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Let’s Talk About Heteroskedasticity
The Amount of Noise in Market Returns is Also Noisy
In my prior articles I have exhibited the empirically obvious, long-standing, lack of Normality in the returns of the S&P 500 Index using data that is readily available to the public and fairly elementary statistical tools. A valid criticism of my approach, in which I make histograms of the entire history of the index, from 1928 to date, is that it is staggeringly naive to assume that the data generating process that existed in, say, the 1930’s and 1940’s bears any resemblance to that that existed in the 1990’s, or now!
In this article I will tackle that issue head-on and bring us to the beginning of an analysis that results in a model, asymmetric GARCH with fundamentally leptokurtotic innovations, that does exhibit remarkable stability through just under a hundred years of data.
I will also point out, as a side comment, that the affection that quants have for non-stationarity (meaning that the parameters change through time) in their models definitely arises from the failure of statistical models estimated in-sample, or on historic data, to subsequently perform well out-of-sample, in live-trading data.
“The Market changed” is the frequent cry of disappointed quants but, perhaps, “my model was wrong” is a more accurate description of the observation.
The Type of Non-Stationarity We Seek
In the prior article in this series I examined, by simulation, the effect of block-randomization of both the mean and the variance of a Normal distribution on the distribution of returns observed by a trader that was unaware of the complexity of the true data generating process.
In that article I show that non-stationarity in the mean of a Normal distribution produces an observed set of returns that has broad, flat, shoulders, which is labeled “platykurtosis” by…
