Essays in time series econometrics and machine learning

Ballarin, Giovanni

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URN:	urn:nbn:de:bsz:180-madoc-673309
Dokumenttyp:	Dissertation
Erscheinungsjahr:	2024
Ort der Veröffentlichung:	Mannheim
Hochschule:	University of Mannheim
Gutachter:	Trenkler, Carsten
Datum der mündl. Prüfung:	24 Mai 2024
Sprache der Veröffentlichung:	Englisch
Einrichtung:	Außerfakultäre Einrichtungen > GESS - CDSE (VWL)
Fachgebiet:	330 Wirtschaft
Freie Schlagwörter (Englisch):	econometrics , time series analysis , machine learning
Abstract:	This dissertation collects three works developed on the broad topic of time series analysis, with a specific focus on machine learning, non- and semi-parametric methods, and regularization. In particular, the discussion will take an econometric perspective with respect to the three key problems of estimation, forecasting and inference. Chapter 1 develops a new ML approach to forecast economic time series - focusing on US GDP growth - within an environment consisting of many series with observations sampled at different frequencies. We introduce a method that is based on a reservoir computing approach, which, broadly speaking, leverages the universal approximation properties of nonlinear state-space models with random coefficients matrices. Our proposed scheme is computationally efficient, empirically effective - reaching or surpassing state-of-the-art forecasting performance - and straightforward to implement even when there are many different data frequencies. Chapter 2 deals instead with the important question of regularization in the estimation of linear time series. Vector autoregressive models (VARs) are a fundamental benchmark and foundational analytical tool of modern econometrics. Yet, even in moderate data environments with a few dozen series, estimation of VARs can be severely impacted by efficiency issues - that is, too many parameters need to be recovered compared to the sample size. This is true even in settings that do not fall within the category of high-dimensional processes. Drawing a comparison with Bayesian methods, I propose to apply anisotropic ridge regression as an estimation procedure in order to effectively exploit prior information or beliefs on the structure of the VAR model. The theory for inference on impulse responses functions and cross-validation is developed, and in simulations I find that the trade-off of ridge penalization can be positive whenever one is correctly informed about the nature of the underlying data generating process. Finally, in Chapter 3 I provide a semi-nonparametric approach for the estimation of impulse responses of nonlinear autoregressive models. Impulse response functions (IRFs) are widely studied objects in macroeconometrics, because they quantify the response of a model economy to an unforeseen shock. For example, central banks are often interested in studying the potential effects of credibly exogenous changes in monetary policy over short and long horizons. If one also wants to incorporate nonlinear relationships in a model, I prove that estimating the linear and nonlinear (functional) autoregressive coefficients with a semi-nonparametric series approach is a uniformly consistent strategy. In turn, this allows the constructions asymptotically consistent nonlinear IRF estimates - meaning that IRFs can be correctly recovered in large samples. The empirical applications I provide showcase the potential impact of nonlinear IRFs on policy: comparing pointwise linear and nonlinear estimates suggest that linear models can underestimate to varying degrees the negative effects of contractionary monetary policy. This, in turn, provides evidence that proper estimation of nonlinear interactions may lead to better quantitative analysis of macroeconomic dynamics.