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Title: Sliced inverse regression for time series Authors:  Markus Matilainen - University of Turku/Turku PET Centre (Finland) [presenting]
Christophe Croux - Edhec Business School (France)
Klaus Nordhausen - University of Jyvaskyla (Finland)
Hannu Oja - University of Turku (Finland)
Abstract: When analysing data with a response variable $y$ and explanatory variables $\mathbf x$, modelling may become infeasible when the number of variables gets higher. It can also cause computational problems and visualization of data becomes harder. To avoid these kind of problems Sliced Inverse Regression (SIR) can be used. It is used to find the subspace of $\mathbf x$ which contains all the essential information needed to model $y$. However, SIR was developed for iid data. An extension for SIR where both ${\mathbf x}_t$ and $y_t$ are time series is suggested. The new method uses several supervised lagged autocovariance matrices and can then also indicate which lags of ${\bf x}_t$ are relevant to the modelling process of $y_t$. Different ways to choose the lags and the number of dimensions to keep are suggested. The method and different selection ways are demonstrated using simulated and real data.