"자기회귀누적이동평균 ARIMA"의 두 판 사이의 차이

2020년 12월 19일 (토) 16:44 판

Some well-known special cases arise naturally or are mathematically equivalent to other popular forecasting models. For example:

An ARIMA(0, 1, 0) model (or $I(1)$ model) is given by [math]\displaystyle{ X_t = X_{t-1} + \varepsilon_t }[/math] — which is simply a random walk.
An ARIMA(0, 1, 0) with a constant, given by [math]\displaystyle{ X_t = c + X_{t-1} + \varepsilon_t }[/math] — which is a random walk with drift.
An ARIMA(0, 0, 0) model is a white noise model.
An ARIMA(0, 1, 2) model is a Damped Holt's model.
An ARIMA(0, 1, 1) model without constant is a basic exponential smoothing model.^[1]
An ARIMA(0, 2, 2) model is given by [math]\displaystyle{ X_t = 2X_{t-1} - X_{t-2} +(\alpha + \beta - 2) \varepsilon_{t-1} + (1-\alpha)\varepsilon_{t-2} + \varepsilon_{t} }[/math] — which is equivalent to Holt's linear method with additive errors, or double exponential smoothing.^[1]

↑ ^1.0 ^1.1 “Introduction to ARIMA models”. 《people.duke.edu》. 2016년 6월 5일에 확인함.

@@ 3번째 줄: / 3번째 줄: @@
 ;자기회귀 누적이동평균, 자기회귀 누적이동평균 모형, ARIMA 모형
 * 자기회귀이동평균(ARMA) 모형의 일반화
+==예시==
+Some well-known special cases arise naturally or are mathematically equivalent to other popular forecasting models.  For example:
+* An ARIMA(0, 1, 0) model (or {{math|I(1)}} model) is given by <math>X_t = X_{t-1} + \varepsilon_t</math> — which is simply a [[random walk]].
+* An ARIMA(0, 1, 0) with a constant, given by <math>X_t = c + X_{t-1} + \varepsilon_t</math> — which is a random walk with drift.
+* An ARIMA(0, 0, 0) model is a [[white noise]] model.
+* An ARIMA(0, 1, 2) model is a Damped Holt's model.
+* An ARIMA(0, 1, 1) model without constant is a [[Exponential smoothing#Basic (simple) exponential smoothing (Holt linear)|basic exponential smoothing]] model.<ref name=":0">{{Cite web|url=http://people.duke.edu/~rnau/411arim.htm#arima010|title=Introduction to ARIMA models|website=people.duke.edu|access-date=2016-06-05}}</ref>
+* An ARIMA(0, 2, 2) model is given by <math>X_t = 2X_{t-1} - X_{t-2} +(\alpha + \beta - 2) \varepsilon_{t-1} + (1-\alpha)\varepsilon_{t-2} + \varepsilon_{t}</math> — which is equivalent to Holt's linear method with additive errors, or [[Exponential smoothing#Double exponential smoothing|double exponential smoothing]].<ref name=":0" />
 ==같이 보기==