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    <p>If you haven't done so already, have a look at <a href="http://cran.r-project.org/web/views/TimeSeries.html" rel="noreferrer">the time series view on CRAN</a>, especially the section on multivariate time series.</p> <p>In finance, one traditional way of doing this is with a factor model, frequently with either a BARRA or Fama-French type model. Eric Zivot's <a href="http://books.google.com/books?id=sxODP2l1mX8C" rel="noreferrer">"Modeling financial time series with S-PLUS"</a> gives a good overview of these topics, but it isn't immediately transferable into R. Ruey Tsay's "<a href="http://rads.stackoverflow.com/amzn/click/0471690740" rel="noreferrer">Analysis of Financial Time Series</a>" (available in the TSA package on CRAN) also has a nice discussion of factor models and principal component analysis in chapter 9. </p> <p>R also has a number of packages that cover <A href="http://en.wikipedia.org/wiki/Vector_autoregression" rel="noreferrer">vector autoregression (VAR)</a> models. In particular, I would recommend looking at Bernhard Pfaff's <a href="http://cran.r-project.org/web/packages/vars/index.html" rel="noreferrer">VAR Modelling (vars)</a> package and <a href="http://cran.r-project.org/web/packages/vars/vignettes/vars.pdf" rel="noreferrer">the related vignette</a>.</p> <p>I strongly recommend looking at <a href="http://faculty.chicagobooth.edu/ruey.tsay/teaching/" rel="noreferrer"><b>Ruey Tsay's homepage</b></a> because it covers all these topics, and provides the necessary R code. In particular, look at the <a href="http://faculty.chicagobooth.edu/ruey.tsay/teaching/ama/" rel="noreferrer">"Applied Multivariate Analysis"</a>, <a href="http://faculty.chicagobooth.edu/ruey.tsay/teaching/bs41202/sp2009/" rel="noreferrer">"Analysis of Financial Time Series"</a>, and <a href="http://faculty.chicagobooth.edu/ruey.tsay/teaching/mts/sp2009/" rel="noreferrer">"Multivariate Time Series Analysis"</a> courses.</p> <p>This is a very large subject and there are many good books that cover it, including both multivariate time series forcasting and seasonality. Here are a few more:</p> <ol> <li>Kleiber and Zeileis. "<a href="http://rads.stackoverflow.com/amzn/click/0387773169" rel="noreferrer">Applied Econometrics with R</a>" doesn't address this specifically, but it covers the overall subject very well (see also the AER package on CRAN).</li> <li>Shumway and Stoffer. "<a href="http://rads.stackoverflow.com/amzn/click/0387293175" rel="noreferrer">Time Series Analysis and Its Applications: With R Examples</a>" has examples of multivariate ARIMA models.</li> <li>Cryer. "<a href="http://rads.stackoverflow.com/amzn/click/0387759581" rel="noreferrer">Time Series Analysis: With Applications in R</a>" is a classic on the subject, updated to include R code.</li> </ol>
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