Class MultivariateForecastOneStep
- java.lang.Object
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- dev.nm.stat.timeseries.linear.multivariate.stationaryprocess.MultivariateForecastOneStep
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public class MultivariateForecastOneStep extends Object
The innovation algorithm is an efficient way to obtain a one step least square linear predictor for a multivariate linear time series with known auto-covariance and these properties (not limited to ARMA processes):- {xt} can be non-stationary.
- E(xt) = 0 for all t.
- See Also:
- "P. J. Brockwell and R. A. Davis, "Proposition. 5.2.2. Chapter 5. Prediction of Stationary Processes," in Time Series: Theory and Methods, Springer, 2006."
- "P. J. Brockwell and R. A. Davis, "Proposition. 11.4.2. Chapter 11.4 Best Linear Predictors of Second Order Random Vectors," in Time Series: Theory and Methods, Springer, 2006."
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Constructor Summary
Constructors Constructor Description MultivariateForecastOneStep(MultivariateIntTimeTimeSeries Xt, MultivariateAutoCovarianceFunction K)Construct an instance of InnovationAlgorithm for a multivariate time series with known auto-covariance structure.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description ImmutableMatrixcovariance(int n)Get the covariance matrix for prediction errors for \(\hat{x}_{n+1}\), made at time n.ImmutableMatrixtheta(int i, int j)Get the coefficients of the linear predictor.ImmutableVectorxHat(int n)Get the one-step prediction \(\hat{X}_{n+1} = P_{\mathfrak{S_n}}X_{n+1}\), made at time n.
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Constructor Detail
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MultivariateForecastOneStep
public MultivariateForecastOneStep(MultivariateIntTimeTimeSeries Xt, MultivariateAutoCovarianceFunction K)
Construct an instance of InnovationAlgorithm for a multivariate time series with known auto-covariance structure.- Parameters:
Xt- an m-dimensional time series, length tK- auto-covariance function K(i, j) = E(Xi * Xj'), a m x m matrix
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Method Detail
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xHat
public ImmutableVector xHat(int n)
Get the one-step prediction \(\hat{X}_{n+1} = P_{\mathfrak{S_n}}X_{n+1}\), made at time n.- Parameters:
n- time, ranging from 0 to T, the end of observation time- Returns:
- the one-step prediction \(\hat{X}_{n+1}\)
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theta
public ImmutableMatrix theta(int i, int j)
Get the coefficients of the linear predictor.- Parameters:
i-i, ranging from 1 to tj-j, ranging from 1 to t- Returns:
- Θ[i][j]
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covariance
public ImmutableMatrix covariance(int n)
Get the covariance matrix for prediction errors for \(\hat{x}_{n+1}\), made at time n.- Parameters:
n- time, ranging from 0 to T, the end of observation time- Returns:
- the covariance matrix for prediction errors at time n
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