Example: Bivariate Time Series

 The time series object econ.cts contains the following three time
series:

 Oneyear: One-Year U.S. Treasury Constant Maturity Rates
 Tenyear: Ten-Year U.S. Treasury Constant Maturity Rates
 Prod: U.S. Industrial Production Index, Seasonally Adjusted.

 Goal: Describe the joint structure of the Ten-Year Maturity Rates
and the Industrial Production Index.

 First, plot all three series. Splus can put them all on one plot:

> par(mfrow=c(3,3))
> tsplot(econ.cts) 

 But the scales aren't similar. Let's do two plots:

> tsplot(econ.cts[,1:2]) # One-Year (econ.cts[,1]) and Ten-Year 
> tsplot(econ.cts[,3])   # Production Index

 What do plots suggest?

> econ.diff <- diff(econ.cts,1,1) # First difference of all 3 series
> tsplot(econ.diff[,2],title="10-year rates: 1st diff")
> mtext("10-year rates: 1st diff",cex=0.7)   
> tsplot(econ.diff[,3])
> mtext("Production Index: 1st diff",cex=0.7)

 Find ACF's of Ten-Year Rates and Production Index, along with CCF  

> acf(econ.diff[,2:3]) 

 Periodograms of Ten-Year Rates and Production Index,
 along with the cross-spectrum information

> spec.econ <- spec.pgram(econ.diff[,2:3], demean=T, span=c(5,9))  

> summary(spec.econ) # some information removed

          Length Class      Mode
     freq  85          numeric
     spec 170          numeric 
      coh  85          numeric  # Coherency
    phase  85          numeric  # Phase

> dim(spec.econ$spec)
[1] 85  2   # spec is an 85 x 2 matrix. First columns is periodogram of
            # 10-year rates. Second column is periodogram of production.

> spec.plot(spec.econ) # Periodograms

> plot(spec.econ$freq,spec.econ$coh, type='l', xlab="Freq",ylab="Coh")
> mtext("Coherency", cex=0.7)

> plot(spec.econ$freq,spec.econ$phase, type='l', xlab="Freq",ylab="Phase")
> mtext("Phase", cex=0.7)