Elsevier

International Journal of Forecasting

Volume 37, Issue 3, July–September 2021, Pages 1085-1091
International Journal of Forecasting

Forecasting exchange rates with elliptically symmetric principal components

https://doi.org/10.1016/j.ijforecast.2020.11.007Get rights and content

Abstract

We extract elliptically symmetric principal components from a panel of 17 OECD exchange rates and use the deviations from the components to forecast future exchange rate movements, following the method in Engel et al. (2015). Instead of using standard factor models, we apply elliptically symmetric principal component analysis (ESPCA), introduced by Solat and Spanos (2018), which captures both contemporaneous and temporal co-variation among the exchange rates. We find that ESPCA is more accurate than forecasts generated by existing standard methods and the random walk model, with or without including macroeconomic fundamentals.

Introduction

The random walk model is hard to beat in forecasting exchange rates, and this finding has more or less survived the numerous studies since Meese and Rogoff (1983b) and Meese and Rogoff (1983a). The model essentially forecasts that the log level of an exchange rate remains the same in the future, and this seemingly simple model beats well-founded, sophisticated models of exchange rates that make use of economic fundamentals like output, interest rates, or inflation rates. It is a well-established finding for horizons from one quarter to three years, while the results are more ambiguous for longer horizons.1

Instead of looking for new fundamentals or econometric methods to beat the random walk, some recent papers look for predictability in the exchange rates themselves. In particular, factors are extracted from a panel of exchange rates, and the deviations of the exchange rates from the factors are used to forecast their future changes.2 Engel et al. (2015) first suggested this new direction and found mixed results. They extracted three factors from a panel of 17 exchange rates (with the US dollar as the base currency), and they found that the factors improved the random walk only for long horizons during the period 1973Q1–2007Q4.

This paper follows the same line of research and extracts factors in a simple and intuitive way using an updated sample from 1973Q1 to 2017Q4. We adopt a more general approach and make use of both temporal (over time) and contemporaneous (synchronous or cross-section) covariations by using elliptically symmetric principal component analysis (ESPCA), proposed in Solat and Spanos (2018).

Though we are agnostic on what the factors represent, we believe that we are better at capturing unobserved fundamentals that make exchange rates persistent and correlated through time. Indeed, we find that relaxing the assumptions imposed on classical principal components analysis (PCA) substantially improves the forecasting performance of the factors in Engel et al. (2015) by beating the random walk at all horizons and in all sample periods.

We use ESPCA to extract the elliptically symmetric principal components (ESPCs) and compare our forecasting performance with that in Engel et al. (2015), using the updated data from 1973Q1 to 2017Q4. In addition, in a shorter sample, we compare our results using only ESPCs with those in Engel et al. (2015) using both factors and auxiliary macroeconomics fundamentals.

Section snippets

Elliptically symmetric principal component analysis

The idea behind all methods of factorization is to capture the most variations in the data using a few factors with some properties of interest, e.g., independence or orthogonality. Some of the popular factor models are principal component analysis (PCA) and factor analysis (FA), both of which aim at capturing the most variation in the cross-section data through decomposition of the contemporaneous covariance matrix in a linear regression model.

Solat and Spanos (2018) propose elliptically

Data

We use end-of-quarter data on the log nominal bilateral US dollar exchange rates of 17 OECD countries from 1973Q1 to 2017Q4.4 The countries are Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Japan, Italy, Korea, Netherlands, Norway, Spain, Sweden, Switzerland, and the United Kingdom. Table 2 presents a descriptive statistical summary of the data.

We construct three sets of out-of-sample forecasts. First,

Conclusion

In this paper, we showed that using factors that incorporate both contemporaneous and temporal correlations substantially improves out-of-sample forecasting performance. Exchange rates were found to converge to such factors, while the convergence was not as clear when traditional methods of extracting factors were used (with or without including macroeconomic fundamentals). What do these factors represent? What are the underlying economic forces? Clearly, these questions go beyond the

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