Скачать или смотреть Python Tutorial: Autocorrelation

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So far, you have looked at the correlation of two time series. Autocorrelation is the correlation of a single time series with a lagged copy of itself. It's also called "serial correlation". Often, when we refer to a series' autocorrelation, we mean the "lag-one" autocorrelation. So when using daily data, for example, the autocorrelation would be the correlation of the series with the same series lagged by one day.

What does it mean when a series has a positive or negative autocorrelation? With financial time series, when returns have a negative autocorrelation, we say it is "mean reverting".

Alternatively, if a series has positive autocorrelation, we say it is "trend-following".

Lest you think these concepts of autocorrelation are purely theoretical, they are actually used on Wall Street to make money. Many hedge fund strategies are only slightly more complex versions of mean reversion and momentum strategies. Since stocks have historically had negative autocorrelation over horizons of about a week, one popular strategy is to buy stocks that have dropped over the last week and sell stocks that have gone up. For other assets like commodities and currencies, they have historically had positive autocorrelation over horizons of several months, so the typical hedge fund strategy there is to buy commodities that have gone up in the last several months and sell those commodities that have gone down.

Here is an example of how you would compute the monthly autocorrelation for the Japanese Yen-US Dollar exchange rate. The data was downloaded from the FRED website, which stands for Federal Reserve Economic Data. The date column was read in as a string, so before you can compute autocorrelations, you will have to convert the dates in the DataFrame index to a DateTime object using the pandas method "to_datetime". Now that it's a DateTime object, downsample the data using the resample method. The "rule" argument indicates the desired frequency. 'M' stands for monthly. The how argument indicates how to do the resampling. For example, you can use the first date of the period, the last date, or even an average. Finally, compute the autocorrelation using the pandas method "autocorr". Notice in this example that the autocorrelation is positive, 0-point-0567, so this series exhibits some momentum.

Now it's your turn. You'll look at a few financial time series that have negative autocorrelation.