Why Asset Prices Can Mislead Your Financial Forecasting Model

I often encounter students and professionals trying to build their financial forecasting models using asset prices. They may use the latest statistical model, but the results somehow just don’t make sense. This brief note explains just one reason things can go off track.

In many problems in quantitative analysis, the model at hand requires the data to be independent and identically-distributed (i.i.d.). When the data observations are not i.i.d., they are likely to exhibit autocorrelation. The Autocorrelated data show that they can be explained by the lagged observations of the same dataset (boring!). To find some interesting inferences, we first need to check whether the data we are working with are i.i.d.

Consider the prices of Bitcoin. Each price contains a large chunk sometimes referred to as a base, which does not easily disappear. This base contributes to the permanence of Bitcoin prices and results in what we call serial dependence. If our data are serially dependent, they are not i.i.d. In other words, the data violate the assumption of independence. To test whether our variables are serially-dependent, we can use autocorrelation. Autocorrelation measures just how much our data correlate with its own past observations.

To our luck, Python already incorporates tests for autocorrelation, and they are built in right into the Python library known as Pandas!

As shown in Figure 1, Bitcoin (BTC-USD) prices exhibit a high positive serial autocorrelation in the near term, and a slightly negative autocorrelation in the longer term, before settling to 0. When autocorrelation is not zero, the variables are not i.i.d! The horizontal lines mark the 95% and 99% confidence “boundaries” to denote the regions where the assumption of i.i.d. is still plausible.

Figure 2 plots the autocorrelation for daily returns in BTC-USD. As the figure shows, the returns fit into the 95% confidence bounds, showing that the returns are not autocorrelated. The same autocorrelation structures show up for most asset prices. Prices are autocorrelated, while returns are not or at least less so! As a result, we usually perform any financial analysis on asset returns, and not prices.