In-Sample vs. Out-of-Sample
The difference between an in-sample analysis and an out-of-sample analysis lies in the way that the rolling window Style Benchmark is calculated. In the one window case, the Style Benchmark is simply the composite series
S = x1C1 + x2C2 + ... + xNCN
where C1, ... , CN are the index series and x1, ... , xN is set of corresponding style weights.
In the rolling window case, we have a whole sequence of sets of style weights rather than one set of style weights. When calculating the Style Benchmark, the question is, which set of style weights must be used for which date?
In the in-sample case, the Style Benchmark is calculated as follows: the first window’s worth of data is filled using the style weights that correspond to that first window. After that, each set of weights is used for the last date inside the corresponding window. If the rolling window is advanced by n time periods, each set of weights is repeated n times to fill the gaps between window end dates.
In the out-of-sample case, each set of weights is used for the date that immediately follows the last date inside the corresponding window. Again, if the rolling window is advanced by n time periods, each set of weights is repeated n times to fill the gaps. Note that the in-sample Style Benchmark covers the entire selected date range, while the out-of-sample Style Benchmark does not start until the earliest date that immediately follows the last date inside the first window.