It is obvious that forecasts are of great importance and widely used in economics and finance. Quite simply, good forecasts lead to good decisions. The importance of forecast evaluation and combination techniques follows immediately-- forecast users naturally have a keen interest in monitoring and improving forecast performance. More generally, forecast evaluation figures prominently in many questions in empirical economics and finance, such as: Are expectations rational? (e.g., Keane and Runkle, 1990; Bonham and Cohen, 1995) Are financial markets efficient? (e.g., Fama, 1970, 1991) Do macroeconomic shocks cause agents to revise their forecasts at all horizons, or just at short- and medium-term horizons? (e.g., Campbell and Mankiw, 1987; Cochrane, 1988) Are observed asset returns "too volatile"? (e.g., Shiller, 1979; LeRoy and Porter, 1981) Are asset returns forecastable over long horizons? (e.g., Fama and French, 1988; Mark, 1995)

this article we review some of these developments. For a given time series X 1 ; . . . ; X n , nonparametric techniques are used to analyze various features of interest. Generally, the idea underlying many of these techniques is that the characteristic of interest is allowed to have a general form which is approximated increasingly precisely with growing sample size. For example, if a process is assumed to be composed of periodic components, a general form of spectral density may be assumed which can be approximated with increasing precision when the sample size gets larger. Similarly, if the autocorrelation structure of a stationary process is of interest the spectral density may be estimated as a summary of the second moment properties. A brief review of this classical method of nonparametric time series analysis is given in Section 2. Because the final objective of many time series analyses is prediction, it is often of interest to study the conditional means, conditional variances or complete conditional densities in some period, given the past of the process. When a point prediction is the final objective, an estimate of some conditional mean may be desired, while the conditional variances are needed if interval forecasts or assessments of future volatility are desired. Moreover, if higher order moments of a series are potentially important, the focus may be on estimating the complete conditional density. In order to analyze the conditional mean nonparametrically one may, for instance, start from a model of the form

Abstract not found

: In order to obtain exact distributional results without imposing restrictive parametric assumptions, several rank counterparts of the Dickey-Fuller statistic are considered. In particular, a rank counterpart of the score statistic is suggested which appears to have attractive theoretical properties. Assuming i.i.d. errors, an exact test is obtained for a random walk model with drift and under assumptions similar to Phillips & Perron (1988) the test is asymptotically valid. In a Monte Carlo study the rank tests are compared with their parametric counterparts. The research for this paper was carried out while the second author was a guest of the "Sonderforschungsbereich 373", Humboldt University Berlin. We wish to thank the "Deutsche Forschungsgemeinschaft" (DFG) for financial support. Furthermore, the comments and suggestions of the Editor and an anonymous referee are gratefully acknowledged. 1 Introduction Unit root tests play an important role in the analysis of economic time s...

The present paper introduces new sign tests for testing for conditionally symmetric martingaledifference assumptions as well as for testing that conditional distributions of two (arbitrary) martingale-difference sequences are the same. Our analysis is based on the results that demonstrate that randomization over zero values of three-valued random variables in a conditionally symmetric martingale-difference sequence produces a stream of i.i.d. symmetric Bernoulli random variables and thus reduces the problem of estimating the critical values of the tests to computing the quantiles or moments of Binomial or normal distributions. The same is the case for randomization over ties in sign tests for equality of conditional distributions of two martingale-difference sequences. The paper also provides sharp bounds on the expected payoffs and fair prices of European call options and a wide range of path-dependent contingent claims in the trinomial financial market model in which, as is well-known, calculation of derivative prices on the base of no-arbitrage arguments is impossible. These applications show, in particular, that the expected payoff of a European call option in the trinomial model with log-returns forming a martingale-difference sequence

We propose a class of simple rank-based tests for the null hypothesis of a unit root. This class is indexed by the choice of a reference density g, which needs not coincide with the unknown actual innovation density f. The validity of these tests, in terms of exact finite sample size, is guaranteed by distribution-freeness, irrespective of the value of the drift and the actual underlying f. When based on a Gaussian reference density g, our tests (of the van der Waerden form) perform uniformly better, in terms of asymptotic relative efficiency, than the Dickey and Fuller test—except under Gaussian f, where they are doing equally well. Under Student t3 density f, the efficiency gain is as high as 110%, meaning that Dickey-Fuller requires over twice as many observations as we do in order to achieve comparable performance. This gain is even larger in case the underlying f has fatter tails; under Cauchy f, where Dickey and Fuller is no longer valid, it can be considered infinite. The test associated with reference density g is semiparametrically efficient when f happens to coincide with g, in the ubiquitous case that the model contains a non-zero drift. Finally, with an estimated density ˆ f (n) substituted for the reference density g, our tests achieve uniform (with respect to f) semiparametric efficiency.

This paper presents a source of statistical distortions induced by present value models that may significantly affect statistical inference in the predictive regression both in finite samples and asymptotically. We show both analytically and by simulation that the regression-based tests including optimal robust tests such as Jansson and Moreira’s conditional test and Campbell and Yogo’s Q-test may suffer from lack of power in the local-to-unity models of the regressor persistence and the discount factor. We also analyze a nonparametric unbiasedness test based on the variance ratio of excess returns that is immune to persistence distortions as well as to some power limitations inherent in regression tests. We provide empirical evidence that supports our assumptions and predictions: (i) the nonparametric unbiasedness test tends to reject more often than the regression-based tests for the unbiased hypothesis of forward exchange rates; (ii) it is not uncommon to observe statistically insignificant negative estimates in the predictive regression when the unbiased hypothesis of foreign exchange rates is not rejected. Then we can conclude that an statistical phenomenon cannot be the main reason for predictable excess returns in foreign exchange markets. Keywords: variance ratio test, regression-based test, Q-test, JM conditional test, small sample biases, predictability of excess returns.

This paper develops a test of contagion in financial markets by considering a measure of co-movement based on the notion of common cycles. In contrast to studies based on simple correlation analysis, as proposed by Forbes and Rigobon (2001, 2002), we rely on the concept of serial correlation common feature (SCCF) to detect short run co-movements between a set of time series. Monte Carlo simulations suggest that robust GMM and nonparametric orthogonality tests are helpful in testing for the stability in the mechanism of crisis transmission across countries even with volatile series. In order to test whether international transmission mechanisms change during financial crisis, we apply our methodology to the international effects of the 1994 Mexican peso crisis and the 1997 Asian crisis. Our results can be interpreted as evidence of a high level of market co-movement during all states of the world and, therefore, question the hypothesis of shift-contagion in the international transmission of financial shocks during the 1997 Asian crisis, and to a lesser extend, the 1994 Mexican peso crisis. This is in line with the findings of Forbes and Rigobon (2002), according to which there is ”no contagion, only interdependence”; large cross-market linkages after a

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