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Abstract

The ability to form accurate predictions of economic and financial variables is of paramount importance to government bodies, international organisations, and financial institutions alike. From forecasting macroeconomic variables that inform policy decisions to quantitative risk management, the practice of forecasting is widespread. Therefore, it constitutes a crucial area of econometrics, with a particular emphasis on (i) developing new forecasting methods and (ii) evaluating their performance. This thesis contributes to both these aspects of the forecasting literature.

The difficulty of identifying new forecasting models and selecting between them is exemplified by the challenging task of predicting foreign exchange rates. Many structural models derived from macroeconomic theory have been shown to be no more accurate than a random walk (Rossi, 2013). In other words, they have no predictive power. Numerous attempts have been made to identify the underlying reasons for this, with one possible explanation being that the parameters in foreign exchange rate models are time-varying [see, for example, Rossi (2006), Bekiros (2014), or Byrne et al. (2018)]. Indeed, survey evidence of UK and US based foreign exchange traders also indicates that their reliance on macroeconomic variables changes over time (Cheung and Chinn, 2001; Cheung et al., 2004). The first chapter of this thesis adds to this literature by analysing the unstable relationship between exchange rates and macroeconomic fundamentals through the lens of a factor model with time-varying loadings. Leveraging the findings of Mikkelsen et al. (2019), we estimate a theoretical model in which macroeconomic fundamentals are treated as latent factors. These factors are extracted as principal components from a novel real-time database that we curated for this chapter. The database encompasses 272 monthly datasets, each comprising over 100 variables from 15 countries. We have made this database publicly available as a contribution of this chapter. To gauge the significance of time-variation, we compare the out-of-sample performance of our model to a factor model with constant loadings and a random walk. Our results demonstrate that the time-varying model consistently outperforms the constant loadings benchmark and even the random walk in multiple instances.

Building on the out-of-sample evaluation conducted in the first chapter, the second chapter introduces a new statistical test to evaluate forecasts. One of the earliest tests for this purpose is proposed by Diebold and Mariano (1995) and compares two primitive forecasts without considering the underlying models that generated them. However, when employing a forecast testing procedure for model selection, it is imperative to address potential concerns such as estimation errors, nested models, and forecast step sizes. In a seminal paper, Giacomini and White (2006) introduce the notion of Conditional Predictive Ability and a testing framework that enables the discrimination between various underlying forecasting methods. Since then, a number of alternative testing procedures have been introduced [see Clark and McCracken (2013) for a survey]. However, existing tests are mostly univariate and only evaluate two competing forecasts at a time. This is problematic because in many econometric applications dependence between variables and forecasting models is the norm. This, in turn, introduces dependencies between univariate test statistics and p-values, as shown in chapter two of this thesis. In consequence, such tests cannot be evaluated individually, which motivates the development of multivariate forecast tests that account for dependence (Qu et al., 2021). The novel approach we introduce in the second chapter combines univariate forecast accuracy tests, without making any assumptions regarding the joint distribution of the test statistics. Our approach builds upon recent advancements in the statistical literature on the combination of dependent p-values (Vovk and Wang, 2020). It allows for the implementation of whichever tests are most appropriate in a given scenario and evaluates whether predictive ability holds in the cross-section. We specify a global null hypothesis that is defined as the intersection of all individual null hypotheses, while also accounting for false discovery and dependence. We establish the statistical size properties of the test in finite samples as well as asymptotically for large cross-sections, and demonstrate its consistency in the asymptotic case. To examine the test further, we report extensive Monte-Carlo simulation results and conduct an empirical application using a large dataset of 84 daily exchange rates.

Together, the first and second chapter have inspired the focus of the third chapter. Although it is widely recognised that individual models, such as predictive stock return regressions, exhibit predictive power only during certain periods (Timmermann, 2008), very few tests consider the possibility that the relative predictive ability of different models may also vary over time. The first test for time-varying predictive ability is proposed by Giacomini and Rossi (2010) and can be viewed as a rolling t-test on the loss differential between forecasts. More recently, Odendahl et al. (2022) introduce a time-varying predictive ability test that accounts for state dependence. We add to this literature by proposing two novel forecast evaluation tests that consider the issue of time-variation in conjunction with dependencies between forecasts. The first test is a time-varying analogue to the Conditional Predictive Ability test proposed by Giacomini and White (2006), which evaluates the null hypothesis conditional on information up to the previous period. The second test, called Total Predictive Ability test, evaluates the null hypothesis conditional on the full-sample information set. Both tests can be applied in a univariate or multivariate framework, where dependencies between forecasts are explicitly modelled. To assess the performance of the tests, we conduct Monte-Carlo simulations and apply the tests in an evaluation of intraday volatility forecasts.

Publication Type:	Thesis (Doctoral)
Additional Information:	Chapter 1 of this thesis contains a published open access article under the terms of the Creative Commons Attribution-Non Commercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes. Please see the reference below: Hillebrand, E. Mikkelsen J. Spreng, L. and Urga, G., Exchange Rates and Macroeconomic Fundamentals: Evidence from Time-Varying Factor Loadings, Journal of Applied Econometrics, forthcoming, https://doi.org/10.1002/jae.2984 Chapter 2 of this thesis contains an open access article distributed under the terms of the Creative Commons CC BY license, which permits unrestricted use, distribution, reproduction in any medium, provided the original work is properly cited. Please see the reference below: Spreng, L. and Urga G., Combining p-Values for Multivariate Predictive Ability Testing, Journal of Business and Economic Statistics, forthcoming, https://doi.org/10.1080/07350015.2022.2067545
Subjects:	H Social Sciences > HG Finance
Departments:	Bayes Business School > Bayes Business School Doctoral Theses Bayes Business School > Finance Doctoral Theses

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