The Auto correlation command can be accessed in the Independence sub menu of the Statistics menu.
The auto correlation calculation used here assumes that the data are taken from a stationary process, that is, the data would appear the same [statistically] for any reasonable subset of the data. In the case of a time series, this implies that the time origin may be shifted without affecting the statistical characteristics of the series. Thus the variance for the whole sample can be used to represent the variance of any subset. For a simulation study, this may mean discarding an early warm-up period (see Law & Kelton1). In many other applications involving ongoing series, including financial, a suitable transformation of the data might have to be made. If the process being studied is not stationary, the calculation and discussion of auto correlation is more complex. (see Box et. al.2).
A graphical view of the auto correlation can be displayed by plotting the scatter of related data points. The Scatter Plot available in the Statistics menu is a plot of adjacent data points, that is, of separation or lag 1. Scatter plots for data points further removed from each other in the series, that is, for lag j, could also be plotted, but the auto correlation is more instructive. The auto correlation, rho, is calculated from the equation:
where j is the lag between data points, sigma is the standard deviation of the population, approximated by the standard deviation of the sample, and xbar is the sample mean. The calculation is carried out to 1/5 of the length of the data set where diminishing pairs start to make the calculation unreliable.
The auto correlation varies between 1 and -1, between positive and negative correlation. If the auto correlation is near either extreme, the data are auto correlated. Note, however, that the auto correlation can assume finite values due to the randomness of the data even though no significant auto correlation exists.
As an example, the two plots shown below are 100 random variates from a distribution before and after sorting. Note that sorting the data gives the direct appearance of broad auto correlation. The numbers after correlation along the x axis are the maximum auto correlation in both the positive and negative directions.
As with all input data graphs in Stat::Fit, the Auto correlation Plot may be customized by using the Graphics Style dialog in the Graphics menu. The graphs may also be copied to the Clipboard or saved as graphic files [.BMP] by using the Copy or Save As commands in the Graphics menu. Note that , while the graph view currently open can still be modified, the copied or saved version is a fixed bitmap.
For large data sets, this plot can take a while to get to the screen. The overall screen redrawing can be improved by viewing this plot and closing it thereafter. The calculation is saved internally and need not be recalculated unless the input data changes.
1. "Simulation Modeling & Analysis", Averill M. Law, W. David Kelton, 1991, McGraw-Hill, p293
2. "Time Series Analysis", George E.P. Box, Gwilym M. Jenkins, Gregory C. Reinsel, 1994, Prentice-Hall
