StatTimeSerAnalysis::ARMAKappa Function

StatTimeSerAnalysis Namespace

Overload List

#SignatureDescription
1double ARMAKappa(TVec *gamma, TVec *maacvf, const int i, const int j, TVec *Phi, TVec *Theta);ARMA process covariances.
2void ARMAKappa(TVec *Data, TVec *Phi, TVec *Theta, TMtx *cov, const int KappaSize);Calculate necessary covariances for ARMA(p,q) process up to kappa(KappaSize,KappaSize)

Overload 1: double ARMAKappa(TVec *gamma, TVec *maacvf, const int i, const int j, TVec *Phi, TVec *Theta);

ARMA process covariances.

#NameTypeDescription
1gammaTVec *Time series ACVF.
2maacvfTVec *The ACVF of a MA part of the model.
3iconst int
4jconst int
5PhiTVec *Stores Phi values for ARMA process.
6ThetaTVec *Stores Theta values for ARMA process.
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
Declared in Dew::Stats::Units::StatTimeSerAnalysis · Dew.Stats/Units.StatTimeSerAnalysis.h · Cross-compiler

Overload 2: void ARMAKappa(TVec *Data, TVec *Phi, TVec *Theta, TMtx *cov, const int KappaSize);

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

#NameTypeDescription
1DataTVec *
2PhiTVec *
3ThetaTVec *
4covTMtx *
5KappaSizeconst int
Declared in Dew::Stats::Units::StatTimeSerAnalysis · Dew.Stats/Units.StatTimeSerAnalysis.h · Cross-compiler