Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more. 
Home Bivariate Data Correlation Autocorrelation Autocorrelation Function  
See also: introduction to autocorrelation, Autocorrelation and Scatter Plots  
Autocorrelation FunctionThe autocorrelation is calculated in the same way as the correlation between two variables (just using the same variable twice). If we consider time signals, the values of the autocorrelation may be calculated by shifting one of the two formal variables by a certain amount Δt. If we plot the results of these calculations against the time shift, we obtain the autocorrelation function, or autocorrelogram. Here's an interactive example which shows the principal function of an autocorrelogram.
The idea is that a timeseries y_{t} (with the measurements
x_{1}, x_{2}, x_{3}, ..., x_{n}) is correlated
with itself. In the first step, the pairs to be correlated are:
The correlation coefficient is obviously 1. In the next step, the second
series is shifted one timestep to the right:
Here's another interactive example which shows the difference between an uncorrelated signal and a signal exhibiting strong autocorrelation.


Home Bivariate Data Correlation Autocorrelation Autocorrelation Function 