A Horse Race in High Dimensional Space

31 Pages Posted: 15 Feb 2019

See all articles by Paolo Andreini

Paolo Andreini

University of Rome Tor Vergata

Donato Ceci

Bank of Italy

Date Written: February 14, 2019


In this paper, we study the predictive power of dense and sparse estimators in a high dimensional space. We propose a new forecasting method, called Elastically Weighted Principal Components Analysis (EWPCA) that selects the variables, with respect to the target variable, taking into account the collinearity among the data using the Elastic Net soft thresholding. Then, we weight the selected predictors using the Elastic Net regression coefficient, and we finally apply the principal component analysis to the new “elastically” weighted data matrix. We compare this method to common benchmark and other methods to forecast macroeconomic variables in a data-rich environment, dived into dense representation, such as Dynamic Factor Models and Ridge regressions and sparse representations, such as LASSO regression. All these models are adapted to take into account the linear dependency of the macroeconomic time series.

Moreover, to estimate the hyperparameters of these models, including the EWPCA, we propose a new procedure called “brute force”. This method allows us to treat all the hyperparameters of the model uniformly and to take the longitudinal feature of the time-series data into account.

Our findings can be summarized as follows. First, the “brute force” method to estimate the hyperparameters is more stable and gives better forecasting performances, in terms of MSFE, than the traditional criteria used in the literature to tune the hyperparameters. This result holds for all samples sizes and forecasting horizons. Secondly, our two-step forecasting procedure enhances the forecasts’ interpretability. Lastly, the EWPCA leads to better forecasting performances, in terms of mean square forecast error (MSFE), than the other sparse and dense methods or naïve benchmark, at different forecasts horizons and sample sizes.

Keywords: Variable selection, High-dimensional time series, Dynamic factor models, Shrinkage methods, Cross-validation

JEL Classification: C22, C52,C53,C55

Suggested Citation

Andreini, Paolo and Ceci, Donato, A Horse Race in High Dimensional Space (February 14, 2019). CEIS Working Paper No. 452, Available at SSRN: https://ssrn.com/abstract=3334458 or http://dx.doi.org/10.2139/ssrn.3334458

Paolo Andreini (Contact Author)

University of Rome Tor Vergata ( email )

Via di Tor Vergata
Rome, Lazio 00133

Donato Ceci

Bank of Italy ( email )

Via Nazionale 91
Rome, 00184

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