# How to interpret autocorrelation

I have calculated autocorrelation on time series data on the patterns of movement of a fish based on its positions: X (x.ts) and Y (y.ts).

By using R, I ran the following functions and produced the following plots:

acf(x.ts,100)


acf(y.ts,100)


My question is, how do I interpret these plots? What information is needed to report any sort of pattern? I have been surfing the internet and have yet to find a concise way that effectively explains it.

Also, how do you decide the correct amount of lag to use? I used 100, but I am not sure if that is too much.

Those plots are showing you the $\textit{correlation of the series with itself, lagged by x time units}$. So imagine taking your time series of length $T$, copying it, and deleting the first observation of copy#1 and the last observation of copy#2. Now you have two series of length $T-1$ for which you calculate a correlation coefficient. This is the value of of the vertical axis at $x=1$ in your plots. It represents the correlation of the series lagged by one time unit. You go on and do this for all possible time lags $x$ and this defines the plot.
The answer to your question of what is needed to report a pattern is dependent on what pattern you would like to report. But quantitatively speaking, you have exactly what I just described: the correlation coefficient at different lags of the series. You can extract these numerical values by issuing the command acf(x.ts,100)\$acf.