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I want to forecast the volatility (with Garch) of a canadian stock in 5 months with daily returns. How many data do I have to collect ?


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There was a post in QF a while ago suggesting at least 5000 data points (in the time series) for a GARCH model – PEL Dec 8 '13 at 23:33

Fitting a time series on a given stock is really trade off between statistical risk and model error. If your time series is too short then your statistical error will be high. If your time series is too long, then the distribution of the market will probably have changed, and the your model error will be high.

5000 days is about 20 trading years. There is no way your choice of distribution will be meaningful a garch forecast. To add insult to injury, your forecast, tends to the unconditional variance very quickly $(\alpha +\beta)^n$ where $n$ is the number of days ahead. So if you are forecasting 105 days ahead, even if $\alpha + \beta$ quite high,$(\alpha +\beta)^{105}$ will be close to zero.

  1. Choose a proper and meaningful forecast horizon
  2. Depending on your forecast horizon choose reasonable time frame.
  3. Do several change of point test to see if your distribution has changed. If it did, try to reduce the time frame.
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