If you have been into statistical modelling and machine learning then you will have this idea.
Intraday data or what is high frequency trading data is not normally distributed and is infact skewed and leptokurtic.
High Frequency Trading data comprises all the intraday timeframes of 1 minute, 5 minute, 15 minute, 30 minute, 60 minute and 240 minute. Daily and Weekly is the low frequency data.
But we are still using the normal distribution assumption when we do the time series analysis of the high frequency trading data.
In this blog post I show you very clearly how this data is not normally distributed.
The question comes why we are modelling returns when we need price information.
I think stationarity and normal distribution has been the major mistake that has been made in the time series analysis.
This is one of the main reason why wavelet analysis and wavelet transform is getting more popular in the quant circles.
Stationarity results when the mean and variance of the time series does not change with time.
There is only on frequency in the stationary data.
Stationarity is a condition that is very hard to satisfy in a real world time series like the financial time series.
Wavelets have many frequencies that they reveal a lot more information about the time series data. More on that in a future post.
