Autocorrelation in Time Series

Why time series data is unique

A time series is a series of data points indexed in time. The fact that time series data is ordered makes it unique in the data space because it often displays serial dependence. Serial dependence occurs when the value of a datapoint at one time is statistically dependent on another datapoint in another time. However, this attribute of time series data violates one of the fundamental assumptions of many statistical analyses — that data is statistically independent.

What is autocorrelation?

Autocorrelation is a type of serial dependence. Specifically, autocorrelation is when a time series is linearly related to a lagged version of itself. By contrast, correlation is simply when two independent variables are linearly related.

Why autocorrelation matters

Often, one of the first steps in any data analysis is performing regression analysis. However, one of the assumptions of regression analysis is that the data has no autocorrelation. This can be frustrating because if you try to do a regression analysis on data with autocorrelation, then your analysis will be misleading.

Additionally, some time series forecasting methods (specifically regression modeling) rely on the assumption that there isn’t any autocorrelation in the residuals (the difference between the fitted model and the data). People often use the residuals to assess whether their model is a…