C47. Unit roots and ARIMA

Topic: Forecasting · more questions on this topic
C49 ›

What is a unit root at one? What do p,d,q mean in an ARIMA(p,d,q) model?

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Definitions/notation. A unit root at one means the autoregressive polynomial has a factor (1-z); the corresponding first-difference operator is (1-B)X_t=X_t-X_{t-1}, where B is the backshift operator. In ARIMA(p,d,q), differencing d times produces a stationary ARMA(p,q) series; p and q are its AR and MA orders and d is its integration order (d=0 gives ARMA).