Generating the time series standard deviations of 5-year rolling winods of X_{t}

[Daeeun Bae]

Hello. I am working on compustat and I would like to generate the time series standard deviations of 5-year rolling winods of Sales. Specifically, the time series for the volatility of X_{t} is

\sigma(X_{t}) = \sqrt{\frac{\sum_{\tau = t-2}^{t+3} (X_{\tau} - \Bar{X}_{t})^2}{5}}

Can any one please help?

[Nick Cox]

The window for time t from t - 2 to t + 3 includes six data points, for t - 2, t - 1, t, t + 1, t + 2, t + 3.

rangestat from SSC is one of several ways to do this. You must install before you can use it.

ssc install rangestat 

Here is an example:

. webuse grunfeld, clear

. rangestat (count) invest (sd) invest, int(year -2 3) by(company)

. l company year invest* in 1/10

     +------------------------------------------------+
     | company   year   invest   invest~t   invest_sd |
     |------------------------------------------------|
  1. |       1   1935    317.6          4   70.390162 |
  2. |       1   1936    391.8          5   61.263442 |
  3. |       1   1937    410.6          6   73.366271 |
  4. |       1   1938    257.7          6   90.875925 |
  5. |       1   1939    330.8          6   93.461273 |
     |------------------------------------------------|
  6. |       1   1940    461.2          6   101.54846 |
  7. |       1   1941      512          6   75.513829 |
  8. |       1   1942      448          6   45.189044 |
  9. |       1   1943    499.6          6   81.577725 |
 10. |       1   1944    547.5          6   80.591789 |
     +------------------------------------------------+

. su invest in 1/6

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
      invest |          6    361.6167    73.36627      257.7      461.2

[Daeeun Bae]

Thank you Nick. Really helpful!