Topic: Title: Sliced inverse regression for time series Authors:  Christophe Croux - Leuven (Belgium)
Klaus Nordhausen - University of Jyvaskyla (Finland)
Hannu Oja - University of Turku (Finland)
Markus Matilainen - University of Turku/Turku PET Centre (Finland) [presenting]
Abstract: When analysing data with a response variable $y$ and explanatory variables $\bf x$, modelling may become infeasible when number of variables gets higher. It can also cause computational problems and visualization of data becomes harder. To avoid this kind of problems we can use Sliced Inverse Regression (SIR), which is a supervised dimension reduction method and it is used to study a relationship between the response $y$ and the variables $\bf x$. However, in case of time series SIR algorithm does not use any information on lagged values directly. One way to deal with this is to treat explanatory variables and their past values and the past values of response variable as explanatory variables. We suggest a new method, which is based on SIR algorithm, but instead of using regular supervised covariance matrices, we use lagged supervised covariance matrices. We show how our new algorithm works with a few illustrative examples.