# How do you graph the confidence intervals that results from a GARCH over a time series?

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

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

Thank you very much

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

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}]


Or with

myStandardDeviations = Sqrt /@ myVariances


and appropriate change of plotting function:

• 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! Feb 3, 2015 at 4:27
• (By the way, I just understood that my original question was pretty dumb) Feb 3, 2015 at 4:40