StatTimeSerAnalysis.ARMAKappa Method

StatTimeSerAnalysis

Overload List

#SignatureDescription
1procedure ARMAKappa(const Data: TVec; const Phi: TVec; const Theta: TVec; const cov: TMtx; const KappaSize: Integer);Calculate necessary covariances for ARMA(p,q) process up to kappa(KappaSize,KappaSize)
2function ARMAKappa(const gamma: TVec; const maacvf: TVec; const i: Integer; const j: Integer; const Phi: TVec; const Theta: TVec): Double;ARMA process covariances.

Overload 1: procedure ARMAKappa(const Data: TVec; const Phi: TVec; const Theta: TVec; const cov: TMtx; const KappaSize: Integer);

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

#NameTypeDescription
1DataTVec
2PhiTVec
3ThetaTVec
4covTMtx
5KappaSizeInteger

Result: stored in self (calling object)

Overload 2: function ARMAKappa(const gamma: TVec; const maacvf: TVec; const i: Integer; const j: Integer; const Phi: TVec; const Theta: TVec): Double;

ARMA process covariances.

#NameDescription
1gammaTime series ACVF.
2maacvfThe ACVF of a MA part of the model.
3PhiStores Phi values for ARMA process.
4ThetaStores Theta values for ARMA process.
5i
6j

Returns: Double

Remarks:

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

κ(i,j)={σ−2γx(i−j),1≤i,j≤mσ−2[γx(i−j)−∑r=1pϕrγx(r−∣i−j∣)],min⁡(i,j)≤m<max⁡(i,j)≤2m∑r=0qθrθr−∣i−j∣,min⁡(i,j)>m0,otherwise\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