# 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

• perhaps what you are looking at is the forecast for the underlying series and not the vol? Jun 5, 2015 at 18:08
• I dont think so because also when I use egarch or gjrgarch: ugarchforecast(gjrGARCH1, data =brentlog1, n.ahead = 21), then I get decreasing sigma and thats the volatility Jun 5, 2015 at 18:10
• The meanforecast is the forecast of the series but the standard deviation is forecast of volatility no? Jun 5, 2015 at 18:10
• it would be probably insightful to grab the estimated parameters and write out the equations to see what the forecast is using for the underlying model Jun 5, 2015 at 18:14
• Yes. But anyway my data is the log daily returns so what is the best way to calculate the realised vol? I only have the daily average return Jun 5, 2015 at 18:15

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.