Why GARCH Volatility Forecasts Revert Toward Their Long-Run Level
Summary
The document asks why volatility forecasts from an ARMA(1,1)-GARCH(1,1) model decline slightly over a multi-step forecast horizon. The displayed output shows the standard deviation estimates decreasing across successive forecast steps, while the questioner is trying to forecast volatility over a longer span.
The accepted answer cautions that GARCH is generally more suited to short-horizon forecasting: as the forecast extends, conditional volatility tends toward its longer-run level, so the forecast can move down when current volatility is above that level. For a horizon of roughly two months, the answer suggests considering monthly data. It gives no parameter estimates, forecast comparison, or evidence for how aggregation changes accuracy, so the recommendation is brief and should not be treated as a universal rule for all GARCH models or assets.
Key ideas
- Multi-step GARCH volatility forecasts can decline as conditional volatility moves toward its long-run level.
- The example uses an ARMA(1,1)-GARCH(1,1) model and shows a gradual decrease in forecast standard deviation.
- The accepted answer recommends GARCH primarily for short-horizon forecasts.
- For a forecast spanning about two months, the answer suggests considering monthly data, without providing comparative validation.
Tags
Full text
# Constant decreasing volatility, GARCH forecasting
# Constant decreasing volatility, GARCH forecasting
I am trying to forecast the volatility using GARCH modelling in R.
I fit an ARMA(1,1)-GARCH(1,1) model, but my sigma predictions are constantly decreasing. Anybody know why?
```
predict(garch1,n.ahead=63)
meanForecast meanError standardDeviation
1 -0.0005595252 0.02732987 0.02732987
2 0.0014640502 0.02736439 0.02732390
3 0.0001896293 0.02737454 0.02731802
4 0.0009922427 0.02737510 0.02731222
5 0.0004867674 0.02737190 0.02730651
6 0.0008051090 0.02736726 0.02730088
7 0.0006046217 0.02736210 0.02729534
8 0.0007308860 0.02735678 0.02728988
9 0.0006513664 0.02735145 0.02728450
10 0.0007014468 0.02734615 0.02727919
11 0.0006699068 0.02734093 0.02727397
12 0.0006897703 0.02733577 0.02726882
13 0.0006772605 0.02733069 0.02726375
14 0.0006851390 0.02732568 0.02725875
15 0.0006801772 0.02732074 0.02725383
16 0.0006833021 0.02731588 0.02724898
```
## Answer by Robert (score 1, accepted)
https://quant.stackexchange.com/a/18200
Garch models are not good to predict "many" periods ahead, but for "very short" times.
If you want to predict 2 months from here, maybe you should be working with monthly data.
I did a similar exercise with some indexes (`symb=c("^BVSP","^MERV","^DJA","^N225")`) using daily returns `from="1991/01/01"`, look the incredible predictions.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.