Independence of time series data

Question

I have a time series data with $52$ observations and I would like to check for the independence between observations. The ACF for correlation and covariance of my data look

I am aware that $covariance = 0$ does not imply independence, except for Gaussian process. I wonder if I can use ACF to show the independence of my data or there are ways to justify it?

Many thanks.

Answer 1

Yes the ACF is ok but you should also check the ACF of the squares of your observations to see if there is no autocorrelations in the higher moments. As formal test you can use : The Box-Pierce , Ljung-Box and the Engle’s LM ARCH test.