ARAutoUnivariate (JMSL Numerical Library (jmsl) 2021.0.0 API)

java.lang.Object
- com.imsl.stat.ARAutoUnivariate

All Implemented Interfaces:: Serializable

public class ARAutoUnivariate
extends Object
implements Serializable

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

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 $0,1,2,\dots,\rm{maxlag}$ 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), $$\mbox{AIC} = (n-\mbox{maxlag})\ln({\hat {\sigma}}^2)+2(p+1)+(n-\mbox{maxlag})(\ln(2\pi)+ 1)$$ 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 $$\mbox{AIC}=(n-\mbox{maxlag})\ln({\hat{\sigma}}^2)+ 2(p+1),$$

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.

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

The Java Logging API can be used to trace the execution of ARAutoUnivariate. The name of this logger is com.imsl.stat.ARAutoUnivariate. Accumulated levels of detail correspond to Java's FINE, FINER, and FINEST logging levels with FINE yielding the smallest amount of information and FINEST yielding the most. The levels of output yield the following:

Level	Output
FINE	A message on entering and exiting method `compute`.
FINER	All of the messages in `FINE`, a message entering and exiting the `compute` method, plus the final computations.
FINEST	All of the messages in `FINER`, plus the intermediate computations.

See Also:: Example 1, Example 2, Serialized Form

Nested Class Summary

Nested Classes
Modifier and Type	Class and Description
`static class`	`ARAutoUnivariate.Formatter` Deprecated. Use `IMSLFormatter` instead.
`static class`	`ARAutoUnivariate.TriangularMatrixSingularException` The input triangular matrix is singular.

Field Summary

Fields
Modifier and Type	Field and Description
`static int`	`LEAST_SQUARES` Indicates that least-squares should be used for estimating the coefficients in the time series.
`static int`	`MAX_LIKELIHOOD` Indicates that maximum likelihood should be used for estimating the coefficients in the time series.
`static int`	`METHOD_OF_MOMENTS` Indicates the method of moments should be used for estimating the coefficients in the time series.

Constructor Summary

Constructors
Constructor and Description

ARAutoUnivariate(int maxlag, double[] z)
ARAutoUnivariate constructor.

Constructors
Constructor and Description
`ARAutoUnivariate(int maxlag, double[] z)` `ARAutoUnivariate` constructor.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`void`	`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 `setEstimationMethod`.
`double[][]`	`forecast(int nForecast)` Returns forecasts and associated confidence interval offsets.
`double`	`getAIC()` Returns the final estimate for Akaike's Information Criterion (AIC) at the optimum.
`double[]`	`getAR()` Returns the final auto regressive parameter estimates at the optimum AIC using the estimation method specified in `setEstimationMethod`.
`int`	`getBackwardOrigin()` Returns the maximum backward origin.
`double`	`getConfidence()` Returns the confidence level for calculating confidence limit deviations returned from `getDeviations`.
`double`	`getConstant()` Returns the estimate for the constant parameter in the ARMA series.
`double`	`getConvergenceTolerance()` Returns the tolerance level used to determine convergence of the nonlinearleast-squares and maximum likelihood algorithms.
`double[]`	`getDeviations()` Returns the deviations used for calculating the forecast confidence limits.
`int`	`getEstimationMethod()` Returns the estimation method used for estimating the autoregressive coefficients.
`double[]`	`getForecast(int nForecast)` Returns forecasts
`double`	`getInnovationVariance()` Returns the final estimate for the innovation variance.
`double`	`getLikelihood()` Returns the final estimate for $L=e^{-(\mbox{AIC} - 2p)/2} $, where p is the AR order, AIC is Akaike's Information Criterion, and L is the likelihood function evaluated for the optimum autoregressive model.
`Logger`	`getLogger()` Returns the logger object.
`int`	`getMaxIterations()` Returns the value currently being used as the maximum number of iterations allowed in the nonlinear equation solver used in both the method of moments and least-squares algorithms.
`int`	`getMaxlag()` Returns the current value used to represent the maximum number of autoregressive lags to achieve the minimum AIC.
`double`	`getMean()` Returns the mean used to center the time series `z`.
`int`	`getOrder()` Returns the order of the AR model selected with the minimum AIC.
`double[]`	`getResiduals()` Returns the current values of the vector of residuals.
`double[]`	`getTimeSeries()` Returns the time series used for estimating the minimum AIC and the autoregressive coefficients.
`double[]`	`getTimsacAR()` Returns the final auto regressive parameter estimates at the optimum AIC estimated by the original TIMSAC routine (UNIMAR).
`double`	`getTimsacConstant()` Returns the estimate for the constant parameter in the ARMA series.
`double`	`getTimsacVariance()` Returns the final estimate for the innovation variance calculated by the TIMSAC automatic AR modeling routine (UNIMAR).
`void`	`setBackwardOrigin(int backwardOrigin)` Sets the maximum backward origin used in calculating the forecasts.
`void`	`setConfidence(double confidence)` Sets the confidence level for calculating confidence limit deviations returned from `getDeviations`.
`void`	`setConvergenceTolerance(double convergenceTolerance)` Sets the tolerance level used to determine convergence of the nonlinear least-squares and maximum likelihood algorithms.
`void`	`setEstimationMethod(int method)` Sets the estimation method used for estimating the final estimates for the autoregressive coefficients.
`void`	`setMaxIterations(int iterations)` Sets the maximum number of iterations used for estimating the autoregressive coefficients.
`void`	`setMean(double mean)` Sets the estimate of the mean used for centering the time series `z`.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - METHOD_OF_MOMENTS
```
public static final int METHOD_OF_MOMENTS
```
    Indicates the method of moments should be used for estimating the coefficients in the time series.
    
    See Also:
    
    Constant Field Values
  - LEAST_SQUARES
```
public static final int LEAST_SQUARES
```
    Indicates that least-squares should be used for estimating the coefficients in the time series.
    
    See Also:
    
    Constant Field Values
  - MAX_LIKELIHOOD
```
public static final int MAX_LIKELIHOOD
```
    Indicates that maximum likelihood should be used for estimating the coefficients in the time series.
    
    See Also:
    
    Constant Field Values
- Constructor Detail
  - ARAutoUnivariate
```
public ARAutoUnivariate(int maxlag,
                        double[] z)
```
    ARAutoUnivariate constructor.
    
    Parameters:
    
    maxlag - an int scalar specifying the maximum number of autoregressive lags to evaluate
    
    z - a double array containing the time series
- Method Detail
  - compute
```
public void compute()
             throws ARMA.MatrixSingularException,
                    ARMA.TooManyCallsException,
                    ARMA.IncreaseErrRelException,
                    ARMA.NewInitialGuessException,
                    ARMA.IllConditionedException,
                    ARMA.TooManyITNException,
                    ARMA.TooManyFcnEvalException,
                    ARMA.TooManyJacobianEvalException,
                    ARMA.ResidualsTooLargeException,
                    ARAutoUnivariate.TriangularMatrixSingularException,
                    ARMAMaxLikelihood.NonStationaryException,
                    ARMAMaxLikelihood.NonInvertibleException
```
    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 setEstimationMethod.
    
    Throws:
    
    ARMA.MatrixSingularException - is thrown if the input matrix is singular.
    
    ARMA.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.
    
    ARMA.IncreaseErrRelException - is thrown if the bound for the relative error is too small.
    
    ARMA.NewInitialGuessException - is thrown if the iteration has not made good progress.
    
    ARMA.IllConditionedException - is thrown if the problem is ill-conditioned.
    
    ARMA.TooManyITNException - is thrown if the maximum number of iterations is exceeded.
    
    ARMA.TooManyFcnEvalException - is thrown if the maximum number of function evaluations is exceeded.
    
    ARMA.TooManyJacobianEvalException - is thrown if the maximum number of Jacobian evaluations is exceeded.
    
    ARMA.ResidualsTooLargeException - is thrown if the residuals computed in one step of the Least Squares estimation of the ARMA coefficients become too large.
    
    ARAutoUnivariate.TriangularMatrixSingularException - is thrown if the input triangular matrix is singular.
    
    ARMAMaxLikelihood.NonStationaryException - is thrown if the final maximum likelihood estimates for the time series are non-stationary
    
    ARMAMaxLikelihood.NonInvertibleException - is thrown if the final maximum likelihood estimates for the time series are noninvertible.
    
    ARMAMaxLikelihood.InitialMAException - is thrown if the initial values provided for the moving average terms using setMA are noninvertible. In this case, ARMAMaxLikelihood terminates and does not compute the time series estimates.
  - getAIC
```
public double getAIC()
              throws ARMA.MatrixSingularException,
                     ARMA.TooManyCallsException,
                     ARMA.IncreaseErrRelException,
                     ARMA.NewInitialGuessException,
                     ARMA.IllConditionedException,
                     ARMA.TooManyITNException,
                     ARMA.TooManyFcnEvalException,
                     ARMA.TooManyJacobianEvalException,
                     ARMA.ResidualsTooLargeException,
                     ARAutoUnivariate.TriangularMatrixSingularException,
                     ARMAMaxLikelihood.NonStationaryException,
                     ARMAMaxLikelihood.NonInvertibleException
```
    Returns the final estimate for Akaike's Information Criterion (AIC) at the optimum.
    
    Returns:
    
    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 (n=z.length).
    
    Throws:
    
    ARMA.MatrixSingularException - is thrown if the input matrix is singular
    
    ARMA.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
    
    ARMA.IncreaseErrRelException - is thrown if the bound for the relative error is too small
    
    ARMA.NewInitialGuessException - is thrown if the iteration has not made good progress
    
    ARMA.IllConditionedException - is thrown if the problem is ill-conditioned
    
    ARMA.TooManyITNException - is thrown if the maximum number of iterations is exceeded
    
    ARMA.TooManyFcnEvalException - is thrown if the maximum number of function evaluations is exceeded
    
    ARMA.TooManyJacobianEvalException - is thrown if the maximum number of Jacobian evaluations is exceeded
    
    ARMA.ResidualsTooLargeException - is thrown if the residuals computed in one step of the Least Squares estimation of the ARMA coefficients become too large.
    
    ARAutoUnivariate.TriangularMatrixSingularException - is thrown if the input triangular matrix is singular
    
    ARMAMaxLikelihood.NonStationaryException - is thrown if the final maximum likelihood estimates for the time series are nonstationary
    
    ARMAMaxLikelihood.NonInvertibleException - is thrown if the final maximum likelihood estimates for the time series are noninvertible
    
    ARMAMaxLikelihood.InitialMAException - is thrown if the initial values provided for the moving average terms using setMA are noninvertible. In this case, ARMAMaxLikelihood terminates and does not compute the time series estimates.
  - getConfidence
```
public double getConfidence()
```
    Returns the confidence level for calculating confidence limit deviations returned from getDeviations.
    
    Returns:
    
    a double scalar value representing the confidence level used in computing forecast confidence intervals.
  - getBackwardOrigin
```
public int getBackwardOrigin()
```
    Returns the maximum backward origin.
    
    Returns:
    
    an int scalar specifying the maximum backward origin.
  - getTimsacConstant
```
public double getTimsacConstant()
                         throws ARMA.MatrixSingularException,
                                ARMA.TooManyCallsException,
                                ARMA.IncreaseErrRelException,
                                ARMA.NewInitialGuessException,
                                ARMA.IllConditionedException,
                                ARMA.TooManyITNException,
                                ARMA.TooManyFcnEvalException,
                                ARMA.TooManyJacobianEvalException,
                                ARMA.ResidualsTooLargeException,
                                ARAutoUnivariate.TriangularMatrixSingularException,
                                ARMAMaxLikelihood.NonStationaryException,
                                ARMAMaxLikelihood.NonInvertibleException
```
    Returns the estimate for the constant parameter in the ARMA series.
    
    Returns:
    
    a double scalar equal to the estimate for the constant parameter in the ARMA series.
    
    Throws:
    
    ARMA.MatrixSingularException - is thrown if the input matrix is singular.
    
    ARMA.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.
    
    ARMA.IncreaseErrRelException - is thrown if the bound for the relative error is too small.
    
    ARMA.NewInitialGuessException - is thrown if the iteration has not made good progress.
    
    ARMA.IllConditionedException - is thrown if the problem is ill-conditioned.
    
    ARMA.TooManyITNException - is thrown if the maximum number of iterations is exceeded.
    
    ARMA.TooManyFcnEvalException - is thrown if the maximum number of function evaluations is exceeded.
    
    ARMA.TooManyJacobianEvalException - is thrown if the maximum number of Jacobian evaluations is exceeded.
    
    ARMA.ResidualsTooLargeException - is thrown if the residuals computed in one step of the Least Squares estimation of the ARMA coefficients become too large.
    
    ARAutoUnivariate.TriangularMatrixSingularException - is thrown if the input triangular matrix is singular.
    
    ARMAMaxLikelihood.NonStationaryException - is thrown if the final maximum likelihood estimates for the time series are non-stationary.
    
    ARMAMaxLikelihood.NonInvertibleException - is thrown if the final maximum likelihood estimates for the time series are noninvertible.
    
    ARMAMaxLikelihood.InitialMAException - is thrown if the initial values provided for the moving average terms using setMA are noninvertible. In this case, ARMAMaxLikelihood terminates and does not compute the time series estimates.
  - getConstant
```
public double getConstant()
                   throws ARMA.MatrixSingularException,
                          ARMA.TooManyCallsException,
                          ARMA.IncreaseErrRelException,
                          ARMA.NewInitialGuessException,
                          ARMA.IllConditionedException,
                          ARMA.TooManyITNException,
                          ARMA.TooManyFcnEvalException,
                          ARMA.TooManyJacobianEvalException,
                          ARMA.ResidualsTooLargeException,
                          ARAutoUnivariate.TriangularMatrixSingularException,
                          ARMAMaxLikelihood.NonStationaryException,
                          ARMAMaxLikelihood.NonInvertibleException
```
    Returns the estimate for the constant parameter in the ARMA series.
    
    Returns:
    
    a double scalar equal to the estimate for the constant parameter in the ARMA series.
    
    Throws:
    
    ARMA.MatrixSingularException - is thrown if the input matrix is singular.
    
    ARMA.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.
    
    ARMA.IncreaseErrRelException - is thrown if the bound for the relative error is too small.
    
    ARMA.NewInitialGuessException - is thrown if the iteration has not made good progress.
    
    ARMA.IllConditionedException - is thrown if the problem is ill-conditioned.
    
    ARMA.TooManyITNException - is thrown if the maximum number of iterations is exceeded.
    
    ARMA.TooManyFcnEvalException - is thrown if the maximum number of function evaluations is exceeded.
    
    ARMA.TooManyJacobianEvalException - is thrown if the maximum number of Jacobian evaluations is exceeded.
    
    ARMA.ResidualsTooLargeException - is thrown if the residuals computed in one step of the Least Squares estimation of the ARMA coefficients become too large.
    
    ARAutoUnivariate.TriangularMatrixSingularException - is thrown if the input triangular matrix is singular.
    
    ARMAMaxLikelihood.NonStationaryException - is thrown if the final maximum likelihood estimates for the time series are non-stationary.
    
    ARMAMaxLikelihood.NonInvertibleException - is thrown if the final maximum likelihood estimates for the time series are noninvertible.
    
    ARMAMaxLikelihood.InitialMAException - is thrown if the initial values provided for the moving average terms using setMA are noninvertible. In this case, ARMAMaxLikelihood terminates and does not compute the time series estimates.
  - getTimeSeries
```
public double[] getTimeSeries()
```
    Returns the time series used for estimating the minimum AIC and the autoregressive coefficients.
    
    Returns:
    
    a double array containing the time series values set in the constructor.
  - setBackwardOrigin
```
public void setBackwardOrigin(int backwardOrigin)
```
    Sets the maximum backward origin used in calculating the forecasts.
    
    Parameters:
    
    backwardOrigin - an int scalar specifying the maximum backward origin. backwardOrigin must be greater than or equal to 0 and less than or equal to z.length - p, where p is the optimum number of AR coeficients determined by ARAutoUnivariate. The forecasted values returned will be z.length - backwardOrigin through z.length. Default: backwardOrigin = 0.
  - forecast
```
public double[][] forecast(int nForecast)
                    throws ARMA.MatrixSingularException,
                           ARMA.TooManyCallsException,
                           ARMA.IncreaseErrRelException,
                           ARMA.NewInitialGuessException,
                           ARMA.IllConditionedException,
                           ARMA.TooManyITNException,
                           ARMA.TooManyFcnEvalException,
                           ARMA.TooManyJacobianEvalException,
                           ARMA.ResidualsTooLargeException,
                           ARAutoUnivariate.TriangularMatrixSingularException,
                           ARMAMaxLikelihood.NonStationaryException,
                           ARMAMaxLikelihood.NonInvertibleException
```
    Returns forecasts and associated confidence interval offsets.
    
    Parameters:
    
    nForecast - an input int representing the number of requested forecasts
    
    Returns:
    
    a double matrix of dimension nForecast by backwardOrigin + 1 containing the forecasts. The forecasts are for lead times $l=1,2,\ldots, \rm{nForecast}$ at origins z.length-backwardOrigin-1+j where $j=1,\ldots, \rm{backwardOrigin}+1$.
    
    Throws:
    
    ARMA.MatrixSingularException - is thrown if the input matrix is singular
    
    ARMA.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
    
    ARMA.IncreaseErrRelException - is thrown if the bound for the relative error is too small
    
    ARMA.NewInitialGuessException - is thrown if the iteration has not made good progress
    
    ARMA.IllConditionedException - is thrown if the problem is ill-conditioned
    
    ARMA.TooManyITNException - is thrown if the maximum number of iterations is exceeded
    
    ARMA.TooManyFcnEvalException - is thrown if the maximum number of function evaluations is exceeded
    
    ARMA.TooManyJacobianEvalException - is thrown if the maximum number of Jacobian evaluations is exceeded
    
    ARAutoUnivariate.TriangularMatrixSingularException - is thrown if the input triangular matrix is singular
    
    ARMAMaxLikelihood.NonStationaryException - is thrown if the final maximum likelihood estimates for the time series are nonstationary
    
    ARMAMaxLikelihood.NonInvertibleException - is thrown if the final maximum likelihood estimates for the time series are noninvertible
    
    ARMAMaxLikelihood.InitialMAException - is thrown if the initial values provided for the moving average terms using setMA are noninvertible. In this case, ARMAMaxLikelihood terminates and does not compute the time series estimates.
    
    ARMA.ResidualsTooLargeException
  - getForecast
```
public double[] getForecast(int nForecast)
                     throws ARMA.MatrixSingularException,
                            ARMA.TooManyCallsException,
                            ARMA.IncreaseErrRelException,
                            ARMA.NewInitialGuessException,
                            ARMA.IllConditionedException,
                            ARMA.TooManyITNException,
                            ARMA.TooManyFcnEvalException,
                            ARMA.TooManyJacobianEvalException,
                            ARMA.ResidualsTooLargeException,
                            ARAutoUnivariate.TriangularMatrixSingularException,
                            ARMAMaxLikelihood.NonStationaryException,
                            ARMAMaxLikelihood.NonInvertibleException
```
    Returns forecasts
    
    Parameters:
    
    nForecast - an input int representing the number of requested forecasts beyond the last value in the series.
    
    Returns:
    
    a double array containing the nForecast+backwardOrigin forecasts. The first backwardOrigin forecasts are one-step ahead forecasts for the last backwardOrigin values in the series. The next nForecast values in the returned series are forecasts for the next values beyond the series.
    
    Throws:
    
    NonStationary - is thrown if the final maximum likelihood estimates for the time series are nonstationary.
    
    NonInvertible - is thrown if the final maximum likelihood estimates for the time series are noninvertible.
    
    InitialMAException - is thrown if the initial values provided for the moving average terms using setMA are noninvertible. In this case, ARMAMaxLikelihood terminates and does not compute the time series estimates.
    
    ARMA.MatrixSingularException - is thrown if the input matrix is singular.
    
    ARMA.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.
    
    ARMA.IncreaseErrRelException - is thrown if the bound for the relative error is too small.
    
    ARMA.NewInitialGuessException - is thrown if the iteration has not made good progress.
    
    ARMA.IllConditionedException - is thrown if the problem is ill-conditioned.
    
    ARMA.TooManyITNException - is thrown if the maximum number of iterations is exceeded.
    
    ARMA.TooManyFcnEvalException - is thrown if the maximum number of function evaluations is exceeded.
    
    ARMA.TooManyJacobianEvalException - is thrown if the maximum number of Jacobian evaluations is exceeded.
    
    ARMA.ResidualsTooLargeException - is thrown if the residuals computed in one step of the Least Squares estimation of the ARMA coefficients become too large.
    
    ARAutoUnivariate.TriangularMatrixSingularException - is thrown if the input triangular matrix is singular.
    
    ARMAMaxLikelihood.NonStationaryException - is thrown if the final maximum likelihood estimates for the time series are non-stationary.
    
    ARMAMaxLikelihood.NonInvertibleException - is thrown if the final maximum likelihood estimates for the time series are noninvertible.
    
    ARMAMaxLikelihood.InitialMAException - is thrown if the initial values provided for the moving average terms using setMA are noninvertible. In this case, ARMAMaxLikelihood terminates and does not compute the time series estimates.
  - getDeviations
```
public double[] getDeviations()
```
    Returns the deviations used for calculating the forecast confidence limits.
    
    Returns:
    
    a double array of length backwardOrigin+nForecast containing the deviations for calculating forecast confidence intervals. The confidence level is specified in confidence. By default, confidence = 0.95.
  - getLikelihood
```
public double getLikelihood()
                     throws ARMA.MatrixSingularException,
                            ARMA.TooManyCallsException,
                            ARMA.IncreaseErrRelException,
                            ARMA.NewInitialGuessException,
                            ARMA.IllConditionedException,
                            ARMA.TooManyITNException,
                            ARMA.TooManyFcnEvalException,
                            ARMA.TooManyJacobianEvalException,
                            ARMA.ResidualsTooLargeException,
                            ARAutoUnivariate.TriangularMatrixSingularException,
                            ARMAMaxLikelihood.NonStationaryException,
                            ARMAMaxLikelihood.NonInvertibleException
```
    Returns the final estimate for $L=e^{-(\mbox{AIC} - 2p)/2} $, where p is the AR order, AIC is Akaike's Information Criterion, and L is the likelihood function evaluated for the optimum autoregressive model. If MAX_LIKELIHOOD is set in the setEstimationMethod, the exact likelihood evaluated for the optimum autoregressive model will be returned. Otherwise it is calculated using the approximation to the AIC.
    
    Returns:
    
    a double scalar equal to the maximum of the likelihood function, $L=e^{-(\mbox{AIC} - 2p)/2} $.
    
    Throws:
    
    ARMA.MatrixSingularException - is thrown if the input matrix is singular.
    
    ARMA.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.
    
    ARMA.IncreaseErrRelException - is thrown if the bound for the relative error is too small.
    
    ARMA.NewInitialGuessException - is thrown if the iteration has not made good progress.
    
    ARMA.IllConditionedException - is thrown if the problem is ill-conditioned.
    
    ARMA.TooManyITNException - is thrown if the maximum number of iterations is exceeded.
    
    ARMA.TooManyFcnEvalException - is thrown if the maximum number of function evaluations is exceeded.
    
    ARMA.TooManyJacobianEvalException - is thrown if the maximum number of Jacobian evaluations is exceeded.
    
    ARMA.ResidualsTooLargeException - is thrown if the residuals computed in one step of the Least Squares estimation of the ARMA coefficients become too large.
    
    ARAutoUnivariate.TriangularMatrixSingularException - is thrown if the input triangular matrix is singular.
    
    ARMAMaxLikelihood.NonStationaryException - is thrown if the final maximum likelihood estimates for the time series are non-stationary.
    
    ARMAMaxLikelihood.NonInvertibleException - is thrown if the final maximum likelihood estimates for the time series are noninvertible.
    
    ARMAMaxLikelihood.InitialMAException - is thrown if the initial values provided for the moving average terms using setMA are noninvertible. In this case, ARMAMaxLikelihood terminates and does not compute the time series estimates.
  - getTimsacVariance
```
public double getTimsacVariance()
                         throws ARMA.MatrixSingularException,
                                ARMA.TooManyCallsException,
                                ARMA.IncreaseErrRelException,
                                ARMA.NewInitialGuessException,
                                ARMA.IllConditionedException,
                                ARMA.TooManyITNException,
                                ARMA.TooManyFcnEvalException,
                                ARMA.TooManyJacobianEvalException,
                                ARMA.ResidualsTooLargeException,
                                ARAutoUnivariate.TriangularMatrixSingularException,
                                ARMAMaxLikelihood.NonStationaryException,
                                ARMAMaxLikelihood.NonInvertibleException
```
    Returns the final estimate for the innovation variance calculated by the TIMSAC automatic AR modeling routine (UNIMAR). This variance depends upon the value of maxlag since the series length in this computation depends on its value. Use getInnovationVariance to return the innovation variance calculated using the maximum series length.
    
    Returns:
    
    a double scalar value equal to the estimate for the innovation variance.
    
    Throws:
    
    ARMA.MatrixSingularException - is thrown if the input matrix is singular.
    
    ARMA.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.
    
    ARMA.IncreaseErrRelException - is thrown if the bound for the relative error is too small.
    
    ARMA.NewInitialGuessException - is thrown if the iteration has not made good progress.
    
    ARMA.IllConditionedException - is thrown if the problem is ill-conditioned.
    
    ARMA.TooManyITNException - is thrown if the maximum number of iterations is exceeded.
    
    ARMA.TooManyFcnEvalException - is thrown if the maximum number of function evaluations is exceeded.
    
    ARMA.TooManyJacobianEvalException - is thrown if the maximum number of Jacobian evaluations is exceeded.
    
    ARMA.ResidualsTooLargeException - is thrown if the residuals computed in one step of the Least Squares estimation of the ARMA coefficients become too large.
    
    ARAutoUnivariate.TriangularMatrixSingularException - is thrown if the input triangular matrix is singular.
    
    ARMAMaxLikelihood.NonStationaryException - is thrown if the final maximum likelihood estimates for the time series are nonstationary.
    
    ARMAMaxLikelihood.NonInvertibleException - is thrown if the final maximum likelihood estimates for the time series are noninvertible.
    
    ARMAMaxLikelihood.InitialMAException - is thrown if the initial values provided for the moving average terms using setMA are noninvertible. In this case, ARMAMaxLikelihood terminates and does not compute the time series estimates.
  - getInnovationVariance
```
public double getInnovationVariance()
                             throws ARMA.MatrixSingularException,
                                    ARMA.TooManyCallsException,
                                    ARMA.IncreaseErrRelException,
                                    ARMA.NewInitialGuessException,
                                    ARMA.IllConditionedException,
                                    ARMA.TooManyITNException,
                                    ARMA.TooManyFcnEvalException,
                                    ARMA.TooManyJacobianEvalException,
                                    ARMA.ResidualsTooLargeException,
                                    ARAutoUnivariate.TriangularMatrixSingularException,
                                    ARMAMaxLikelihood.NonStationaryException,
                                    ARMAMaxLikelihood.NonInvertibleException
```
    Returns the final estimate for the innovation variance.
    
    Returns:
    
    a double scalar value equal to the estimate for the innovation variance.
    
    Throws:
    
    ARMA.MatrixSingularException - is thrown if the input matrix is singular.
    
    ARMA.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.
    
    ARMA.IncreaseErrRelException - is thrown if the bound for the relative error is too small.
    
    ARMA.NewInitialGuessException - is thrown if the iteration has not made good progress.
    
    ARMA.IllConditionedException - is thrown if the problem is ill-conditioned.
    
    ARMA.TooManyITNException - is thrown if the maximum number of iterations is exceeded.
    
    ARMA.TooManyFcnEvalException - is thrown if the maximum number of function evaluations is exceeded.
    
    ARMA.TooManyJacobianEvalException - is thrown if the maximum number of Jacobian evaluations is exceeded.
    
    ARMA.ResidualsTooLargeException - is thrown if the residuals computed in one step of the Least Squares estimation of the ARMA coefficients become too large.
    
    ARAutoUnivariate.TriangularMatrixSingularException - is thrown if the input triangular matrix is singular.
    
    ARMAMaxLikelihood.NonStationaryException - is thrown if the final maximum likelihood estimates for the time series are non-stationary.
    
    ARMAMaxLikelihood.NonInvertibleException - is thrown if the final maximum likelihood estimates for the time series are noninvertible.
    
    ARMAMaxLikelihood.InitialMAException - is thrown if the initial values provided for the moving average terms using setMA are noninvertible. In this case, ARMAMaxLikelihood terminates and does not compute the time series estimates.
  - getMean
```
public double getMean()
               throws ARMA.MatrixSingularException,
                      ARMA.TooManyCallsException,
                      ARMA.IncreaseErrRelException,
                      ARMA.NewInitialGuessException,
                      ARMA.IllConditionedException,
                      ARMA.TooManyITNException,
                      ARMA.TooManyFcnEvalException,
                      ARMA.TooManyJacobianEvalException,
                      ARMA.ResidualsTooLargeException,
                      ARAutoUnivariate.TriangularMatrixSingularException,
                      ARMAMaxLikelihood.NonStationaryException,
                      ARMAMaxLikelihood.NonInvertibleException
```
    Returns the mean used to center the time series z.
    
    Returns:
    
    a double containing the value used to center the series before searching for the optimum number of AR lags. This is equal to the mean of the time series z unless the mean was set in the setMean method.
    
    Throws:
    
    ARMA.MatrixSingularException - is thrown if the input matrix is singular.
    
    ARMA.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.
    
    ARMA.IncreaseErrRelException - is thrown if the bound for the relative error is too small.
    
    ARMA.NewInitialGuessException - is thrown if the iteration has not made good progress.
    
    ARMA.IllConditionedException - is thrown if the problem is ill-conditioned.
    
    ARMA.TooManyITNException - is thrown if the maximum number of iterations is exceeded.
    
    ARMA.TooManyFcnEvalException - is thrown if the maximum number of function evaluations is exceeded.
    
    ARMA.TooManyJacobianEvalException - is thrown if the maximum number of Jacobian evaluations is exceeded.
    
    ARMA.ResidualsTooLargeException - is thrown if the residuals computed in one step of the Least Squares estimation of the ARMA coefficients become too large.
    
    ARAutoUnivariate.TriangularMatrixSingularException - is thrown if the input triangular matrix is singular.
    
    ARMAMaxLikelihood.NonStationaryException - is thrown if the final maximum likelihood estimates for the time series are nonstationary.
    
    ARMAMaxLikelihood.NonInvertibleException - is thrown if the final maximum likelihood estimates for the time series are noninvertible.
    
    ARMAMaxLikelihood.InitialMAException - is thrown if the initial values provided for the moving average terms using setMA are noninvertible. In this case, ARMAMaxLikelihood terminates and does not compute the time series estimates.
  - setMean
```
public void setMean(double mean)
```
    Sets the estimate of the mean used for centering the time series z.
    
    Parameters:
    
    mean - a double containing the estimate of the mean for the time series z. By default, the time series z is centered about its sample mean.
  - setConvergenceTolerance
```
public void setConvergenceTolerance(double convergenceTolerance)
```
    Sets the tolerance level used to determine convergence of the nonlinear least-squares and maximum likelihood algorithms.
    
    Parameters:
    
    convergenceTolerance - a double scalar containing the tolerance level used to determine convergence of the nonlinear least-squares and maximum likelihood algorithms. convergenceTolerance represents the minimum relative decrease in sum of squares between two iterations required to determine convergence. Hence, convergenceTolerance must be greater than or equal to 0. By default, convergenceTolerance = $10^{-10}$.
  - getConvergenceTolerance
```
public double getConvergenceTolerance()
```
    Returns the tolerance level used to determine convergence of the nonlinearleast-squares and maximum likelihood algorithms.
    
    Returns:
    
    a double scalar containing the tolerance level used to determine convergence of the nonlinear least-squares algorithm. convergenceTolerance represents the minimum relative decrease in sum of squares between two iterations required to determine convergence.
  - setMaxIterations
```
public void setMaxIterations(int iterations)
```
    Sets the maximum number of iterations used for estimating the autoregressive coefficients.
    
    Parameters:
    
    iterations - an int scalar specifying the maximum number of iterations allowed in the nonlinear equation solver used in both the method of moments and least-squares algorithms. Default: iterations = 300.
    
    Throws:
    
    IllegalArgumentException - is thrown if iterations is less than or equal to 0.
  - setConfidence
```
public void setConfidence(double confidence)
```
    Sets the confidence level for calculating confidence limit deviations returned from getDeviations.
    
    Parameters:
    
    confidence - a double scalar specifying the confidence level used in computing forecast confidence intervals. Typical choices for confidence are 0.90, 0.95, and 0.99. confidence must be greater than 0.0 and less than 1.0. Default: confidence = 0.95.
  - getMaxIterations
```
public int getMaxIterations()
```
    Returns the value currently being used as the maximum number of iterations allowed in the nonlinear equation solver used in both the method of moments and least-squares algorithms.
    
    Returns:
    
    an int containing the maximum number of iterations allowed.
  - setEstimationMethod
```
public void setEstimationMethod(int method)
```
    Sets the estimation method used for estimating the final estimates for the autoregressive coefficients.
    
    Parameters:
    
    method - an int scalar specifying the estimation method. Specify METHOD_OF_MOMENTS for the method of moments, LEAST_SQUARES for the least squares method, or MAX_LIKELIHOOD for the maximum likelihood estimates. Default: method = LEAST_SQUARES.
  - getEstimationMethod
```
public int getEstimationMethod()
```
    Returns the estimation method used for estimating the autoregressive coefficients.
    
    Returns:
    
    an int equal to 0, 1, or 2, representing the autoregressive coefficient estimation method, which implies METHOD_OF_MOMENTS, LEAST_SQUARES, or MAX_LIKELIHOOD respectively.
  - getTimsacAR
```
public double[] getTimsacAR()
                     throws ARMA.MatrixSingularException,
                            ARMA.TooManyCallsException,
                            ARMA.IncreaseErrRelException,
                            ARMA.NewInitialGuessException,
                            ARMA.IllConditionedException,
                            ARMA.TooManyITNException,
                            ARMA.TooManyFcnEvalException,
                            ARMA.TooManyJacobianEvalException,
                            ARMA.ResidualsTooLargeException,
                            ARAutoUnivariate.TriangularMatrixSingularException,
                            ARMAMaxLikelihood.NonStationaryException,
                            ARMAMaxLikelihood.NonInvertibleException
```
    Returns the final auto regressive parameter estimates at the optimum AIC estimated by the original TIMSAC routine (UNIMAR). These estimates vary depending upon the value of maxlag since its value changes the length of the series used to estimate these parameters. Use the getAR method to obtain the best estimates from the estimation method specified by setEstimationMethod calculated using the maximum number of available observations.
    
    Returns:
    
    a double array of length p containing the estimates for the autoregressive parameters.
    
    Throws:
    
    ARMA.MatrixSingularException - is thrown if the input matrix is singular.
    
    ARMA.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.
    
    ARMA.IncreaseErrRelException - is thrown if the bound for the relative error is too small.
    
    ARMA.NewInitialGuessException - is thrown if the iteration has not made good progress.
    
    ARMA.IllConditionedException - is thrown if the problem is ill-conditioned.
    
    ARMA.TooManyITNException - is thrown if the maximum number of iterations is exceeded.
    
    ARMA.TooManyFcnEvalException - is thrown if the maximum number of function evaluations is exceeded.
    
    ARMA.TooManyJacobianEvalException - is thrown if the maximum number of Jacobian evaluations is exceeded.
    
    ARMA.ResidualsTooLargeException - is thrown if the residuals computed in one step of the Least Squares estimation of the ARMA coefficients become too large.
    
    ARAutoUnivariate.TriangularMatrixSingularException - is thrown if the input triangular matrix is singular.
    
    ARMAMaxLikelihood.NonStationaryException - is thrown if the final maximum likelihood estimates for the time series are non-stationary.
    
    ARMAMaxLikelihood.NonInvertibleException - is thrown if the final maximum likelihood estimates for the time series are noninvertible.
    
    ARMAMaxLikelihood.InitialMAException - is thrown if the initial values provided for the moving average terms using setMA are noninvertible. In this case, ARMAMaxLikelihood terminates and does not compute the time series estimates.
  - getAR
```
public double[] getAR()
               throws ARMA.MatrixSingularException,
                      ARMA.TooManyCallsException,
                      ARMA.IncreaseErrRelException,
                      ARMA.NewInitialGuessException,
                      ARMA.IllConditionedException,
                      ARMA.TooManyITNException,
                      ARMA.TooManyFcnEvalException,
                      ARMA.TooManyJacobianEvalException,
                      ARMA.ResidualsTooLargeException,
                      ARAutoUnivariate.TriangularMatrixSingularException,
                      ARMAMaxLikelihood.NonStationaryException,
                      ARMAMaxLikelihood.NonInvertibleException
```
    Returns the final auto regressive parameter estimates at the optimum AIC using the estimation method specified in setEstimationMethod.
    
    Returns:
    
    a double array containing the estimates for the autoregressive parameters.
    
    Throws:
    
    ARMA.MatrixSingularException - is thrown if the input matrix is singular.
    
    ARMA.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.
    
    ARMA.IncreaseErrRelException - is thrown if the bound for the relative error is too small.
    
    ARMA.NewInitialGuessException - is thrown if the iteration has not made good progress.
    
    ARMA.IllConditionedException - is thrown if the problem is ill-conditioned.
    
    ARMA.TooManyITNException - is thrown if the maximum number of iterations is exceeded.
    
    ARMA.TooManyFcnEvalException - is thrown if the maximum number of function evaluations is exceeded.
    
    ARMA.TooManyJacobianEvalException - is thrown if the maximum number of Jacobian evaluations is exceeded.
    
    ARMA.ResidualsTooLargeException - is thrown if the residuals computed in one step of the Least Squares estimation of the ARMA coefficients become too large.
    
    ARAutoUnivariate.TriangularMatrixSingularException - is thrown if the input triangular matrix is singular.
    
    ARMAMaxLikelihood.NonStationaryException - is thrown if the final maximum likelihood estimates for the time series are nonstationary.
    
    ARMAMaxLikelihood.NonInvertibleException - is thrown if the final maximum likelihood estimates for the time series are noninvertible.
    
    ARMAMaxLikelihood.InitialMAException - is thrown if the initial values provided for the moving average terms using setMA are noninvertible. In this case, ARMAMaxLikelihood terminates and does not compute the time series estimates.
  - getResiduals
```
public double[] getResiduals()
```
    Returns the current values of the vector of residuals.
    
    Returns:
    
    a double array of length backwardOrigin containing the residuals for the last backwardOrigin values in the time series. This array will be null unless compute and either the forecast or getForecast methods are called previously.
  - getOrder
```
public int getOrder()
             throws ARMA.MatrixSingularException,
                    ARMA.TooManyCallsException,
                    ARMA.IncreaseErrRelException,
                    ARMA.NewInitialGuessException,
                    ARMA.IllConditionedException,
                    ARMA.TooManyITNException,
                    ARMA.TooManyFcnEvalException,
                    ARMA.TooManyJacobianEvalException,
                    ARMA.ResidualsTooLargeException,
                    ARAutoUnivariate.TriangularMatrixSingularException,
                    ARMAMaxLikelihood.NonStationaryException,
                    ARMAMaxLikelihood.NonInvertibleException
```
    Returns the order of the AR model selected with the minimum AIC.
    
    Returns:
    
    an int containing the optimum AR order selected by ARAutoUnivariate's minimum AIC selection.
    
    Throws:
    
    ARMA.MatrixSingularException - is thrown if the input matrix is singular.
    
    ARMA.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.
    
    ARMA.IncreaseErrRelException - is thrown if the bound for the relative error is too small.
    
    ARMA.NewInitialGuessException - is thrown if the iteration has not made good progress.
    
    ARMA.IllConditionedException - is thrown if the problem is ill-conditioned.
    
    ARMA.TooManyITNException - is thrown if the maximum number of iterations is exceeded.
    
    ARMA.TooManyFcnEvalException - is thrown if the maximum number of function evaluations is exceeded.
    
    ARMA.TooManyJacobianEvalException - is thrown if the maximum number of Jacobian evaluations is exceeded.
    
    ARMA.ResidualsTooLargeException - is thrown if the residuals computed in one step of the Least Squares estimation of the ARMA coefficients become too large.
    
    ARAutoUnivariate.TriangularMatrixSingularException - is thrown if the input triangular matrix is singular.
    
    ARMAMaxLikelihood.NonStationaryException - is thrown if the final maximum likelihood estimates for the time series are non-stationary.
    
    ARMAMaxLikelihood.NonInvertibleException - is thrown if the final maximum likelihood estimates for the time series are noninvertible.
    
    ARMAMaxLikelihood.InitialMAException - is thrown if the initial values provided for the moving average terms using setMA are noninvertible. In this case, ARMAMaxLikelihood terminates and does not compute the time series estimates.
  - getMaxlag
```
public int getMaxlag()
```
    Returns the current value used to represent the maximum number of autoregressive lags to achieve the minimum AIC.
    
    Returns:
    
    an int containing the maximum number of autoregressive lags evaluated.
  - getLogger
```
public Logger getLogger()
```
    Returns the logger object.
    
    Returns:
    
    the logger object, if present, or null.

Class ARAutoUnivariate

Nested Class Summary

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

METHOD_OF_MOMENTS

LEAST_SQUARES

MAX_LIKELIHOOD

Constructor Detail

ARAutoUnivariate

Method Detail

compute

getAIC

getConfidence

getBackwardOrigin

getTimsacConstant

getConstant

getTimeSeries

setBackwardOrigin

forecast

getForecast

getDeviations

getLikelihood

getTimsacVariance

getInnovationVariance

getMean

setMean

setConvergenceTolerance

getConvergenceTolerance

setMaxIterations

setConfidence

getMaxIterations

setEstimationMethod

getEstimationMethod

getTimsacAR

getAR

getResiduals

getOrder

getMaxlag

getLogger