Using Autocovariance and Autocorrelation to Analyze Financial Time Series

Summary

This guide explains autocovariance and autocorrelation as measures of how a time series relates to its own past values. Autocovariance retains the units and scale of the data, while autocorrelation standardizes the relationship by variance, making it bounded between minus one and one. The article also covers lag zero, where autocovariance equals variance and autocorrelation equals one, and defines partial autocorrelation by accounting for intervening lags.

Worked return examples illustrate calculation at lag one, followed by descriptions of computing and plotting these functions in Python and R. The guide presents sample Microsoft return values and connects the functions to identifying ARMA model structure. It notes that the standard interpretation assumes a stationary series, with stable mean and variance. Although autocorrelation can reveal linear dependence relevant to time-series research, the examples do not establish a profitable trading signal; any use in momentum or mean-reversion strategies would require further testing.

Key ideas

• Autocovariance measures co-movement between a series and a lagged version of itself, in the series' original scale.
• Autocorrelation standardizes autocovariance by variance and ranges from minus one to one.
• At lag zero, autocovariance is the variance and autocorrelation is one.
• Partial autocorrelation estimates a lag relationship after accounting for shorter lags.
• The functions help inspect stationary time series and inform ARMA model selection, but do not by themselves demonstrate a tradable edge.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.