Dear learned researchers,
I am trying to figure out a way to find some measures of volatility in fuel price using monthly level data. My observations are also at monthly level so need a measure of volatility which gives me volatility at monthly level.
Thanks for ideas.
If I understood correctly, you are looking for the level of volatility each month for your monthly collected data. If this is the case, compute the squared returns.
Thanks guys for your responses. I only have data at monthly level (which is given to me by taking average over the days in that particular month). I do not know daily or weekly prices.
Hello dear Kushnee,
Before considering any model you must take into account the amount of data you have. If you have a large sample you can generate log returns, and if they meet the condition of stationarity you can estimate a SARMA-GARCH model, to take into account the possible seasonal effects of the monthly series in the esyimated volatility. If you have a small sample, you must use a nonparametric method, such as historical volatility, because the effectiveness to estimate parameters of methods such as maximum likelihood, depends directly on the number of data.
Regards,
If you have a data which has a trend, then taking simply standard deviation over certain intervals will bias your results upward as the length of interval is growing.
So what I suggested for commodity prices in an article was to first fit a time-series model on the data (ARMA, ARMAX) and the look at the residuals. An ARCH/GARCH is even better.
But it all depends on your application.
In pricing derivatives, however, usually a simple standard deviation of the change of log prices is used. This removes the stochastic trend and you have the volatility of the returns (not the price).
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