![]() The result of the command ot (soi, rec, 10) is shown below. In the "astsa" library that we’ve been using, Stoffer included a script that produces scatterplots of y t versus x t+h for negative \(h\) from 0 back to a lag that you specify. And, a below average of SOI is associated with a likely above average recruit value about 6 months later. The correlations in this region are negative, indicating that an above average value of SOI is likely to lead to a below average value of “recruit” about 6 months later. The result, showing lag (the \(h\) in x t+h) and correlation with y t : The following two commands will do that for our example. It’s difficult to read the lags exactly from the plot, so we might want to give an object name to the ccf and then list the object contents. ![]() The most dominant cross correlations occur somewhere between \(h\) =−10 and about \(h\) = −4. The CCF below was created with these commands: soi= scan("soi.dat") We see SOI as a potential predictor of recruit. The data are monthly estimates for n = 453 months. The text describes the relationship between a measure of weather called the Southern Oscillation Index (SOI) and “recruitment,” a measure of the fish population in the southern hemisphere. Example: Southern Oscillation Index and Fish Populations in the southern hemisphere. For instance, ccf(x,y, 50) will give the CCF for values of \(h\) = 0, ☑, …, ±50. If you wish to specify how many lags to show, add that number as an argument of the command. The CCF command is ccf(x-variable name, y-variable name) Thus, we’ll usually be looking at what’s happening at the negative values of \(h\) on the CCF plot. ![]() In many problems we consider, though, we’ll examine the x-variable(s) to be a leading variable of the y-variable because we will want to use values of the x-variable to predict future values of y. In some problems, the goal may be to identify which variable is leading and which is lagging. In the relationship between two time series (\(y_\), it is sometimes said that x lags y. The basic problem we’re considering is the description and modeling of the relationship between two time series.
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