# Overlapping Data

I have a daily time series data spanning over 22 years. I need to compute some meaningful yearly standard deviation statistics / generate probability distribution and estimate tail risk. 22 years obviously is not enough, so was wondering about perhaps generating overlapping 1-year change time series and analyzing the daily change in it - that would give me around 5200 observations. Struggling a bit on how to interpret the distribution that I generated - it appears to be a daily change of the yearly change, so was wondering if it could be used at all or if there is a better way to use overlapping data?

Thanks a lot for the inputs,

D>

• Hi: The crucial question is what distribution you are interested in ? The daily distribution, the weekly, the yearly ? Then, that determines how to calculate the returns etc. Also, don't think of it as a daily return of a yearly return. Just think of it as a daily return and then sum of those daily's result in whatever other return ( weekly, yearly etc ). – mark leeds Sep 17 '18 at 17:25
• Hi - thanks for the response. I want yearly distribution, but believe limitation is that I have only 22 end of year data points - not sure how to overcome that if I want to estimate tail risk? – 291890964 Sep 17 '18 at 17:27
• Note, to be more precise, it's not really the sum. For small returns, the sum is okay. Generally speaking, you take the smaller timescale return and calculate the cumulative product of that return ( over whatever period you're interested in ) and then subtract 1.0. – mark leeds Sep 17 '18 at 17:28
• Hi - the data is built from delta in 2 yield curves - based on the 1 year data point in each curve for each day since 1996 – 291890964 Sep 17 '18 at 17:29
• yearly, is a problem. maybe it's best to take some smaller time scale estimate ( say daily ) and then assume independence so that you can use the $n \times \sigma^2$ estimate to get the time scale comprising $n = 252$ periods of the daily. Others may have better ideas. Obviously, you'd prefer more years. – mark leeds Sep 17 '18 at 17:30