ARARFit Routine

Summary

Fit ARAR algorithm.

Declaration

Procedure ARARFit(S: TVec; Phi: TVec; out l1, l2, l3: Integer; out Sigma2: TSample; MaxLag: Integer);

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

Description

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:

The fitted model then has the form:

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

See Also
ARARForecast
ShortenFilter

Example 1

Fit and then forecast time series values by using ARAR algorithm. Before applying the ARAR algorithm, use the shortening filter on original series.

  Uses MtxExpr, StatTimeSerAnalysis, Math387;
  procedure Example;
  var timeseries,s,filter,phi: Vector;
    forecasts,stderrs: Vector;
    l1,l2,l3,tau: Integer;
    s2,rmse: TSample;
   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;

  #include "MtxVecCpp.h"
  #include "StatTimeSerAnalysis.hpp"
  void __fastcall Example();
  {
    Vector timeseries,s,filter,phi,forecasts,stderrs;
    int l1,l2,l3,tau;
    double s2;
    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(),s2,100,forecasts,stderrs,rmse);
  }

  using Dew.Math;
  using Dew.Stats;
  using Dew.Stats.Units;
  namespace Dew.Examples
  {
    private void Example()
    {
      Vector timeseries = new Vector(0);
      Vector s = new Vector(0);
      Vector filter = new Vector(0);
      Vector phi = new Vector(0);
      Vector forecasts = new Vector(0);
      Vector stderrs = new Vector(0);
      int l1,l2,l3,tau;
      double s2, rmse;
      timeseries.LoadFromFile("deaths.vec");
      // #1: shorten series
      StatTimeSerAnalysis.ShortenFilter(timeSeries,s,tau,Filter);
      // #2 : fit ARAR model on shortened series
      StatTimeSerAnalysis.ARARFit(s,Phi,out l1,out l2,out l3,out s2,13);
      // #3: forecast 100 values by using ARAR fit parameters
      StatTimeSerAnalysis.ARARForecast(timeseries,Phi,Filter,tau,l1,l2,l3,s.Mean(),s2,100,forecasts,stderrs,out rmse);
    }
  }