StatTimeSerAnalysis.ARARFit Method

procedure ARARFit(const S: TVec; const Phi: TVec; out l1: Integer; out l2: Integer; out l3: Integer; out Sigma2: Double; const MaxLag: Integer);

Fit ARAR algorithm.

#	Name	Description
1	S	Memory-shortened time series. If no memory-shortening was performed, then S defines the original unshortened time series.
2	Phi	Returns ARAR model phi coefficients (phi[1],phi[l1],phi[l2],phi[l3]). Size of Phi vector is adjusted automatically (4).
3	l1	Returns ARAR model phil1 lag.
4	l2	Returns ARAR model phil2 lag.
5	l3	Returns ARAR model phil3 lag.
6	Sigma2	Returns ARAR model estimated WN variance.
7	MaxLag	Defines upper limit for l3, where 1 < l1 < l2 < l3 <= MaxLag.

Result: stored in self (calling object)

Remarks:

Fit ARAR algorithm to (optionaly) memory-shortened series. Let S[t] denote memory-shortened series, derived from Y[t] and let avg(S) denote sample mean of S[t]. The ARAR algorithm tries to fit an autoregressive (AR) process to the mean-corrected series:

X[t] =S[t]-\langle S \rangle

The fitted model then has the form:

X[t] =\phi _1 X[t-1] + \phi _{l1} X[t-l1] + \phi _{l2} X[t-l2] + \phi _{l3} X[t-l3] + Z[t]

where Z[t] is WN(0,sigma2).

Examples

Uses MtxExpr, StatTimeSerAnalysis, Math387;
procedure Example;
var timeseries,s,filter,phi: Vector;
forecasts,stderrs: Vector;
l1,l2,l3,tau: Integer;
s2,rmse: double;
begin
    timeseries.LoadFromFile('deaths.vec');
    // #1: shorten series
    ShortenFilter(timeSeries,s,tau,Filter);
    // #2 : fit ARAR model on shortened series
    ARARFit(s,Phi,l1,l2,l3,s2,13);
    // #3: forecast 100 values by using ARAR fit parameters
    ARARForecast(timeseries,Phi,Filter,tau,l1,l2,l3,s.mean,100,forecasts,stderrs,rmse);
end;