In the last post, we found evidence that there is month-to-month trending and that there is a non-zero mean in the time series of the principal factor explaining hedge fund returns.

However, we don't have many data points (96) and all time series analysis is subject to temporal bias and financial time series seem to be particularly prone to not smoothely exploring their available phase space. And we know that recently, hedge funds just suck! So an important question is whether the positive autocorrelation we are finding in the data is, in fact, driven by just our recent experience in which there have been a few months of consecutive terrible returns.

The only real way to find out is to wait for more data to roll in and see if the best estimate, or a Bayesian adjustment to a lower value, is the better predictor. But that's going to take time, so an alternative is to pry into the data and see if it looks like the estimate is driven by recent history.

The chart shows the confidence bounds for estimating the AR(1) parameter for every sub-interval ending on dates between December 2001 and December 2008 (the sample always starts on January 2001, so the estimates are not independent of each other).

It's clear that the recent problems in the market have kicked up the estimated autocorrelation to a higher level than prior history but also that there was definitely a prior autocorrelation which was also significant.

So what value should we use? I guess in my heart I'm a frequentist so my instinct is to use all the data rather than make a bet about which subset is more accurate. We should learn from recent experience that these trends are possible rather than dismissing them as anomalous or "once in a hundred years floods."

My strongest preference is that confidence intervals are more reliable estimates than point estimates, so I'd bet that the true parameter lies somewhere between the green lines on the right-hand most edge of the chart.