f3 xu h\u01b0\u1edbng mang t\u00ednh chu k\u1ef3 r\u00f5 r\u00e0ng.<\/p>\n<\/li>\n<li>\n<p><strong>ARIMA theo m\u00f9a (SARIMA)<\/strong>: \u0110\u00e2y l\u00e0 ph\u1ea7n m\u1edf r\u1ed9ng c\u1ee7a ARIMA h\u1ed7 tr\u1ee3 r\u00f5 r\u00e0ng th\u00e0nh ph\u1ea7n theo m\u00f9a trong m\u00f4 h\u00ecnh.<\/p>\n<\/li>\n<\/ol>\n<h2>\u1ee8ng d\u1ee5ng th\u1ef1c t\u1ebf c\u1ee7a ARIMA v\u00e0 gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1<\/h2>\n<p>ARIMA c\u00f3 nhi\u1ec1u \u1ee9ng d\u1ee5ng, bao g\u1ed3m d\u1ef1 b\u00e1o kinh t\u1ebf, d\u1ef1 b\u00e1o doanh s\u1ed1 b\u00e1n h\u00e0ng, ph\u00e2n t\u00edch th\u1ecb tr\u01b0\u1eddng ch\u1ee9ng kho\u00e1n, v.v.<\/p>\n<p>M\u1ed9t v\u1ea5n \u0111\u1ec1 ph\u1ed5 bi\u1ebfn g\u1eb7p ph\u1ea3i v\u1edbi ARIMA l\u00e0 trang b\u1ecb qu\u00e1 m\u1ee9c, trong \u0111\u00f3 m\u00f4 h\u00ecnh qu\u00e1 kh\u1edbp v\u1edbi d\u1eef li\u1ec7u hu\u1ea5n luy\u1ec7n v\u00e0 ho\u1ea1t \u0111\u1ed9ng k\u00e9m tr\u00ean d\u1eef li\u1ec7u m\u1edbi, ch\u01b0a \u0111\u01b0\u1ee3c nh\u00ecn th\u1ea5y. Gi\u1ea3i ph\u00e1p n\u1eb1m \u1edf vi\u1ec7c s\u1eed d\u1ee5ng c\u00e1c k\u1ef9 thu\u1eadt nh\u01b0 x\u00e1c th\u1ef1c ch\u00e9o \u0111\u1ec3 tr\u00e1nh trang b\u1ecb qu\u00e1 m\u1ee9c.<\/p>\n<h2>So s\u00e1nh v\u1edbi c\u00e1c ph\u01b0\u01a1ng ph\u00e1p t\u01b0\u01a1ng t\u1ef1<\/h2>\n<table>\n<thead>\n<tr>\n<th>T\u00ednh n\u0103ng<\/th>\n<th>ARIMA<\/th>\n<th>L\u00e0m m\u1ecbn theo c\u1ea5p s\u1ed1 nh\u00e2n<\/th>\n<th>M\u1ea1ng th\u1ea7n kinh t\u00e1i ph\u00e1t (RNN)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>X\u1eed l\u00fd d\u1eef li\u1ec7u kh\u00f4ng c\u1ed1 \u0111\u1ecbnh<\/td>\n<td>\u0110\u00fang<\/td>\n<td>KH\u00d4NG<\/td>\n<td>\u0110\u00fang<\/td>\n<\/tr>\n<tr>\n<td>Xem x\u00e9t l\u1ed7i, xu h\u01b0\u1edbng v\u00e0 t\u00ednh th\u1eddi v\u1ee5<\/td>\n<td>\u0110\u00fang<\/td>\n<td>\u0110\u00fang<\/td>\n<td>KH\u00d4NG<\/td>\n<\/tr>\n<tr>\n<td>C\u1ea7n d\u1eef li\u1ec7u l\u1edbn<\/td>\n<td>\u0110\u00fang<\/td>\n<td>KH\u00d4NG<\/td>\n<td>\u0110\u00fang<\/td>\n<\/tr>\n<tr>\n<td>D\u1ec5 gi\u1ea3i th\u00edch<\/td>\n<td>Cao<\/td>\n<td>Cao<\/td>\n<td>Th\u1ea5p<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Vi\u1ec5n c\u1ea3nh t\u01b0\u01a1ng lai c\u1ee7a ARIMA<\/h2>\n<p>ARIMA ti\u1ebfp t\u1ee5c l\u00e0 m\u00f4 h\u00ecnh c\u01a1 b\u1ea3n trong l\u0129nh v\u1ef1c d\u1ef1 b\u00e1o chu\u1ed7i th\u1eddi gian. Vi\u1ec7c t\u00edch h\u1ee3p ARIMA v\u1edbi c\u00e1c k\u1ef9 thu\u1eadt h\u1ecdc m\u00e1y v\u00e0 c\u00f4ng ngh\u1ec7 AI \u0111\u1ec3 d\u1ef1 \u0111o\u00e1n ch\u00ednh x\u00e1c h\u01a1n l\u00e0 xu h\u01b0\u1edbng quan tr\u1ecdng trong t\u01b0\u01a1ng lai.<\/p>\n<h2>M\u00e1y ch\u1ee7 proxy v\u00e0 ARIMA<\/h2>\n<p>C\u00e1c m\u00e1y ch\u1ee7 proxy c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c h\u01b0\u1edfng l\u1ee3i t\u1eeb c\u00e1c m\u00f4 h\u00ecnh ARIMA trong d\u1ef1 \u0111o\u00e1n l\u01b0u l\u01b0\u1ee3ng truy c\u1eadp, gi\u00fap qu\u1ea3n l\u00fd c\u00e2n b\u1eb1ng t\u1ea3i v\u00e0 ph\u00e2n b\u1ed5 t\u00e0i nguy\u00ean m\u00e1y ch\u1ee7. B\u1eb1ng c\u00e1ch d\u1ef1 \u0111o\u00e1n l\u01b0u l\u01b0\u1ee3ng truy c\u1eadp, m\u00e1y ch\u1ee7 proxy c\u00f3 th\u1ec3 t\u1ef1 \u0111\u1ed9ng \u0111i\u1ec1u ch\u1ec9nh t\u00e0i nguy\u00ean \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o ho\u1ea1t \u0111\u1ed9ng t\u1ed1i \u01b0u.<\/p>\n<h2>Li\u00ean k\u1ebft li\u00ean quan<\/h2>\n<ul>\n<li><a href=\"https:\/\/www.wiley.com\/en-us\/Time+Series+Analysis%3A+Forecasting+and+Control%2C+4th+Edition-p-9780470272848\" target=\"_new\" rel=\"noopener nofollow\">Box, GEP, Jenkins, GM v\u00e0 Reinsel, GC (2008) Ph\u00e2n t\u00edch chu\u1ed7i th\u1eddi gian: D\u1ef1 b\u00e1o v\u00e0 ki\u1ec3m so\u00e1t. Wiley.<\/a><\/li>\n<li><a href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0957417420302903\" target=\"_new\" rel=\"noopener nofollow\">ARIMA\/SARIMA so v\u1edbi LSTM v\u1edbi Th\u00f4ng tin chi ti\u1ebft v\u1ec1 h\u1ecdc t\u1eadp t\u1ed5ng h\u1ee3p cho d\u1eef li\u1ec7u chu\u1ed7i th\u1eddi gian<\/a><\/li>\n<li><a href=\"https:\/\/www.mathworks.com\/help\/econ\/autoregressive-integrated-moving-average-arima.html\" target=\"_new\" rel=\"noopener nofollow\">\u0110\u01b0\u1eddng trung b\u00ecnh \u0111\u1ed9ng t\u00edch h\u1ee3p t\u1ef1 h\u1ed3i quy (ARIMA) \u2013 MATLAB &amp; Simulink<\/a><\/li>\n<\/ul>","protected":false},"featured_media":467678,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-475954","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about <mark>Autoregressive Integrated Moving Average (ARIMA): A Comprehensive Analysis<\/mark>","faq_items":[{"question":"What is the Autoregressive Integrated Moving Average (ARIMA)?","answer":"<p>Autoregressive Integrated Moving Average (ARIMA) is a statistical model used to analyze and forecast time series data. It combines three methods: Autoregressive (AR), Integrated (I), and Moving Average (MA).<\/p>"},{"question":"Who introduced the ARIMA model and when?","answer":"<p>The ARIMA model was introduced in the early 1970s by statisticians George Box and Gwilym Jenkins. The model extended earlier work around autoregressive (AR) and moving average (MA) models and introduced the concept of differencing to handle non-stationary time series.<\/p>"},{"question":"What are the three parts of the ARIMA model?","answer":"<p>The three parts of the ARIMA model are Autoregressive (AR), Integrated (I), and Moving Average (MA). The AR part measures the influence of past periods\u2019 values on the current period. The I part removes the trend from the data to make it stationary. The MA part incorporates the dependency between an observation and a residual error from a moving average model applied to lagged observations.<\/p>"},{"question":"What are the key features of ARIMA?","answer":"<p>ARIMA models can forecast future data points based on past and present data. They can handle time series data that are non-stationary and are particularly effective when data show a clear trend or seasonal pattern. However, ARIMA requires a large amount of data to yield accurate results.<\/p>"},{"question":"What are the types of ARIMA models?","answer":"<p>There are two main types of ARIMA models: Non-Seasonal ARIMA, used for non-seasonal data where there are no definitive cyclic trends, and Seasonal ARIMA (SARIMA), an extension of ARIMA that explicitly supports a seasonal component in the model.<\/p>"},{"question":"What problems are commonly encountered with ARIMA and how can they be solved?","answer":"<p>One common problem encountered with ARIMA is overfitting, where the model fits too closely to the training data and performs poorly on new, unseen data. Techniques such as cross-validation can be used to avoid overfitting.<\/p>"},{"question":"How is ARIMA relevant to proxy servers?","answer":"<p>Proxy servers could potentially benefit from ARIMA models in traffic prediction, helping to manage load balancing and server resource allocation. By predicting traffic, proxy servers can dynamically adjust resources to ensure optimal operation.<\/p>"}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/475954","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":0,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/475954\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media\/467678"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media?parent=475954"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}