Fit ARIMA Models
Fits ARIMA models (with diagnostics) in a short command. It can also be used to perform regression with autocorrelated errors.
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)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 |
tol |
controls the relative tolerance (reltol in |
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., |
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.
fit |
the |
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 |
AICc |
value of the AICc |
BIC |
value of the BIC |
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 parameters x = sarima.sim( ar=c(0,-.9), n=200 ) + 50 sarima(x, 2,0,0, fixed=c(0,NA,NA))
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