com.numericalmethod.suanshu.stats.timeseries.linear.univariate.stationaryprocess

Class InnovationAlgorithm

java.lang.Object

com.numericalmethod.suanshu.stats.timeseries.linear.univariate.stationaryprocess.InnovationAlgorithm

All Implemented Interfaces:

java.io.Serializable

public class InnovationAlgorithm
extends java.lang.Object
implements java.io.Serializable

The innovation algorithm is an efficient way of obtaining a one step least square linear predictor for a linear time series {X_t} with known auto-covariance.

• {X_t} can be non-stationary.
• E{X_t} = 0 for all t.

See Also:

"P. J. Brockwell and R. A. Davis, "Proposition. 5.2.2. Chapter 5. Multivariate Time Series," in Time Series: Theory and Methods, Springer, 2006.", Serialized Form

Constructor Summary

Constructors

Constructor and Description
InnovationAlgorithm(TimeSeries Xt, AutoCovarianceFunction K) Construct an instance of InnovationAlgorithm for a univariate time series with known auto-covariance structure.

Method Summary

Modifier and Type	Method and Description
double	var(int t) Get the mean squared error for prediction errors at time t for X^t+1, i.e., E(X_(t+1) - X^_(t+1))
TimeSeries	XtHat() Get all the one-step predictions X^t+1, t ∈ [0, t]
double	XtHat(int t) Get the one-step prediction X^t+1.

Methods inherited from class java.lang.Object

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

Constructor Detail

InnovationAlgorithm

public InnovationAlgorithm(TimeSeries Xt,
                           AutoCovarianceFunction K)

Construct an instance of InnovationAlgorithm for a univariate time series with known auto-covariance structure.

Parameters:

Xt - an univariate time series, length t

K - the auto-covariance function

Method Detail

XtHat

public double XtHat(int t)

Get the one-step prediction X^_t+1.

Parameters:

t - time, ranging from 0 to t

Returns:

the one-step prediction X^_t+1

XtHat

public TimeSeries XtHat()

Get all the one-step predictions X^_t+1, t ∈ [0, t]

Returns:

all the one-step predictions

var

public double var(int t)

Get the mean squared error for prediction errors at time t for X^_t+1, i.e., E(X_(t+1) - X^_(t+1))

Parameters:

t - time, ranging from 0 to t

Returns:

the mean squared error (variance)