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, java.io.Serializable

public class ConditionalSumOfSquares
extends java.lang.Object
implements ARMAFitting

This class does fitting for an ARIMA model by minimizing the conditional sum of squares (CSS). The CSS estimates are conditional on the assumption that the past unobserved errors are 0s.

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

The values produced here can be used as a starting point for the maximum likelihood algorithm.

The R equivalent functions is arima.

See Also:

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

Constructor Summary

Constructors

Constructor and Description
ConditionalSumOfSquares(TimeSeries xt, int p, int d, int q) Fit an ARIMA model for the observations.

Method Summary

Modifier and Type	Method and Description
double	AIC() Compute the AIC, a model selection criterion.
double	AICC() Compute the AICC, a model selection criterion.
Matrix	covariance() Compute the asymptotic covariance matrix for the estimated parameters, φ and θ.
ARMAModel	getFittedARMA() Get the ARMA coefficients, φ.
int	nParams() Compute the number of parameters for the estimation/fitting.
ImmutableVector	stderr() Compute the asymptotic standard errors for 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(TimeSeries xt,
                               int p,
                               int d,
                               int q)

Fit an ARIMA model for the observations.

If the differenced input time series is not zero-mean, we first de-mean it before running the algorithm as in Brockwell and Davis. When we output the model, we will compute the intercept to match the mean.

We only fit an ARMA model. d is supplied as an argument.

Parameters:

xt - the time series of observations

p - the number of AR terms

d - the order of integration

q - the number of MA terms

Method Detail

getFittedARMA

public ARMAModel getFittedARMA()

Description copied from interface: ARMAFitting

Get the ARMA coefficients, φ.

Specified by:

getFittedARMA in interface ARMAFitting

Returns:

φ and θ

var

public double var()

Description copied from interface: ARMAFitting

Get the variance of the white noise.

Specified by:

var in interface ARMAFitting

Returns:

σ^2

covariance

public Matrix covariance()

Compute the asymptotic covariance matrix for 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," in Time Series: Theory and Methods, Springer, 2006."

stderr

public ImmutableVector stderr()

Compute the asymptotic standard errors for 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," in Time Series: Theory and Methods, Springer, 2006."

nParams

public int nParams()

Compute the number of parameters for the estimation/fitting.

the AR terms, MA terms, and variance (sigma^2)

Returns:

the number of parameters

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," in Time Series: Theory and Methods, Springer, 2006."

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object