Let x be the closeBid price of EUR/USD, sampled every 5 minutes during year 2015 (historical data). This is the variation (is it correct to call it 5-minutes returns?) for each 5-minutes period:
r = x[1:] / x[:-1] - 1
What's the formula to have the (moving) volatility over 1 year?
I tried this way:
rolling_stddev(r, 288*10) # 10 days, since 288 periods of 5 minutes in 1 day
The results is:
Is it a correct measure of volatility? (i.e. standard deviation of the returns)
First I thought about voting to close this question as it deals with Matlab synthax a lot. I ignore the Matlab stuff.
You have 5-minutes data. So an estmator of volatility over any sample of size $N$ (e.g. 100) will be an estimator of the vol of your 5-min returns. Usually volatility is quotes as "per annum" or "pa". This means that using the square root of time rule you can multiply your estimate by the number of 5-minute intervals in a year. Thus if you want to quote vola pa then $$ T = 12*24*260 = 288*260 $$ assuming 260 banking days and you multiply your estimate by $\sqrt{T}$. If you do the calculation for 10 days then $T=288*10$.
The $T$, the holding period, is independent from the number of returns that you use in order to estimate the 5-minutes vol.
Doing the things rolling does not change anything of the things above. You just push a window forward by 1 return each time.
It's better to use an exponentially weighted moving average.
There's a nice tutorial video by the Bionic Turtle here
