A forecast evaluation of PCA-based adaptive forecasting schemes for the EURIBOR swap term structure
In Chapters 1 to 4 we adopt a principal components analysis (PCA) to reduce the dimensionality of the term structure and employ autoregressive (AR) models to forecast principal components which, in turn, are used to forecast swap rates. Arguing in favour of structural variation, we propose data-driven, adaptive model selection strategies based on the PCA/AR model. To evaluate ex-ante forecasting performance for particular rates, distinct forecast features, such as mean squared errors, directional accuracy and directional forecast value, are considered. It turns out that, relative to benchmark models, the adaptive approach offers additional forecast accuracy in terms of directional accuracy and directional forecast value. In Chapter 3 we use the Henrikkson–Merton statistic to measure the economic value of directional forecasts in the sense of Merton (1981). Common approaches to test for the latter value are based on the classical Chi-square–test for independence, Fisher’s exact test or the Pesaran and Timmerman (1992) test for market timing. These tests are asymptotically valid for serially independent observations. Yet, in the presence of serial correlation they are highly oversized as confirmed in a simulation study. We summarize serial correlation robust test procedures and propose a bootstrap approach in Chapter 5. By means of a Monte Carlo study we illustrate the relative merits of the latter. Two empirical applications demonstrate the relevance to account for serial correlation in economic time series when testing for the value of directional forecasts. By doing this, we provide further support for the preferred Median strategy introduced in Chapter 4. Finally, we close with some concluding remarks in Chapter 6. We point out that directional forecasts can provide a convenient framework to assess the economic forecast value when loss functions (or success measures) are properly formulated to account for realized signs and realized magnitudes of directional movements. We discuss a general approach to evaluate (directional) forecasts which is simple to implement, robust to outlying or unreasonable forecasts and which provides an economically interpretable loss/success functional framework. As such, the measure of directional forecast value is a readily available alternative to the commonly used squared error loss criterion.
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