Explain auto correlation for time series data



Can anyone kindly explain the Auto correlation plot obtained for time series data

I have attached an image with this post. The image has acf() plot obtained for a time series data
The plot does not converge to zero at any point, it is irregular.

Checked for stationarity, the time series data are found to be stationary.

I would like to know, how to select the max q value for the model.
Can similar procedures be followed for pacf() function also??

Thank you in advance


Hi @sridharbabu,

Unlike regular sampling data, time-series data are ordered. The autocorrelation function is one of the tools used to find patterns in the data. Specifically, the autocorrelation function is a measure of the correlation between observations of a time series that are separated by k time units.

The ACF tells us how correlated points are with each other, based on how many time steps they are separated by. For example: ACF(0)=1 means all data are perfectly correlated with themselves, ACF(1)=.9 means the correlation between a point and the next point is 0.9.

In the ACF plot, it can be seen that there is a large spike at lag 1 that decreases after a few lags. So, there is an autoregressive term in the data. We can use the partial autocorrelation function to determine the order of the autoregressive term. Since the spike is decreasing but not converging to 0, so the q value can be taken as 0.

To learn more on ACF and PACF plots, refer this article on time series.