# Identifying autocorrelation / serial correlation from graph?

I'm new to statistics and I'm currently working on some exercises to identify serial correlation visually. This is from a time series exercise of Dollar-Pound Exchange Rate.

After running a simple OLS regression in STATA, i used these commands for the residuals:

predict residuals, res
gen residuals_lag = L1.residuals
scatter residuals residuals_lag


I'm not sure what conclusion to draw from the second graph. The examples of serial correlation in my text book has a clear pattern and shape, but the example of no serial correlation has a wider random distribution than my output.

My guess is that the graph suggests no serial correlation as the residuals look to be random around 0, with a few outliers. But what do you guys think? Any input is appreciated!

Thanks!

• Can you show us a plot of the original data as well? – user2974951 Jan 28 at 13:15
• @user2974951 Sure! Have updated the original post. The data is a time series of Dollar-Pound Exchange Rate. – Woo Won Jan 28 at 14:09

Often, the series such as these are modeled with ornsein-uhlenbek type of process: $$dx_t=a(x_t-\mu_t)+\sigma dW_t$$ where $$dW$$ - is Brownian motion, and $$a,\sigma$$ - are constants, and $$\mu_t$$ - potentially time varying deterministic or exogenous mean. This type of process would produce the residual plots similar to yours. It has characteristics of the random walk process (Brownian motion) in short run, and mean reversion process in long run. So, if you take differences, they'll look completely random, yet the levels will be persistent.