StatTimeSerAnalysis.Innovations Method

Overload List

#	Signature	Description
1	procedure Innovations(const kappa: TDenseMtxVec; const Theta: TVec; out Sigma2: Double; const NumEvals: Integer; const ThetaVar: TVec; const SumSqr: TVec);	The innovations algorithm.
2	procedure Innovations(const kappa: TDenseMtxVec; const q: Integer; const ThetaMtx: TMtx; const Variances: TVec; const NumEvals: Integer);	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
1	kappa	TDenseMtxVec
2	q	Integer
3	ThetaMtx	TMtx
4	Variances	TVec
5	NumEvals	Integer

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.