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River Flow

The measures of the annual minimum mean daily flows, in cubic meters per second, of the Mahanadi River in central India:
Wolfram Language code: data = ExampleData[{"Statistics", "MahanadiRiverFlow"}]
In order to fit a fractionally integrated ARMA process the data needs to be centralized:
Wolfram Language code: mean = Mean[data]; data0 = data - mean;
Find process parameters:
Wolfram Language code: eproc = EstimatedProcess[data0, FARIMAProcess[4, 3]]
Compare correlation functions for the data and estimated process:
Wolfram Language code: ListPlot[CorrelationFunction[#, {0, 10}]& /@ {TemporalData@data, eproc}, PlotRange -> All, PlotStyle -> PointSize[Large], Filling -> 1 -> {2}, PlotLegends -> Placed[PointLegend[{"Data", "Model"}, LegendFunction -> "Frame", LegendLayout -> "Row"], {Center, Top}], PlotLabel -> "Correlation Function", ImageSize -> 400]
Forecast the annual minimum mean daily flows for 10 years ahead:
Wolfram Language code: forecast = TimeSeriesForecast[eproc, data0, {0, 10}] + mean
Wolfram Language code: ListLinePlot[{TemporalData@data, forecast}, Filling -> Axis, PlotLegends -> Placed[LineLegend[{"Data", "Forecast"}, LegendFunction -> "Frame"], {Right, Top}], PlotLabel -> "Annual Minimum Mean Daily Flows", ImageSize -> 400]