astsa (version 1.6)

sarima: Fit ARIMA Models

Description

Fits ARIMA models (including improved diagnostics) in a short command. It can also be used to perform regression with autocorrelated errors. This is a front end to arima() with a different back door.

Usage

sarima(xdata, p, d, q, P = 0, D = 0, Q = 0, S = -1,  details = TRUE, xreg=NULL, tol = sqrt(.Machine$double.eps),  no.constant = FALSE)

Arguments

xdata

univariate time series

p

AR order

d

difference order

q

MA order

P

SAR order; use only for seasonal models

D

seasonal difference; use only for seasonal models

Q

SMA order; use only for seasonal models

S

seasonal period; use only for seasonal models

xreg

Optionally, a vector or matrix of external regressors, which must have the same number of rows as xdata.

details

turns on or off the output from the nonlinear optimization routine, which is optim. The default is TRUE, use details=FALSE to turn off the output.

tol

controls the relative tolerance (reltol in optim) used to assess convergence. The default is sqrt(.Machine$double.eps), the R default.

no.constant

controls whether or not sarima includes a constant in the model. In particular, if there is no differencing (d = 0 and D = 0) you get the mean estimate. If there is differencing of order one (either d = 1 or D = 1, but not both), a constant term is included in the model. These two conditions may be overridden (i.e., no constant will be included in the model) by setting this to TRUE; e.g., sarima(x,1,1,0,no.constant=TRUE). Otherwise, no constant or mean term is included in the model. If regressors are included (via xreg), this is ignored.

Value

Details

If your time series is in x and you want to fit an ARIMA(p,d,q) model to the data, the basic call is sarima(x,p,d,q). The results are the parameter estimates, standard errors, AIC, AICc, BIC (as defined in Chapter 2) and diagnostics. To fit a seasonal ARIMA model, the basic call is sarima(x,p,d,q,P,D,Q,S). For example, sarima(x,2,1,0) will fit an ARIMA(2,1,0) model to the series in x, and sarima(x,2,1,0,0,1,1,12) will fit a seasonal ARIMA$(2,1,0)*(0,1,1)_{12}$ model to the series in x.

References

http://www.stat.pitt.edu/stoffer/tsa4/

See Also

sarima.for

Examples

sarima(log(AirPassengers),0,1,1,0,1,1,12)
(dog <- sarima(log(AirPassengers),0,1,1,0,1,1,12))
summary(dog$fit)  # fit has all the returned arima() values
plot(resid(dog$fit))  # plot the innovations (residuals)