Please, does someone know how to draw a confidence intervals (from the results of a GARCH (1,1)) in a way similar to these:

enter image description here

*Asume an ARMA(1,1) fit the time series.

Thank you very much

  • $\begingroup$ Do you mean the forecast confidence intervals? $\endgroup$ Feb 2, 2015 at 22:39
  • $\begingroup$ I just understood that my original question was pretty dumb. (Thank you for the corrections in my other question) $\endgroup$ Feb 3, 2015 at 4:45

1 Answer 1


I interpret your question as focusing on the method of graphing, not the specifics of the GARCH algorithm. As such, here is a time series, the variance (calculated on five sequential points), and the moving averages, and a combined ListPlot.

myTimeSeries = Table[.3 Sin[.1 i] + RandomReal[], {i, 1, 100}];

myVariances = Variance /@ Partition[myTimeSeries, 5, 1];

myAverages = MovingAverage[myTimeSeries, 5];

ListPlot[{myTimeSeries, myAverages, myAverages + myVariances, myAverages - myVariances},
 Joined -> {False, True, True, True},
 PlotStyle -> {Green, Blue, Red, Red}]

enter image description here

Or with

myStandardDeviations = Sqrt /@ myVariances

and appropriate change of plotting function:

enter image description here

  • $\begingroup$ Thank you very much David! (although I ment the specifics of the GARCH algorithm). I will use that code in my report, nonetheless. Thank you again! $\endgroup$ Feb 3, 2015 at 4:27
  • $\begingroup$ (By the way, I just understood that my original question was pretty dumb) $\endgroup$ Feb 3, 2015 at 4:40

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