In the prior post we presented evidence that the forecasting skill of our AR(1) model of the returns due to the dynamic trading risk factor was +18% relative to the null hypothesis forecast based on the sample mean return. However, we did not give a statement of the significance of this excess skill based on the sample data recorded.

The principal reason for this omission was that I don't know the sampling distribution of the skill statistic, and so cannot easily assess it's sample variance. In this post we will use the Jackknife, which is a statistical resampling technique, to estimate the bias and variance of the skill statistic.

For N data points, the basic technique is to compute the statistic we are interested in over the N subsets of the data that may be selected by leaving one of the data points out in each group. Unlike bootstrapping, we do not select subsets at random — we consider every possible subset that may be formed with just one datum left out. We may then use the sample distribution of these leave-one-out estimators of the skill to estimate the bias and variance of our whole sample statistic. 

Our data has a null forecast of 0.46% per month and a relative skill of 18%. From the data below, we compute a Jackknife bias of −2% in skill, leading to a Jackknife estimator of 20% skill with a Jackknife variance estimator of 0.0207 (std.err. of 14% in skill).