# representing data for multivariate time series analysis

Please give a simple example of how to represent data for multivariate (vector) time series in Mathematica, so to use TimeSeriesModelFit?

Multivariate support for TimeSeriesModelFit is not currently implemented (version 10.4.1.).

Here is a way to generate multi-variate data using the first, single variable example in the function page of TimeSeriesModelFit.

data = {5., 9., 8., 10., 6.1, 10.4, 9.1, 11.6, 7.5, 12.1, 10.4, 13.5,
9., 14.1, 11.9, 15.7, 10.8, 16.4, 13.7, 18.3, 12.9, 19., 15.8, 21.2,
15.3, 22.1, 18.3, 24.6};

data = Transpose[{Range[Length[data]], data,
data + RandomReal[2, Length[data]]}]

ts = TimeSeries[data[[All, 2 ;; 3]], {data[[All, 1]]}]

ListLinePlot[ts, PlotTheme -> "Detailed"]


TimeSeriesModelFit[ts]


TimeSeriesModelFit::mvtsni: The data TimeSeries[...] is not scalar-valued. Multivariate support is not currently implemented. >>

Of course we can do the model fit separately for each of the time series.

mts = With[{p = ts["Path"]},
Map[TimeSeries[#, {p[[All, 1]]}] &, Transpose@p[[All, 2]]]];

tmodels = TimeSeriesModelFit /@ mts;

Table[ListLinePlot[{mts[[i]], TimeSeriesForecast[tmodels[[i]], {10}]},
PlotTheme -> "Detailed"], {i, Length[mts]}]