com.numericalmethod.suanshu.stats.timeseries.linear.univariate.stationaryprocess.arma
Class ConditionalSumOfSquares

java.lang.Object
  com.numericalmethod.suanshu.stats.timeseries.linear.univariate.stationaryprocess.arma.ConditionalSumOfSquares

All Implemented Interfaces:

ARMAFitting

public class ConditionalSumOfSquares
extends java.lang.Object
implements ARMAFitting

The method Conditional Sum of Squares (CSS) fits an ARIMA model by minimizing the conditional sum of squares. The CSS estimates are conditional on the assumption that the past unobserved errors are 0s. The estimation produced by CSS can be used as a starting point for a better algorithm, e.g., the maximum likelihood.

Note that the order of integration is taken as an input, not estimated.

The R equivalent function is arima.

See Also:

"P. J. Brockwell and R. A. Davis, "Chapter 8.7, Model Building and Forecasting with ARIMA Processes," Time Series: Theory and Methods, Springer, 2006."

Constructor Summary

ConditionalSumOfSquares(double[] x, int p, int d, int q)
Fit an ARIMA model for the observations using CSS.

ConditionalSumOfSquares(double[] x, int p, int d, int q, double epsilon)
Fit an ARIMA model for the observations using CSS.

Method Summary

double	AIC() Compute the AIC, a model selection criterion.
double	AICC() Compute the AICC, a model selection criterion.
Matrix	covariance() Get the asymptotic covariance matrix of the estimated parameters, φ and θ.
ARMAModel	getARMAModel() Get the fitted ARMA model.
ARIMAModel	getModel() Get the fitted ARMA model.
int	nParams() Get the number of parameters for the estimation/fitting.
ImmutableVector	stderr() Get the asymptotic standard errors of the estimated parameters, φ and θ.
java.lang.String	toString()
double	var() Get the variance of the white noise.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

ConditionalSumOfSquares

public ConditionalSumOfSquares(double[] x,
                               int p,
                               int d,
                               int q,
                               double epsilon)

Fit an ARIMA model for the observations using CSS. Note that the algorithm fits only an ARMA model. d is taken as an input. If the differenced input time series is not zero-mean, it is first de-mean-ed before running the algorithm as in Brockwell and Davis. When reporting the model, we compute the intercept to match the mean.

Parameters:

x - the time series of observations

p - the number of AR terms

d - the order of integration

q - the number of MA terms

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

ConditionalSumOfSquares

public ConditionalSumOfSquares(double[] x,
                               int p,
                               int d,
                               int q)

Fit an ARIMA model for the observations using CSS. Note that the algorithm fits only an ARMA model. d is taken as an input. If the differenced input time series is not zero-mean, it is first de-mean-ed before running the algorithm as in Brockwell and Davis. When reporting the model, we compute the intercept to match the mean.

Parameters:

x - the time series of observations

p - the number of AR terms

d - the order of integration

q - the number of MA terms

Method Detail

nParams

public int nParams()

Get the number of parameters for the estimation/fitting. They are the AR terms, MA terms, and variance (sigma^2).

Returns:

the number of parameters

getModel

public ARIMAModel getModel()

Description copied from interface: ARMAFitting

Get the fitted ARMA model.

Specified by:

getModel in interface ARMAFitting

Returns:

the fitted ARMA model

getARMAModel

public ARMAModel getARMAModel()

Get the fitted ARMA model.

Returns:

the fitted ARMA model

var

public double var()

Description copied from interface: ARMAFitting

Get the variance of the white noise.

Specified by:

var in interface ARMAFitting

Returns:

σ²

covariance

public Matrix covariance()

Get the asymptotic covariance matrix of the estimated parameters, φ and θ. The estimators are asymptotically normal.

Specified by:

covariance in interface ARMAFitting

Returns:

the asymptotic covariance matrix

See Also:

"P. J. Brockwell and R. A. Davis, "Eq. 10.8.27, Thm. 10.8.2, Chapter 10.8, Model Building and Forecasting with ARIMA Processes," Time Series: Theory and Methods, Springer, 2006."

stderr

public ImmutableVector stderr()

Get the asymptotic standard errors of the estimated parameters, φ and θ. The estimators are asymptotically normal.

Specified by:

stderr in interface ARMAFitting

Returns:

the asymptotic errors

See Also:

"P. J. Brockwell and R. A. Davis, "Eq. 10.8.27, Thm. 10.8.2, Chapter 10.8, Model Building and Forecasting with ARIMA Processes," Time Series: Theory and Methods, Springer, 2006."

AIC

public double AIC()

Compute the AIC, a model selection criterion.

Specified by:

AIC in interface ARMAFitting

Returns:

the AIC

See Also:

Wikipedia: Akaike information criterion

AICC

public double AICC()

Compute the AICC, a model selection criterion.

Specified by:

AICC in interface ARMAFitting

Returns:

the AICC

See Also:

"P. J. Brockwell and R. A. Davis, "Eq. 9.2.1, Chapter 9.2, Model Building and Forecasting with ARIMA Processes," Time Series: Theory and Methods, Springer, 2006."

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object