public void TimeSeriesFitAR1()
{
double alpha = 0.3;
double mu = 0.2;
double sigma = 0.4;
int n = 24;
// For our fit to AR(1), we have incorporated bias correction (at least
// for the most important parameter alpha), so we can do a small-n test.
FrameTable data = new FrameTable();
data.AddColumn <UncertainValue>("mu");
data.AddColumn <UncertainValue>("alpha");
data.AddColumn <UncertainValue>("sigma");
data.AddColumn <SymmetricMatrix>("covariance");
data.AddColumn <double>("p");
for (int i = 0; i < 128; i++)
{
TimeSeries series = GenerateAR1TimeSeries(alpha, mu, sigma, n, n * i + 271828);
AR1FitResult result = series.FitToAR1();
data.AddRow(
result.Mu, result.Alpha, result.Sigma,
result.Parameters.CovarianceMatrix, result.GoodnessOfFit.Probability
);
}
data.AddComputedColumn("alphaValue", r => ((UncertainValue)r["alpha"]).Value);
data.AddComputedColumn("muValue", r => ((UncertainValue)r["mu"]).Value);
// Check that fit parameters agree with inputs
Assert.IsTrue(data["mu"].As((UncertainValue v) => v.Value).PopulationMean().ConfidenceInterval(0.99).ClosedContains(mu));
Assert.IsTrue(data["alpha"].As((UncertainValue v) => v.Value).PopulationMean().ConfidenceInterval(0.99).ClosedContains(alpha));
Assert.IsTrue(data["sigma"].As((UncertainValue v) => v.Value).PopulationMean().ConfidenceInterval(0.99).ClosedContains(sigma));
// Check that reported variances agree with actual variances
Assert.IsTrue(data["mu"].As((UncertainValue v) => v.Value).PopulationStandardDeviation().ConfidenceInterval(0.99).ClosedContains(data["mu"].As((UncertainValue v) => v.Uncertainty).Median()));
Assert.IsTrue(data["alpha"].As((UncertainValue v) => v.Value).PopulationStandardDeviation().ConfidenceInterval(0.99).ClosedContains(data["alpha"].As((UncertainValue v) => v.Uncertainty).Median()));
Assert.IsTrue(data["sigma"].As((UncertainValue v) => v.Value).PopulationStandardDeviation().ConfidenceInterval(0.99).ClosedContains(data["sigma"].As((UncertainValue v) => v.Uncertainty).Median()));
// Check that reported co-variances agree with actual co-variances
Assert.IsTrue(data["mu"].As((UncertainValue v) => v.Value).PopulationCovariance(data["alpha"].As((UncertainValue v) => v.Value)).ConfidenceInterval(0.99).ClosedContains(data["covariance"].As((SymmetricMatrix c) => c[0, 1]).Median()));
// For small n, the fitted alpha can vary considerably, and the formula for var(m) varies
// quite strongly with alpha, so the computed var(m) have a very long tail. This pushes the
// mean computed var(m) quite a bit higher than a typical value, so we use medians instead
// of means for our best guess for the predicted variance.
TestResult ks = data["p"].As <double>().KolmogorovSmirnovTest(new UniformDistribution());
Assert.IsTrue(ks.Probability > 0.05);
// This is an onerous way to store values, but it does let us test how the data-frame machinery deals with
// non-trivial storage types.
}
public void TimeSeriesBadFit()
{
// Fit AR1 to MA1; the fit should be bad
TimeSeries series = GenerateMA1TimeSeries(0.4, 0.3, 0.2, 1000);
AR1FitResult result = series.FitToAR1();
Assert.IsTrue(result.GoodnessOfFit.Probability < 0.01);
}
public void TimeSeriesFitAR1()
{
double alpha = 0.3;
double mu = 0.2;
double sigma = 0.4;
int n = 20;
// For our fit to AR(1), we have incorporated bias correction (at least
// for the most important parameter alpha), so we can do a small-n test.
MultivariateSample parameters = new MultivariateSample(3);
MultivariateSample covariances = new MultivariateSample(6);
Sample tests = new Sample();
for (int i = 0; i < 100; i++)
{
TimeSeries series = GenerateAR1TimeSeries(alpha, mu, sigma, n, i + 314159);
FitResult result = series.FitToAR1();
parameters.Add(result.Parameters);
covariances.Add(
result.CovarianceMatrix[0, 0],
result.CovarianceMatrix[1, 1],
result.CovarianceMatrix[2, 2],
result.CovarianceMatrix[0, 1],
result.CovarianceMatrix[0, 2],
result.CovarianceMatrix[1, 2]
);
tests.Add(result.GoodnessOfFit.Probability);
}
// Check that fit parameters agree with inputs
Assert.IsTrue(parameters.Column(0).PopulationMean.ConfidenceInterval(0.99).ClosedContains(alpha));
Assert.IsTrue(parameters.Column(1).PopulationMean.ConfidenceInterval(0.99).ClosedContains(mu));
Assert.IsTrue(parameters.Column(2).PopulationMean.ConfidenceInterval(0.99).ClosedContains(sigma));
// Check that reported variances agree with actual variances
Assert.IsTrue(parameters.Column(0).PopulationVariance.ConfidenceInterval(0.99).ClosedContains(covariances.Column(0).Median));
Assert.IsTrue(parameters.Column(1).PopulationVariance.ConfidenceInterval(0.99).ClosedContains(covariances.Column(1).Median));
Assert.IsTrue(parameters.Column(2).PopulationVariance.ConfidenceInterval(0.99).ClosedContains(covariances.Column(2).Median));
Assert.IsTrue(parameters.TwoColumns(0, 1).PopulationCovariance.ConfidenceInterval(0.99).ClosedContains(covariances.Column(3).Mean));
Assert.IsTrue(parameters.TwoColumns(0, 2).PopulationCovariance.ConfidenceInterval(0.99).ClosedContains(covariances.Column(4).Mean));
Assert.IsTrue(parameters.TwoColumns(1, 2).PopulationCovariance.ConfidenceInterval(0.99).ClosedContains(covariances.Column(5).Mean));
// For small n, the fitted alpha can vary considerably, and the formula for var(m) varies
// quite strongly with alpha, so the computed var(m) have a very long tail. This pushes the
// mean computed var(m) quite a bit higher than a typical value, so we use medians instead
// of means for our best guess for the predicted variance.
TestResult ks = tests.KolmogorovSmirnovTest(new UniformDistribution());
Assert.IsTrue(ks.Probability > 0.05);
}
