What are ACF and PACF curves? Why do we use them?




What are PACF(partial correlation function) and ACF(auto-correlation function) curves in a time series model? What is their relevance and what do they depict in a time series model?



Hi Mukesh
Any questions on time series are difficult to answer without bringing in maths, notations, linear algebra and that unfortunately makes learning time series (IMHO) the most challenging among all data science/machine learning discipline. :slight_smile:
ACF - Auto correlation function, as the word suggests, auto-correlation, means it is really correlation on itself. With time series we just have a single stream of values, or in other words there is just the X no Y. So suppose your time series is like this X = 3,5,6,6,7,4,5,6,7,2,3,4,… correlation between 4 and 3, 3 and 2, 2 and 7 (lag 1) will be say y1; correlation between 4 and 2, 3 and 7, 2 and 6 (lag 2) will be say y2; and so on at lags 3 = y3, lag 4 = y4.
What interests us is the pattern or lack of pattern in y1,y2,y3… This plot is called auto correlation function. We look for 1. is the curve decaying exponentially or 2. does the curve cut off suddenly
PACF - Partial auto correlation function, as the word suggests, is partial not complete. Here again we are plot the correlations at various lags 1,2,3 BUT after adjusting for the effects of intermediate numbers.

What is the use of ACF and PACF? - The pattern of the acf/pacf plot gives us an idea towards which model could be the best fit for doing prediction.


Thanks a lot! this was really helpful! :smile:


You can also look at this article:


Will ACF and PACF always give the best values for the parameters p and q?

I am working on a problem where the p and q values given by the plots do not give good forecast values.