3.1 SARIMA models: estimation and forecasting
We have covered the estimation of ARIMA model in the last tutorial. Extension to SARIMA models is immediate: simply use
- argument seasonal
(a vector of length 3) for forecast::Arima
- arguments P
, D
, Q
and the period S
in the function astsa::sarima
- a list seasonal
with components order
and period
(the latter is facultative if supplying ts
objects) for stats::arima
.
Estimation is done using a state-space formulation of the model; an alternative would be to fit the parameters using an artificial regression.
We have yet to address the matter of prediction. The latter proceeds by one-step ahead forecasting and emploies again the state-space representation. Note however that
The standard errors of prediction exclude the uncertainty in the estimation of the ARMA model and the regression coefficients. According to Harvey (1993, pp. 58–9) the effect is small.
The predict.Arima
method gives forecast for \(h\)-lags ahead for arima
objects. For objects of class Arima
, the forecast
function from the eponym package handles the additional features from forecast::Arima
, namely Box–Cox transformation viz lambda
and bootstrap prediction intervals, as a logical supplied to the argument bootstrap
(more later on this). If you use astsa::sarima
, the forecast function astsa::sarima.for
allows you to do estimation and prediction all in one go.