StatTimeSerAnalysis.ARARFit Method

void ARARFit(TVec S, TVec Phi, ref Int32 l1, ref Int32 l2, ref Int32 l3, ref Double Sigma2, Int32 MaxLag)

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

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, s22;
        double s2, rmse;
        timeseries.LoadFromFile("deaths.vec");
        // #1: shorten series
        StatTimeSerAnalysis.ShortenFilter(timeseries, s, out tau, filter, 15);
        // #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(), 100, forecasts, stderrs, out rmse);
    }
}