ARARForecast Routine

Summary

Forecast time series by ARAR.

Declaration

Procedure ARARForecast(Data: TVec; Phi, Filter: TVec; tau, l1, l2, l3: Integer; SMean: TSample; n: Integer; Result, StdErrs: TVec; out RMSE: TSample);

Parameter	Description
Data	Defines original time series.
Phi	Defines ARAR model Phi coefficients (phi[0],phi[1],phi[2],phi[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]).
tau	Defines memory-shortening optimal lag, obtained from memory-shortening operation. In case no memory-shortening is performed, set it to 1.
l1	Defines optimal lag for phi[l1] (see equation above).
l2	Defines optimal lag for phi[l2] (see equation above).
l3	Defines optimal lag for phi[l3] (see equation above).
SMean	Defines memory-shortened series mean.
n	Defines number of forecasts.
Result	Returns forecasts. Size and complex properties of Result are adjusted automatically.
StdErrs	Returns forecasts standard errors. Size and complex properties of StdErrs are adjusted automatically.
MSE	Returns fit root mean square error (RMSE).

Description

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

See Also
ARARFit
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);
    }
  }