ARAutoUnivariate.AIC Property

ARAutoUnivariateAIC Property

The final estimate for Akaike's Information Criterion (AIC) at the optimum.

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

Syntax

public double AIC { get; }

Public ReadOnly Property AIC As Double
	Get

public:
property double AIC {
	double get ();
}

member AIC : float with get

Property Value

Type: Double
A double scalar value which is an approximation to $\mbox{AIC} = -2\ln(L)+2p$ , where L is the value of the maximum likelihood function evaluated at the parameter estimates. The approximation uses the calculation

$\mbox{AIC} \approx (\rm{n-maxlag})\ln({\hat {\sigma}}^2)+2(p+1)+(\rm{n-maxlag})(\ln(2\pi)+1),$

where ${\hat {\sigma}}^2$ is an estimate of the residual variance of the series, commonly known in time series analysis as the innovation variance, and n is the number of observations in the time series z(n=z.Length).

Exceptions

Exception	Condition
MatrixSingularException	is thrown if the input matrix is singular.
TooManyCallsException	is thrown if the number of calls to the function has exceeded the maximum number of iterations times the number of moving average (MA) parameters + 1.
IncreaseErrRelException	is thrown if the bound for the relative error is too small.
NewInitialGuessException	is thrown if the iteration has not made good progress.
IllConditionedException	is thrown if the problem is ill-conditioned.
TooManyIterationsException	is thrown if the maximum number of iterations is exceeded.
TooManyFunctionEvaluationsException	is thrown if the maximum number of function evaluations is exceeded.
TooManyJacobianEvalException	is thrown if the maximum number of Jacobian evaluations is exceeded.
SingularTriangularMatrixException	is thrown if the input triangular matrix is singular.
NonStationaryException	is thrown if the final maximum likelihood estimates for the time series are nonstationary.

Reference

ARAutoUnivariate Class

Imsl.Stat Namespace