ARAutoUnivariate Class |
Namespace: Imsl.Stat
The ARAutoUnivariate type exposes the following members.
Name | Description | |
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ARAutoUnivariate | ARAutoUnivariate constructor.
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Name | Description | |
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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.
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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.
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GetAR |
Returns the final autoregressive parameter estimates at the
optimum AIC using the estimation method specified in
EstimationMethod.
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GetDeviations |
Returns the deviations for each forecast used for calculating the
forecast confidence limits.
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GetForecast |
Returns a specified number of forecasts beyond the last value in the series.
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GetHashCode | Serves as a hash function for a particular type. (Inherited from Object.) | |
GetResiduals |
Returns the current values of the vector of residuals.
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GetTimeSeries |
Returns the time series used for estimating the minimum AIC and the
autoregressive coefficients.
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GetTimsacAR |
Returns the final auto regressive parameter estimates at the
optimum AIC estimated by the original TIMSAC routine (UNIMAR).
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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.) |
Name | Description | |
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AIC |
The final estimate for Akaike's Information Criterion (AIC)
at the optimum.
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BackwardOrigin |
The maximum backward origin used in calculating the forecasts.
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Confidence |
The confidence level for calculating confidence limit deviations
returned from GetDeviations.
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Constant |
The estimate for the constant parameter in the ARMA series.
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ConvergenceTolerance |
The tolerance level used to determine convergence of the nonlinear
least-squares and maximum likelihood algorithms.
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EstimationMethod |
The estimation method used for estimating the final estimates for
the autoregressive coefficients.
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InnovationVariance |
The final estimate for the innovation variance.
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Likelihood |
The final estimate for ,
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.
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MaxIterations |
The maximum number of iterations used for estimating the
autoregressive coefficients.
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Maxlag |
The current value used to represent the maximum number of
autoregressive lags to achieve the minimum AIC.
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Mean |
The mean used to center the time series z.
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NumberOfProcessors |
Perform the parallel calculations with the maximum possible number of
processors set to NumberOfProcessors.
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Order |
The order of the AR model selected with the minimum AIC.
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TimsacConstant |
The estimate for the constant parameter in the ARMA series.
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TimsacVariance |
The final estimate for the innovation variance calculated
by the TIMSAC automatic AR modeling routine (UNIMAR).
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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 autoregressive coefficients. For each model, Akaike's Information Criterion (AIC) is calculated based on the formula
Class ARAutoUnivariate uses the approximation to this formula developed by Ozaki and Oda (1979), where 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 the calculation is simplified toThe 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.