Forecasting foreign exchange rates with large regularised factor models

Sammanfattning: Vector autoregressive (VAR) models for time series analysis of high-dimensional data tend to suffer from overparametrisation as the number of parameters in a VAR model grows quadratically with the number of included predictors. In these cases, lower-dimensional structural assumptions are commonly imposed through factor models or regularisation. Factor models reduce the model dimension by projecting the observations onto a common lower-dimensional subspace, decomposing the variables into common and idiosyncratic terms, and might be preferred when predictors are highly collinear. Regularisation reduces overfitting by penalising certain features of the model estimates and might be preferred when, for example, only a few predictors are assumed important. We propose a regularised factor model where factors are constructed by projection onto a common subspace and where the transition matrices in a time series model with the resulting factors are estimated with regularisation. By the subspace estimation we hope to uncover underlying latent factors that explain the predictor dynamics and the additional penalisation is used to encourage additional sparsity and to impose a priori structural knowledge into the estimate. We investigate unsupervised and supervised subspace extraction and extend earlier results on dynamic subspace extraction. Additionally, we investigate element-wise regularisation by the ridge and lasso penalties and two extensions of the lasso penalty that encourage structural sparsity. The performance of the model is tested by forecasting log returns of exchange rates.