StatTimeSerAnalysis.ARARForecast Method

procedure ARARForecast(const Data: TVec; const Phi: TVec; const Filter: TVec; const tau: Integer; const l1: Integer; const l2: Integer; const l3: Integer; const SMean: Double; const N: Integer; const aResult: TVec; const StdErrs: TVec; out RMSE: Double);

Forecast time series by ARAR.

#	Name	Description
1	Data	Defines original time series.
2	Phi	Defines ARAR model Phi coefficients (phi[0],phi[1],phi[2],phi[3]).
3	Filter	Defines memory shortening filter, obtained from memory-shortening operation. In case no memory-shortening is performed, set filter to 1.0 by using Filter.SetIt([1.0]).
4	tau	Defines memory-shortening optimal lag, obtained from memory-shortening operation. In case no memory-shortening is performed, set it to 1.
5	l1	Defines optimal lag for phi[l1] (see equation above).
6	l2	Defines optimal lag for phi[l2] (see equation above).
7	l3	Defines optimal lag for phi[l3] (see equation above).
8	SMean	Defines memory-shortened series mean.
9	N	Defines number of forecasts.
10	aResult	Returns forecasts. Size and complex properties of Result are adjusted automatically.
11	StdErrs	Returns forecasts standard errors. Size and complex properties of StdErrs are adjusted automatically.
12	RMSE	Returns fit root mean square error (RMSE).

Result: stored in self (calling object)

Remarks:

Forecast time series values by using ARAR model, defined by the following relation:

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

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;