ARAutoUnivariate Class

Automatically determines the best autoregressive time series model using Akaike's Information Criterion.

Inheritance Hierarchy

SystemObject
Imsl.StatARAutoUnivariate

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

Syntax

C++

Copy

[SerializableAttribute]
public class ARAutoUnivariate

<SerializableAttribute>
Public Class ARAutoUnivariate

[SerializableAttribute]
public ref class ARAutoUnivariate

[<SerializableAttribute>]
type ARAutoUnivariate =  class end

The ARAutoUnivariate type exposes the following members.

Constructors

	Name	Description
	ARAutoUnivariate	ARAutoUnivariate constructor.

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Methods

	Name	Description
	Compute	Determines the autoregressive model with the minimum AIC by fitting autoregressive models from 0 to maxlag lags using the method of moments or an estimation method specified by the user through EstimationMethod.
	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.)
	Forecast	Returns forecasts and associated confidence interval offsets.
	GetAR	Returns the final autoregressive parameter estimates at the optimum AIC using the estimation method specified in EstimationMethod.
	GetDeviations	Returns the deviations for each forecast used for calculating the forecast confidence limits.
	GetForecast	Returns a specified number of forecasts beyond the last value in the series.
	GetHashCode	Serves as a hash function for a particular type. (Inherited from Object.)
	GetResiduals	Returns the current values of the vector of residuals.
	GetTimeSeries	Returns the time series used for estimating the minimum AIC and the autoregressive coefficients.
	GetTimsacAR	Returns the final auto regressive parameter estimates at the optimum AIC estimated by the original TIMSAC routine (UNIMAR).
	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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Properties

	Name	Description
	AIC	The final estimate for Akaike's Information Criterion (AIC) at the optimum.
	BackwardOrigin	The maximum backward origin used in calculating the forecasts.
	Confidence	The confidence level for calculating confidence limit deviations returned from GetDeviations.
	Constant	The estimate for the constant parameter in the ARMA series.
	ConvergenceTolerance	The tolerance level used to determine convergence of the nonlinear least-squares and maximum likelihood algorithms.
	EstimationMethod	The estimation method used for estimating the final estimates for the autoregressive coefficients.
	InnovationVariance	The final estimate for the innovation variance.
	Likelihood	The final estimate for $L \approx e^{-(\mbox{AIC} - 2p)/2}$ , where p is the AR order, AIC is the value of Akaike's Information Criterion, and L is the likelihood function evaluated for the optimum autoregressive model.
	MaxIterations	The maximum number of iterations used for estimating the autoregressive coefficients.
	Maxlag	The current value used to represent the maximum number of autoregressive lags to achieve the minimum AIC.
	Mean	The mean used to center the time series z.
	NumberOfProcessors	Perform the parallel calculations with the maximum possible number of processors set to NumberOfProcessors.
	Order	The order of the AR model selected with the minimum AIC.
	TimsacConstant	The estimate for the constant parameter in the ARMA series.
	TimsacVariance	The final estimate for the innovation variance calculated by the TIMSAC automatic AR modeling routine (UNIMAR).

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Remarks

ARAutoUnivariate automatically selects the order of the AR model that best fits the data and then computes the AR coefficients. The algorithm used in ARAutoUnivariate is derived from the work of Akaike, H., et. al (1979) and Kitagawa and Akaike (1978). This code was adapted from the UNIMAR procedure published as part of the TIMSAC-78 Library.

The best fit AR model is determined by successively fitting AR models with $0,1,2,\dots,\mbox{maxlag}$ autoregressive coefficients. For each model, Akaike's Information Criterion (AIC) is calculated based on the formula

$\mbox{AIC} = -2\ln(likelihood)+2p$

Class ARAutoUnivariate uses the approximation to this formula developed by Ozaki and Oda (1979),

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

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. By dropping the constant

$(n-\mbox{maxlag})(\ln(2\pi)+1),$

the calculation is simplified to

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

The best fit model is the model with minimum AIC. If the number of parameters in this model selected by ARAutoUnivariate is equal to the highest order autoregressive model fitted, i.e., p=maxlag, then a model with smaller AIC might exist for larger values of maxlag. In this case, increasing maxlag to explore AR models with additional autoregressive parameters might be warranted.

Property EstimationMethod can be used to specify the method used to calculate the AR coeficients. If EstimationMethod is set to MethodOfMoments, estimates of the autoregressive coefficients for the model with minimum AIC are calculated using method of moments as described in the ARMA class. If LeastSquares is specified, the coefficients are determined by the method of least squares applied in the form described by Kitagawa and Akaike (1978). If MaximumLikelihood is specified, the coefficients are estimated using maximum likelihood as described in the ARMAMaxLikelihood class.

Reference

Imsl.Stat Namespace

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