public class LackOfFit extends Object
LackOfFit
may be used to diagnose lack of fit in both ARMA
and transfer function models. Typical arguments for these situations are:
Model  lagMin 
lagMax 
npFree 
ARMA (p, q)  1  p + q  
Transfer function  0  r + s 
LackOfFit
performs a portmanteau lack of fit test for a time
series or transfer function containing nObservations
observations given the appropriate sample correlation function
for
k = L, L+1,...,K where L =
lagMin
and K = lagMax
.
The basic form of the test statistic Q is
with L = 1 if
is an autocorrelation function. Given that the model is adequate, Q
has a chisquared distribution with degrees of
freedom where m = npFree
is the number of parameters
estimated in the model. If the mean of the time series is estimated,
Woodfield (1990) recommends not including this in the count of the parameters
estimated in the model. Thus, for an ARMA(p, q) model set
npFree
= p + q regardless of whether the mean is
estimated or not. The original derivation for time series models is due to
Box and Pierce (1970) with the above modified version discussed by Ljung and
Box (1978). The extension of the test to transfer function models is
discussed by Box and Jenkins (1976, pages 394395).
Modifier and Type  Method and Description 

static double[] 
compute(int nObservations,
double[] correlations,
int npFree,
int lagMax)
Performs lackoffit test for a univariate time series or transfer
function given the appropriate correlation function using a minimum lag
of 1.

static double[] 
compute(int nObservations,
double[] correlations,
int npFree,
int lagMax,
int lagMin)
Performs lackoffit test for a univariate time series or transfer
function given the appropriate correlation function.

public static double[] compute(int nObservations, double[] correlations, int npFree, int lagMax)
nObservations
 an int
containing the number of
observations of the stationary time series.correlations
 a double
array of length lagMax+1
containing the correlation function.npFree
 an int
scalar specifying the number of free
parameters in the formulation of the time series model.
npfree
must be greater than or equal to zero
and less than lagMax
. Woodfield (1990)
recommends npFree = p + q
.lagMax
 an int
scalar specifying the maximum lag of
the correlation function.double
array of length 2 with the test statistic,
Q, and its pvalue, p. Under the null hypothesis, Q
has an approximate chisquared distribution with
lagMaxlagMin+1npFree
degrees of freedom.public static double[] compute(int nObservations, double[] correlations, int npFree, int lagMax, int lagMin)
nObservations
 an int
containing the number of
observations of the stationary time series.correlations
 a double
array of length lagMax+1
containing the correlation function.npFree
 an int
scalar specifying the number of free
parameters in the formulation of the time series model.
npfree
must be greater than or equal to zero
and less than lagMax
. Woodfield (1990)
recommends npFree = p + q
.lagMax
 an int
scalar specifying the maximum lag of
the correlation function.lagMin
 an int
scalar specifying the minimum lag of
the correlation function. lagMin
corresponds
to the lower bound of summation in the lack of fit test
statistic. Default value is 1.double
array of length 2 with the test statistic,
Q, and its pvalue, p. Under the null hypothesis, Q
has an approximate chisquared distribution with
lagMaxlagMin+1npFree
degrees of freedom.Copyright © 19702015 Rogue Wave Software
Built October 13 2015.