Autocorrelation is a measure of persistence within a data set, which can be defined as the tendency for successive data points to be similar (Wilks, 2011). In atmospheric science temporal autocorrelation can be a helpful tool for model evaluation. Temporal autocorrelation is also a fundamental concept for synthetic weather generation (for more detail see Julie’s fantastic series of blog posts on synthetic weather generation here). Calculating autocorrelation within a sample data set can also be a helpful for assessing the applicability of classical statistical methods requiring independence of data points within a sample. Should a data set prove to be strongly persistent, such methods will likely yield inaccurate results.
Autocorrelation is commonly computed by making a copy of the original data set, shifting the copy k points forward (where k is the lag over which you would like to compute the autocorrelation) and computing the Pearson correlation coefficient between the original data set and the copy.
The calculation of autocorrelation for a number of different lags at once is known as the autocorrelation function. Plotting the autocorrelation graphically can be a helpful tool for quickly assessing the presence of autocorrelation within a data set.
You can generate such plots in Matlab using the simple command shown below:
autocorr(T,k) % T is your data set and k is the number of lags you would like to compute
The command generates a plot of the autocorrelation function. Below are two examples, the first is the autocorrelation function of a set of observed temperature values in Des Moines Iowa, the second is autocorrelation function of the temperature values at the same location as modeled by the MM5I regional climate model:
Note the cyclical nature of the autocorrelation functions, this is a reflection of the daily temperature cycle. The autocorrelations function of the maximum or minimum temperatures would show more constant persistence.
Wilks, D. S. (2011). Statistical methods in the atmospheric sciences. Burlington, MA: Academic Press.