{"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\/tr\/wiki\/auto-regressive-models\/","title":{"rendered":"Otomatik regresif modeller"},"content":{"rendered":"

Otomatik gerileyen modeller, do\u011fal dil i\u015fleme, zaman serisi analizi ve g\u00f6r\u00fcnt\u00fc olu\u015fturma dahil olmak \u00fczere \u00e7e\u015fitli alanlarda yayg\u0131n olarak kullan\u0131lan bir istatistiksel model s\u0131n\u0131f\u0131d\u0131r. Bu modeller, \u00f6nceden g\u00f6zlemlenen de\u011ferlere dayal\u0131 bir de\u011fer dizisini tahmin ederek s\u0131ral\u0131 verileri i\u00e7eren g\u00f6revler i\u00e7in onlar\u0131 \u00e7ok uygun hale getirir. Otomatik regresif modellerin ger\u00e7ek\u00e7i veriler \u00fcretmede ve gelecekteki sonu\u00e7lar\u0131 tahmin etmede olduk\u00e7a etkili oldu\u011fu kan\u0131tlanm\u0131\u015ft\u0131r.<\/p>\n\n\n\n

Otomatik gerileyen modellerin k\u00f6keninin tarihi ve ilk s\u00f6z\u00fc<\/h2>\n\n\n\n

Otomatik regresyon kavram\u0131n\u0131n k\u00f6keni, \u0130ngiliz istatistik\u00e7i Yule'nin 1927'de yapt\u0131\u011f\u0131 \u00f6nc\u00fc \u00e7al\u0131\u015fmayla 20. y\u00fczy\u0131l\u0131n ba\u015flar\u0131na kadar uzan\u0131yor. Ancak, modern otomatik regresif modellerin temelini atan, 1940'larda matematik\u00e7i Norbert Wiener'in \u00e7al\u0131\u015fmas\u0131yd\u0131. Wiener'in stokastik s\u00fcre\u00e7ler ve tahmin \u00fczerine ara\u015ft\u0131rmas\u0131, bug\u00fcn bildi\u011fimiz otoregresif modellerin geli\u015ftirilmesinin temelini att\u0131.<\/p>\n\n\n\n

\u201cOtoregresif\u201d terimi ekonomi alan\u0131nda ilk kez 1920'lerin sonlar\u0131nda Ragnar Frisch taraf\u0131ndan tan\u0131t\u0131ld\u0131. Frisch bu terimi, bir de\u011fi\u015fkeni kendi gecikmeli de\u011ferlerine g\u00f6re regrese eden ve b\u00f6ylece bir de\u011fi\u015fkenin kendi ge\u00e7mi\u015fine ba\u011f\u0131ml\u0131l\u0131\u011f\u0131n\u0131 yakalayan bir modeli tan\u0131mlamak i\u00e7in kulland\u0131.<\/p>\n\n\n\n

Otomatik Gerilemeli Modeller: Ayr\u0131nt\u0131l\u0131 Bilgi<\/h2>\n\n\n\n

Otomatik regresif (AR) modeller, ge\u00e7mi\u015f verilere dayal\u0131 olarak gelecekteki de\u011ferleri tahmin etmek i\u00e7in kullan\u0131lan, zaman serisi analizinde \u00f6nemli ara\u00e7lard\u0131r. Bu modeller ge\u00e7mi\u015f de\u011ferlerin mevcut ve gelecekteki de\u011ferleri do\u011frusal bir \u015fekilde etkiledi\u011fini varsaymaktad\u0131r. Ekonomi, finans, hava tahmini ve zaman serisi verilerinin yayg\u0131n oldu\u011fu di\u011fer \u00e7e\u015fitli alanlarda yayg\u0131n olarak kullan\u0131l\u0131rlar.<\/p>

Matematiksel G\u00f6sterim<\/h3>

Otomatik gerileyen bir d\u00fczen modeli P<\/mi><\/mrow>P<\/annotation><\/semantics><\/math><\/span><\/span>P<\/span><\/span><\/span><\/span> (AR(p)) matematiksel olarak \u015fu \u015fekilde ifade edilir:\ne<\/mi>T<\/mi><\/msub>=<\/mo>\u03d5<\/mi>1<\/mn><\/msub>e<\/mi>T<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>+<\/mo>\u03d5<\/mi>2<\/mn><\/msub>e<\/mi>T<\/mi>\u2212<\/mo>2<\/mn><\/mrow><\/msub>+<\/mo>\u22ef<\/mo>+<\/mo>\u03d5<\/mi>P<\/mi><\/msub>e<\/mi>T<\/mi>\u2212<\/mo>P<\/mi><\/mrow><\/msub>+<\/mo>\u03f5<\/mi>T<\/mi><\/msub><\/mrow>Y_t = \\phi_1 Y_{t-1} + \\phi_2 Y_{t-2} + \\cdots + \\phi_p Y_{tp} + \\epsilon_t<\/annotation><\/semantics><\/math><\/span><\/span>e<\/span><\/span>T<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u03d5<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>e<\/span><\/span>T<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u03d5<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>e<\/span><\/span>T<\/span>\u2212<\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u22ef<\/span><\/span>+<\/span><\/span><\/span><\/span>\u03d5<\/span><\/span>P<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>e<\/span><\/span>T<\/span>\u2212<\/span>P<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u03f5<\/span><\/span>T<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>

Nerede:<\/p>