Plot the confidence interval bands from TimeSeriesForecast

Question

Here is my function ploting the temporal data and the forecast of a given time series:

Function[{dates, trees, keys, diff},
  Manipulate[Module[{ts, tsm},
    ts = TimeSeries[Transpose@{dates, trees[key]}];
    tsm = TimeSeriesModelFit[ts, "SARMA"];
    DateListPlot[{tsm["TemporalData"], TimeSeriesForecast[tsm, {90}]},
     PlotLabel -> tsm,
     PlotLegends -> {"TemporalData", "Forecast"},
     ImageSize -> imageSize]]
   , {key, keys}]
  ];

I want to show the 50% and 95% confidence interval as bands on the forecasting part, is there a way to modify my function to show it?

trees is just the name of my dataset.

Answer 1

There is a lot in documentation, e.g.

For illustration:

This is times series of AUD US exchange rate 1990 to 2016.

tsm = TimeSeriesModelFit[aus, "ARIMA"];
forecast = TimeSeriesForecast[tsm, {0, 5}]
q[ci_] := Quantile[NormalDistribution[], 1 - (1 - ci)/2]
se = Sqrt[forecast["MeanSquaredErrors"]];
tsci[ci_, u_] := TimeSeriesThread[{1, u q[ci]}.# &, {forecast, se}];
Manipulate[
 DateListPlot[{aus, forecast, tsci[ci, 1], tsci[ci, -1]}, 
  Filling -> {3 -> {4}}, 
  PlotStyle -> {Black, Red, {Red, Dashed}, {Red, Dashed}}],
 {ci, {0.9, 0.95, 0.99}}]

Answer 2

Also in the documentation of TimeSeriesModelFit - see the examples in Applications section for use of TimeSeriesModel with property of "PredictionLimits".