ИСТИНА

We forecast weekly returns, volatility, as well as trading vol- umes of the S&P500 index by representing the system in the state space and extract the subspace of the principal compo- nents. In general, an autoregressive system can be represented in the state space as follows xt+1 = Axt + Kεt, yt = Cxt + εt, where xt is an unobservable vector of k×1 state variables, yt is a vector of l×1 observable quantities, and εt – unobservable white noise. The observable vector yt contains the weekly opening and closing prices, maximum and minimum prices, as well as trading volumes. To select the k dimension of the state space, we use the av- erage (out of 300) absolute prediction error (mean absolute pre- diction error MAPE) for 4 weeks according to the rolling-sample scheme with an interval size for modeling of 200 weeks. It turns out that k = 1, 3, 7 are the best for predicting re- turns and volatility. Although the in-sample error falls for higher dimensions k the out-of-sample error increases.