How can I use WienerProcess with TimeSeriesForecast?

Question

I created a TimeSeries from Date-Value-Pairs, which I imported from a .csv-File

diffp = Import["path/difficultyp.csv", "Data"];

tsdiff = TimeSeries[diffp];

I have no problems when I use the inbuild TimeSeriesModelFit function, for example

tsdfit = TimeSeriesModelFit[tsdiff, {"SARIMA", 9}];

and afterwards create a Forecast with

tsdforecast = TimeSeriesForecast[tsdfit, {100}]

This works and tsdforecast is of "type" TemporalData. However, I want to use a WienerProcess instead, following the second example in this doc of EstimatedProcess. What I did:

eproc = EstimatedProcess[tsdiff, WienerProcess[a, b], ProcessEstimator ->"MaximumLikelihood"]
forec = TimeSeriesForecast[eproc, tsdiff, {20}]

However, this doesn't work and the last line returns not something of "type" TemporalData but just "Out: TimeSeriesForecast[WienerProcess[...],TimeSeries[...], {20}]". When I try to plot the results with

DateListPlot[{tsdiff, forec}]

I get an error message

DateListPlot::ldata: {TemporalData[TimeSeries,{{{82.938,80.878,82.224,81.678,82.534,84.138,84.534,87.76,88.902,90.508,90.111,88.552,82.166,76.928,78.75,82.528,80.947,79.482,78.498,78.996,81.073,79.895,80.591,80.545,87.318,90.096,91.837,93.445,94.534,97.382,98.722,99.096,99.976,101.356,102.517,103.641,104.134,103.817,102.053,107.184,106.857,108.358,108.811,111.109,109.885,110.021,111.654,112.707,111.597,110.677,<<260>>}},<<5>>,{<<1>>}},True,10.3],<<1>>} is not a valid dataset or list of datasets. >>

Which probably is a type error. But I can't get my head around this to solve it. Can anyone shed some light on this issue?

Answer 1

By design TimeSeriesForecast supports only time series processes, which are discrete time processes. WienerProcess is a continuous time process. It is stochastic difference equations vs stochastic differential equations.

P.S. Also, TimeSeriesForecast is computing conditional mean (future trend) conditioning on data, which makes sense for time series processes with autoregressive components. WienerProcess has independent increments.