StatTimeSerAnalysis.Innovations Method

Overload List

#	Signature	Description
1	void Innovations(TDenseMtxVec kappa, TVec Theta, ref Double Sigma2, Int32 NumEvals, TVec ThetaVar, TVec SumSqr)	The innovations algorithm.
2	void Innovations(TDenseMtxVec kappa, Int32 q, TMtx ThetaMtx, TVec Variances, Int32 NumEvals)	Uses the Innnovations algorithm to recursively calculate Theta[1,1]...Theta[n,n] coefficients (all coefficients).

The innovations algorithm.

#	Name	Description
1	kappa	Defines covariances for innovations algorithm.
2	Theta	Returns Theta[n,1]...Theta[n,n] coefficients.
3	Sigma2	Returns variance.
4	NumEvals	Defines number of iterations of the innovation algorithm.
5	ThetaVar	If not nil, returns theta[n,1]..Theta[n,n] variances.
6	SumSqr	If not nil, returns sum of squares for each theta[n,i] element.

Result: stored in self (calling object)

Remarks:

Uses the Innnovations algorithm to recursively calculate Theta[n,1]...Theta[n,n] coefficients.

See Also: StatTimeSerAnalysis.DurbinLevinson

Uses the Innnovations algorithm to recursively calculate Theta[1,1]...Theta[n,n] coefficients (all coefficients).

#	Name	Type	Description
1	kappa	TDenseMtxVec	source TVec or TMtx
2	q	Int32
3	ThetaMtx	TMtx	source TMtx
4	Variances	TVec	source TVec
5	NumEvals	Int32

Result: stored in self (calling object)

Remarks:

The recursion relations are defined by the following equations:

\begin{aligned} v_0 &= \kappa (1,1) \\ \theta_{n,n-k}&= v_k ^{-1} \left( \kappa (n+1,k+1) - \sum _{j=0} ^{k-1} \theta_{k,k-j}\theta_{n,n-j}v_j \right) \quad , \quad 0\leq k < n \\ v_n &= \kappa(n+1,n+1) - \sum _{j=0} ^{n-1} \theta_{n,n-j} ^2 v_j \quad . \end{aligned}

where kappa(i,j) are covariances. Use this overloaded variant only when you need all theta[1,1]..theta[n,n] values, otherwise use vector version.