astsa (version 1.9)

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, Model=TRUE,
       fixed=NULL, tol = sqrt(.Machine$double.eps), 
       no.constant = FALSE)

Arguments

xdata

univariate time series

p

AR order (must be specified)

d

difference order (must be specified)

q

MA order (must be specified)

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.

Model

if TRUE (default), the model orders are printed on the diagnostic plot.

fixed

optional numeric vector of the same length as the total number of parameters. If supplied, only parameters corresponding to NA entries will be estimated.

details

if FALSE, turns off the diagnostic plot and the output from the nonlinear optimization routine, which is optim. The default is TRUE.

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

fit

the arima object

degrees_of_freedom

Error degrees of freedom

ttable

a little t-table with two-sided p-values

AIC

value of the AIC - all ICs are the values reported in fit divided by the essential number of observations (after differencing)

AICc

value of the AICc

BIC

value of the BIC

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 values p,d,q, must be specified as there is no default. 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. The difference between the information criteria given by sarima() and arima() is that they differ by a scaling factor of the effective sample size.

References

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

See Also

sarima.for

Examples

# NOT RUN {
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) 
sarima(log(AirPassengers),0,1,1,0,1,1,12,details=FALSE)$BIC  # print model BIC only
# fixed paramters
x = arima.sim(list(order=c(2,0,0), ar=c(0,-.9)), n=200) + 50 
sarima(x, 2,0,0, fixed=c(0,NA,NA))
# }