LackOfFit Class

LackOfFit Class

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

Inheritance Hierarchy

SystemObject
Imsl.StatLackOfFit

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

C++

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[SerializableAttribute]
public class LackOfFit

<SerializableAttribute>
Public Class LackOfFit

[SerializableAttribute]
public ref class LackOfFit

[<SerializableAttribute>]
type LackOfFit =  class end

The LackOfFit type exposes the following members.

Methods

	Name	Description
	Compute(Int32, Double, Int32, Int32)	Performs lack-of-fit test for a univariate time series or transfer function given the appropriate correlation function using a minimum lag of 1.
	Compute(Int32, Double, Int32, Int32, Int32)	Performs lack-of-fit test for a univariate time series or transfer function given the appropriate correlation function.
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetHashCode	Serves as a hash function for a particular type. (Inherited from Object.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	ToString	Returns a string that represents the current object. (Inherited from Object.)

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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 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).

Reference

Imsl.Stat Namespace

Other Resources

Example