While developing a model, historical data alone may not be sufficient to test its robustness. One way to generate test data is to re-sample historical data. This “re-arrangement” of past time-series can then be fed to the model to see how it behaves.<\/p>\n\n\n\n
The problem with sampling historical market data is that it may not sufficiently account for fat-tails<\/a>. Typically, a uniform sample<\/em> is taken. The problem with this is it under-represents the tails. This leads to models that work on average but blow up on occasion. Something you’d like to avoid.<\/p>\n\n\n\n One way to overcome this problem is through stratified sampling<\/em>. You chop the data into intervals and use their frequencies to probability weight the sample. This preserves the original distribution in the sample.<\/p>\n\n\n\n Notice the skew and the tails in the “STRAT” densities for both NIFTY and MIDCAP indices. This distribution is far more likely to result in a robust model compared to the one that just uses uniform sampling.<\/p>\n\n\n\n![\"\"](\"https:\/\/github.com\/stockviz\/blog\/raw\/master\/fat-tails\/plots\/simulation.NIFTY%2050-density.png\")
<\/figure>\n\n\n\n![\"\"](\"https:\/\/github.com\/stockviz\/blog\/raw\/master\/fat-tails\/plots\/simulation.NIFTY%20MIDCAP%20150-density.png\")
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