Three Essays on Multi-step forecasting with Partial Least Squares.

Summary In this thesis, we compare IMS, DMS and PLS forecasts at multiple horizons, focusing on the combinatorial properties of PLS. We build on an interesting paper by Franses & Legerstee (2010), which suggests how the so-called partial least squares (PLS) method can be considered, in the context of multi-step forecasting, as an intermediate technique between IMS and DMS. In fact, rather than an "intermediate", we like to think of PLS as a form of combination of IMS and DMS.This thesis consists of four chapters.In Chapter 1, we provide a review of the literature that serves as background for the following chapters. In Chapter 2, we explore the functionality of PLS as a combination of IMS and DMS. We study the properties of PLS using an algorithm suggested by Garthwaite (1994).We investigate the relationship between IMS, DMS and PLS and compare the accuracy of their predictions at several horizons. We analyze the combinatorial properties of PLS in multistage forecasting using a simple AR model (2). To compare forecasting performance, we evaluate their asymptotic properties under well-specified and misspecified models. We confirm our analytical study through extensive simulations of the relative forecast accuracy of different multistage forecasting techniques. Through these simulations, we support the asymptotic analysis and investigate the conditions that make PLS better than IMS or DMS.In Chapter 3, we conduct an empirical study of multi-step forecasting based on univariate AR models and focus on the 121 monthly macroeconomic time series in the U.S. We provide an empirical analysis to determine the circumstances that make PLS preferable to IMS or DMS. For easier comparison with the literature, we follow Marcellino et al. (2006) and McCracken & McGillicuddy (2019) in many respects. In addition, we extend their results in some directions, such as path prediction evaluation, alternative measurement techniques, and different subsamples.We explore the benefits in relation to the persistence of the series measured by the degree of fractional integration.Through this empirical analysis, we reconfirm the results of previous studies and discover several new facts: (i) the relative advantages of PLS over IMS tend to disappear as the forecast horizon expands. (ii) PLS is generally better when the model uses short lags. and (iii) PLS performs better than IMS when the data undergo periods of high volatility.The final chapter extends Chapter 3 to multivariate models. We compare a brief analytical study of the rationale for PLS and then empirically compare the forecasting performance of IMS, IMS, and DMS in the context of bivariate forecasting models. For each forecasting model, we generate and evaluate forecasts over a single horizon and over trajectories (ranges of horizons). Our results confirm those of the univariate models: PLS is favored in the short run, but the crucial issue is data persistence. In this respect, the data for the nominal prices, wages and money group show a form of persistence that does not clearly follow an I (1) or I (2) trend and produces much better PLS performance. Overall, we also find that PLS is generically preferred to DMS, so it should be an alternative for the practitioner whenever direct forecasting techniques can be considered.