WOLFRAM

Wolfram Language & System Documentation Center

Analyze Time Series Model Residuals

Fit a MAProcess[3] to the data:
Wolfram Language code: data = TemporalData[Automatic, {{{0.359431952050076, 0.1866539833635727, -0.36641699166840047, -0.9169379467434212, -0.4466564157696784, 0.48031513860278385, -0.2340607103049802, -0.2730210796929566, -0.36790928767225356, -0.5061302867683104, -0 ... 920204587889013, 0.04108386026226077, -0.20607652828229475, -0.8054771629790362, -0.6105816570028402, -0.05614428001553993, -0.3663737673270948, 0.387029925025942}}, {{1, 5000, 1}}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {}}, False, 9.];
Wolfram Language code: model = EstimatedProcess[data, MAProcess[3]]
Use KalmanFilter to find residuals and plot the histogram:
Wolfram Language code: residuals = Rest[data["PathStates"] - KalmanFilter[model, data]["PathStates"]]; Histogram[residuals]
The null hypothesis of normality of the residuals cannot be rejected:
Wolfram Language code: DistributionFitTest[residuals, Automatic, {"TestDataTable", All}]