No free lunch for cross validation

It is known theoretically that an algorithm cannot be good for an arbitrary prior. We show that in practical terms this also applies to the technique of ``cross validation'', which has been widely regarded as defying this general rule. Numerical examples are analysed in detail. Their implications to researches on learning algorithms are discussed.

Post-Bretton Woods evidence on PPP under different exchange rate regimes

This article investigates the behaviour of exchange rates across different regimes for a post-Bretton Woods period. The exchange rate regime classification is based on the classification of Frankel et al. (2004) who condensed the 10 categories of exchange rate regimes reported by the International Monetary Fund (IMF) into three categories. Panel unitroot tests and panel cointegration are used to examine the Purchasing Power Parity (PPP) hypothesis. The latter test is used to check for both the weak and strong forms of PPP. The panel unit-root tests show no evidence of PPP and suggest there is no difference in the behaviour of exchange rates across different regimes. However, failure to detect PPP across any of the regimes could be due to structural breaks. This assumption is reinforced by the results of cointegration tests, which suggest that there exists at least a weak form of PPP for the different regimes. The evidence for strong PPP decreases as the exchange rate regime moves away from a flexible exchange rate regime.

Stock price reaction following large one-day price changes: UK evidence

We examine the short-term price reaction of 424 UK stocks to large one-day price changes. Using the GJR-GARCH(1,1), we find no statistical difference amongst the cumulative abnormal returns (CARs) of the Single Index, the Fama–French and the Carhart–Fama–French models. Shocks bigger or equal to 5% are followed by a significant one-day CAR of 1% for all the models. Whilst shocks smaller or equal to -5% are followed by a significant one-day CAR of -0.43% for the Single Index, the CARs are around -0.34% for the other two models. Positive shocks of all sizes and negative shocks maller or equal to -5% are followed by return continuations, whilst the market is efficient following larger negative shocks. The price reaction to shocks is unaffected when we estimate the CARs using the conditional covariances of the pricing variables.