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Model Seasonal Data

    
Fit a SARMAProcess model for the hourly measurements of temperature in August:
Wolfram Language code: td = TemporalData[Automatic, {{{21.1, 20.6, 20, 19.4, 18.9, 20.6, 22.8, 25, 27.2, 28.9, 30, 30.6, 31.7, 32.2, 32.2, 32.8, 32.2, 30.6, 26.7, 23.9, 21.7, 21.7, 19.4, 18.3, 18.3, 17.2, 16.7, 16.1, 15.6, 17.2, 22.8, 26.1, 28.9, 31.7, 32.8, 33.9, 3 ... 55438780, 3555442380, 3555445980}]}, 1, {"Discrete", 1}, {"Discrete", 1}, 1, {MetaInformation -> {"Source" -> Defer[WeatherData["Champaign", "Temperature", {2012, 8}]], "Unit" -> "DegreesCelsius"}, TemporalRegularity -> True}}, True, 10.];
Wolfram Language code: DateListPlot[td, Filling -> Bottom, Joined -> True]
Find process parameters:
Wolfram Language code: eproc = EstimatedProcess[td, SARMAProcess[2, 1, {24, 0, 2}], ProcessEstimator -> "MaximumConditionalLikelihood"]
Check if the process is weakly stationary:
Wolfram Language code: WeakStationarity[eproc]
Compare correlation functions:
Wolfram Language code: ListPlot[CorrelationFunction[#, {100}]& /@ {td, eproc}, PlotLegends -> Placed[{"data", "model"}, {Right, Top}], PlotStyle -> {PointSize[Medium], PointSize[Large]}, ImageSize -> 300]