///<summary>
/// This function computes predictive means (one-step, two-step, ...)
/// along with the predictive mean-squared error. It
/// assumes that data is regularly spaced in time.
///</summary>
///<param name="startData">existing data that we assume comes from the model</param>
///<param name="futureTimes">times in the future</param>
///<returns></returns>
private TimeSeriesBase <DistributionSummary> GetForecasts(TimeSeries startData, IList <DateTime> futureTimes)
{
// now do forecasting, using the standard Durbin-Levison Algorithm
int nobs = startData.Count;
int horizon = futureTimes.Count;
// Numerically stable approach: use innovations algorithm if possible
double[] nus;
double[] forecs;
ComputeSpecialResiduals(startData, out nus, horizon, out forecs);
//// now compute MSEs of 1...horizon step predictors
//// compute psis in causal expansion,
//// by phi(B) (1-B)^d psi(B) = theta(B) and match coefficients
// Vector psis = ComputePsiCoefficients(horizon);
var psis = Vector <double> .Build.Dense(horizon + 1);
// Use approximation (B&D eqn (5.3.24)) as before to get predictive variances
var localFmse = Vector <double> .Build.Dense(horizon);
localFmse[0] = 1.0;
for (int i = 1; i < horizon; ++i)
{
localFmse[i] = localFmse[i - 1] + psis[i] * psis[i];
}
localFmse = localFmse * Sigma * Sigma;
var predictors = new TimeSeriesBase <DistributionSummary>();
for (int i = 0; i < horizon; ++i)
{
var dn = new DistributionSummary();
dn.Mean = forecs[i];
dn.Variance = localFmse[i];
// dn.FillGaussianQuantiles(0.04);
predictors.Add(futureTimes[i], dn, false);
}
return(predictors);
}
public override object BuildForecasts(object otherData, object inputs)
{
var futureTimes = inputs as List <DateTime>;
if (futureTimes == null)
{
return(null); // need future times to forecast
}
var startData = otherData as TimeSeries;
if (startData == null)
{
return(null); // need data to forecast
}
// Now we can forecast:
// for ARMA models, we don't do any kind of analysis of the future times, we just
// assume they are the next discrete time points in a typical ARMA model with
// times t=1,2,3,...,n. So all we care about is the number of inputs.
TimeSeriesBase <DistributionSummary> preds = GetForecasts(startData, futureTimes);
return(preds);
}