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title: "cross correlation function"
output: html_document
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## Cross correlation function

Compare uncorrelated and correlated times series with the cross correlation function:

First simulate correlated and uncorrelated time series data as follows: 

- Simulate  x and y as two independent ARMA processes. Then create z = x - y 

Then x and y are uncorrelated, but z is correlated with both x and y.

- Make cross correlation plots comparing the processes, and inverpret.

- Construct a new process w as a delayed version of x. 

- Draw the cross-correlation plots comparing w with x,y and z, resepctively. Can you identify the delay from the ccf?