Contents
How do you find the seasonal ARIMA model?
Identifying a Seasonal Model
- Step 1: Do a time series plot of the data.
- Step 2: Do any necessary differencing.
- Step 3: Examine the ACF and PACF of the differenced data (if differencing is necessary).
- Step 4: Estimate the model(s) that might be reasonable on the basis of step 3.
What is ARIMA model equation?
A nonseasonal ARIMA model is classified as an “ARIMA(p,d,q)” model, where: p is the number of autoregressive terms, d is the number of nonseasonal differences needed for stationarity, and. q is the number of lagged forecast errors in the prediction equation.
How to calculate the seasonal period of an ARIMA model?
The model includes a non-seasonal AR (1) term, a seasonal AR (1) term, no differencing, no MA terms and the seasonal period is S = 12. The non-seasonal AR (1) polynomial is ϕ ( B) = 1 − ϕ 1 B . The seasonal AR (1) polynomial is Φ ( B 12) = 1 − Φ 1 B 12. The model is ( 1 − ϕ 1 B) ( 1 − Φ 1 B 12) ( x t − μ) = w t.
When do you add a regressor to an ARIMA model?
When you add a regressor to an ARIMA model in Statgraphics, it literally just adds the regressor to the right-hand-side of the ARIMA forecasting equation. To use a simple case, suppose you first fit an ARIMA(1,0,1) model with no regressors. Then the forecasting equation fitted by Statgraphics is: which can be rewritten as:
What are the autocorrelations of an ARIMA model?
= w t + θ 1 w t − 1 + Θ 1 w t − 12 + θ 1 Θ 1 w t − 13. Thus the model has MA terms at lags 1, 12, and 13. This leads many to think that the identifying ACF for the model will have non-zero autocorrelations only at lags 1, 12, and 13.
How to calculate the seasonal AR ( 1 ) polynomial?
The seasonal AR (1) polynomial is Φ ( B 12) = 1 − Φ 1 B 12. The model is ( 1 − ϕ 1 B) ( 1 − Φ 1 B 12) ( x t − μ) = w t. If we let z t = x t − μ (for simplicity), multiply the two AR components and push all but zt to the right side we get z t = ϕ 1 z t − 1 + Φ 1 z t − 12 + ( − ϕ 1 Φ 1) z t − 13 + w t.