Non-Seasonal box-Jenkins models
1 Non-Seasonal Box-Jenkins Models
Box-Jenkins(ARIMa) Models The Box-Jenkins methodology refers to a set of procedures for identifying and estimating time series models within the class of autoregressive integrated moving average(ARIMA)models ARIMA models are regression models that use lagged values of the dependent variable and/or random disturbance term as explanatory variables ARIMa models rely heavily on the autocorrelation pattern in the data This method applies to both non-seasonal and seasonal data. In this course we will only deal with non-seasonal data
2 Box-Jenkins (ARIMA) Models The Box-Jenkins methodology refers to a set of procedures for identifying and estimating time series models within the class of autoregressive integrated moving average (ARIMA) models. ARIMA models are regression models that use lagged values of the dependent variable and/or random disturbance term as explanatory variables. ARIMA models rely heavily on the autocorrelation pattern in the data This method applies to both non-seasonal and seasonal data. In this course, we will only deal with non-seasonal data
Box-Jenkins(ARIMa) Models Three basic ARIMA models for a stationary time series yt (1)Autoregressive model of order p(ar(p) y1=0+y1+如2y12+…+yn+E1 1. e,, y, depends on its p previous values (2) Moving Average model of order g malg) y 6+8,-61E,1-6,E t-2 t-9 1. e, y, depends on g previous random error terms
3 Box-Jenkins (ARIMA) Models Three basic ARIMA models for a stationary time series yt : (1) Autoregressive model of order p (AR(p)) i.e., yt depends on its p previous values (2) Moving Average model of order q (MA(q)) i.e., yt depends on q previous random error terms, t 1 t 1 2 t 2 p t p t y = + y + y + + y + − − − , t t 1 t 1 2 t 2 q t q y = + − − − − − − −
Box-Jenkins(ARIMa) Models (3)Autoregressive-moving average model of order p and g (arma(p, q) y=6+y=1+n2y2+…+yp +E.-6 t-1 g t-g . e, y, depends on its p previous values and q previous random error terms
4 Box-Jenkins (ARIMA) Models (3) Autoregressive-moving average model of order p and q (ARMA(p,q)) i.e., yt depends on its p previous values and q previous random error terms , 1 1 2 2 1 1 2 2 t t t q t q t t t p t p y y y y − − − − − − + − − − − = + + + +
Box-Jenkins(ARIMa) Models In an arima model. the random disturbance term E, is typically assumed to be"white noise;.e, it is identically and independently distributed with a mean of o and a common variance o across all observations e write d(0,a)
5 Box-Jenkins (ARIMA) Models In an ARIMA model, the random disturbance term is typically assumed to be “white noise”; i.e., it is identically and independently distributed with a mean of 0 and a common variance across all observations. We write ~ i.i.d.(0, ) t 2 t 2