I have a year long stock data sampled at 5 min frequency and would like to estimate monthly volatility using it. I am thinking using GARCH or TGARCH for volatility estimation. However, I am not sure if at frequency I should estimating volatility. After that should I scale volatility by square root of appropriate period?
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$\begingroup$ 1) For estimation of monthly vol, data sampled at daily interval should be fine enough. 2) Yes, you should scale vol using the square root rule: i.e., monthly_vol = daily_vol * sqrt(21), assuming there are 21 business days in a month. $\endgroup$ – Simon Oct 9 '14 at 5:06
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1$\begingroup$ Square root scaling is known to overestimate the variance. Following paper makes this point and suggests a way around: ssc.upenn.edu/~fdiebold/papers/paper18/dsi.pdf $\endgroup$ – vdesai Oct 9 '14 at 22:22
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You can try out a range of frequencies and then pick the one with the lowest fitting error (e.g. Root Mean Squared Error).
