I want do fit some sort of multi-variate time series model using R.
Here is a sample of my data:
u cci bci cpi gdp dum1 dum2 dum3 dx
16.50 14.00 53.00 45.70 80.63 0 0 1 6.39
17.45 16.00 64.00 46.30 80.90 0 0 0 6.00
18.40 12.00 51.00 47.30 82.40 1 0 0 6.57
19.35 7.00 42.00 48.40 83.38 0 1 0 5.84
20.30 9.00 34.00 49.50 84.38 0 0 1 6.36
20.72 10.00 42.00 50.60 85.17 0 0 0 5.78
21.14 6.00 45.00 51.90 85.60 1 0 0 5.16
21.56 9.00 38.00 52.60 86.14 0 1 0 5.62
21.98 2.00 32.00 53.50 86.23 0 0 1 4.94
22.78 8.00 29.00 53.80 86.24 0 0 0 6.25
The data is quarterly, the dummy variables are for seasonality.
What I would like to do is to predict dx with reference to some of the others, while (possibly) allowing for seasonality. For argument's sake, lets say I want to use "u", "cci" and "gdp".
How would I go about doing this?
If you haven't done so already, have a look at the time series view on CRAN, especially the section on multivariate time series.
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 "Modeling financial time series with S-PLUS" gives a good overview of these topics, but it isn't immediately transferable into R. Ruey Tsay's "Analysis of Financial Time Series" (available in the TSA package on CRAN) also has a nice discussion of factor models and principal component analysis in chapter 9.
R also has a number of packages that cover vector autoregression (VAR) models. In particular, I would recommend looking at Bernhard Pfaff's VAR Modelling (vars) package and the related vignette.
I strongly recommend looking at Ruey Tsay's homepage because it covers all these topics, and provides the necessary R code. In particular, look at the "Applied Multivariate Analysis", "Analysis of Financial Time Series", and "Multivariate Time Series Analysis" courses.
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: