StatTimeSerAnalysis.ARMAKappa Method

Overload List

#	Signature	Description
1	void ARMAKappa(TVec Data, TVec Phi, TVec Theta, TMtx cov, Int32 KappaSize)	Calculate necessary covariances for ARMA(p,q) process up to kappa(KappaSize,KappaSize)
2	Double ARMAKappa(TVec gamma, TVec maacvf, Int32 i, Int32 j, TVec Phi, TVec Theta)	ARMA process covariances.

Calculate necessary covariances for ARMA(p,q) process up to kappa(KappaSize,KappaSize)

#	Name	Type	Description
1	Data	TVec	source TVec
2	Phi	TVec	source TVec
3	Theta	TVec	source TVec
4	cov	TMtx	source TMtx
5	KappaSize	Int32

Result: stored in self (calling object)

ARMA process covariances.

#	Name	Description
1	gamma	Time series ACVF.
2	maacvf	The ACVF of a MA part of the model.
3	Phi	Stores Phi values for ARMA process.
4	Theta	Stores Theta values for ARMA process.
5	i
6	j

Returns: Double

Remarks:

Calculates ARMA (p,q) process covariances. For ARMA process, covariances are defined as:

\kappa (i,j) = \begin{cases} \sigma^{-2} \gamma_x (i-j) \quad , & 1\leq i, j\leq m \\ \sigma^{-2} \left[ \gamma_x(i-j)-\sum_{r=1}^{p} \phi_r \gamma_x(r-|i-j|)\right]\quad , & \min (i,j) \leq m < \max (i,j) \leq 2m \\ \sum_{r=0} ^q \theta_r \theta_{r-|i-j|} \quad , & \min (i,j) > m \\ 0 \quad , & \text{otherwise} \end{cases}

where gamma is time series autocovariance function, sigma^2 is estimated white noise, m=max(p,q) and phi, theta are AR and MA coefficients.

See Also: StatTimeSerAnalysis.ARMAAcf