Performs lack-of-fit test for a univariate time series or transfer function given the appropriate correlation function.

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0

Syntax

C#
[SerializableAttribute]
public class LackOfFit
Visual Basic (Declaration)
<SerializableAttribute> _
Public Class LackOfFit
Visual C++
[SerializableAttribute]
public ref class LackOfFit

Remarks

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 \sqrt{ \texttt{nObservations}} p + q
Transfer function 0 \sqrt{ \texttt{nObservations}} 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 \hat{\rho}(k) for k = L, L+1,...,K where L = lagMin and K = lagMax.

The basic form of the test statistic Q is

Q=n(n+2)\sum_{k=L}^{K}(n-k)^{-1}\hat{\rho}(k)

with L = 1 if \hat{\rho}(k) is an autocorrelation function. Given that the model is adequate, Q has a chi-squared distribution with K-L+1-m 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 394-395).

Inheritance Hierarchy

System..::.Object
Imsl.Stat..::.LackOfFit

See Also