Compute Diagnostics for ARIMA Model
DESCRIPTION:
Computes diagnostics for an ARIMA model. The diagnostics include the autocorrelation function of the residuals, the standardized residuals, and the portmanteau goodness of fit test statistic.
USAGE: 
arima.diag(z, acf.resid=T, gof.lag=10, lag.max=<<see below>>, resid=F,
           std.resid=T, plot=T, ...)
REQUIRED ARGUMENTS:
z:
a list like the output from arima.mle.
OPTIONAL ARGUMENTS:
acf.resid:
logical flag: if TRUE, the autocorrelation of the residuals will be returned.
lag.max:
the maximum number of lags at which to estimate the autocovariance. If this is not supplied, it is the maximum between gof.lag plus the number of model parameters and a number proportional to the logarithm of the length of the series.
gof.lag:
if gof.lag>0, then gof.lag plus the number of model parameters is the number of lags to use for computing the Portmanteau goodness of fit statistic. If gof.lag=0, then the statistic will not be computed
resid:
logical flag: if TRUE, then the residuals will be returned.
std.resid:
logical flag: if TRUE, then the standardized residuals will be returned.
plot:
logical flag: if TRUE, the diagnostics will be plotted using the function arima.diag.plot
...:
additional arguments may be passed to the function arima.diag.plot
VALUE:
a list (which is returned invisibly when plot=TRUE) with the following elements:
acf.list:
a list representing the autocorrelation function of the residuals. See acf for details.
gof:
a list representing the Portmanteau goodness of fit statistics computed for a range of lags. The list has four elements: lag, statistic, df, p.value. lag is a vector of the number of lags used to compute the statistics. statistic is the vector of statistics corresponding to each lag used. df is the number of degrees of freedom the test statistics have under the null hypothesis that the model is correct. p.value is a vector of the p-values for the statistics using a Chi-Squared distribution with the appropriate degrees of freedom.
resid:
the residuals or innovations for the process.
std.resid:
the standardized residuals. The residuals are standardized to have unit variance under the assumption that the model is correct and the process is Gaussian.
series:
the name of x, including transformations.
SIDE EFFECTS:
if plot is TRUE, the diagnostics will be plotted using the function arima.diag.plot
DETAILS:
The residuals (both standardized and raw) are computed using the function arima.filt. The autocorrelation function of the residuals is computed using the function acf. The portmanteau test statistic is derived from the autocorrelation function of the residuals (see the chapter "Analyzing Time Series" of the S-PLUS Guide to Statistical and Mathematical Analysis for details).
REFERENCES:
Box, G. E. P. and Jenkins, G. M. (1976). Time Series Analysis: Forecasting and Control. Holden-Day, Oakland, Calif. Chapter 8.

The chapter "Analyzing Time Series" of the S-PLUS Guide to Statistical and Mathematical Analysis.

SEE ALSO:
arima.diag.plot , arima.filt , arima.mle .
EXAMPLES: 
# compute and plot diagnostics for simulated AR(1) series with mean 5
x <- arima.sim(model=list(ar=.9)) + 5
xreg <- rep(1,100)
fit <- arima.mle(x,model=list(ar=.9), xreg=xreg)
diag <- arima.diag(fit)


lynx.arma11 <- arima.mle(lynx, model=list(ar=0, ma=0))
arima.diag(lynx.arma11)