In this article we test the random walk hypothesis for weekly stock market returns by comparing variance estimators derived from data sampled at different frequencies. The random walk model is strongly rejected for the entire sample period (1962--1985) and for all subperiod for a variety of aggregate returns indexes and size-sorted portofolios. Although the rejections are due largely to the behavior of small stocks, they cannot be attributed completely to the effects of infrequent trading or timevarying volatilities. Moreover, the rejection of the random walk for weekly returns does not support a mean-reverting model of asset prices.

This paper examines the effects of uncertainty about the stock return predictability on optimal dynamic portfolio choice in a continuous time setting for a long horizon investor. Uncertainty about the predictive relation affects the optimal portfolio choice through dynamic learning, and leads to a state-dependent relation between the optimal portfolio choice and the investment horizon. There is substantial market timing in the optimal hedge demands, which is caused by stochastic covariance between stock return and dynamic learning. The opportunity cost of ignoring predictability or learning is found to be quite substantial. How much should a “long horizon ” investor allocate to equity? The conventional wisdom says that a long horizon investor should invest more in equity because, over long horizons, aboveaverage returns tend to offset below-average returns. This is the notion of “time diversification.” Samuelson (1989, 1990), among others, has argued that the notion of “time diversification ” is spurious: when stock returns are i.i.d., for example, the optimal portfolio is independent of the horizon for an investor with an isoelastic utility function. When stock returns are predictable, however, the optimal stock allocation does depend on the investment horizon, even if the investor has an isoelastic utility.

This paper presents a methodology for the calculation of bilateral equilibrium exchange rates for a panel of currencies in a way that guarantees consistency at the global level. A theoretical model, which encompasses the balance of payments and the Balassa-Samuelson approaches to real exchange rate determination, shows that the stock of net foreign assets and the evolution of sectoral prices are the fundamentals underlying the behavior of the real exchange rate. An unobserved components methodology in a cointegration framework allows us to identify a time-varying equilibrium real exchange rate, and deviations from this equilibrium provide an estimate of the degree of multilateral misalignment. Finally, an algebraic transformation converts these multilateral equilibrium real rates into bilateral equilibrium nominal rates. The results uncover, inter alia, that by the start of Stage III of EMU the euro was significantly undervalued against the dollar and even more against the pound, but overvalued relative to the yen. Regarding EMU currencies, it is shown that the four major EMU currencies locked their parities with the euro at a rate close to equilibrium. 1

We propose in this paper a likelihood-based framework for cointegration analysis in panels of a xed number of vector error correction models. Maximum likelihood estimators of the cointegrating vectors are constructed using iterated Generalized Method of Moments estimators. Using these estimators we construct likelihood ratio statistics to test for a common cointegration rank across the individual vector error correction models, both with heterogeneous and homogeneous cointegrating vectors. The corresponding limiting distributions are a summation of the limiting behavior of Johansen (1991) trace statistics. We also incorporate both unrestricted and restricted deterministic components which are either homogeneous or heterogeneous. The proposed framework is applied on a data set of exchange rates and appropriate monetary fundamentals. The test results show strong evidence for the validity of the monetary exchange rate model within a panel of vector error correction models for three major...

We examine the mean-reverting properties of real exchange rates, by comparing the unit root properties of a group of international real exchange rates with two groups of intranational real exchange rates. Strikingly, we find that while the international real rates taken as a group appear mean reverting, the intranational rates are not. This is consistent with the view that while nominal shocks may be mean reverting over the medium term, underlying real factors do generate long-term trends in real exchange rates. [JEL C12, C23, F31] ε+ ε> = y + β( P = P S The proposition that exchange rates are volatile when allowed to float freely has become something of a stylized fact in the international finance literature (see, for example, Frenkel and Mussa, 1980; MacDonald and Taylor, 1992; and Frankel and Rose, 1995). Indeed, the volatility of exchange rates during the recent floating experience has led economists to advocate moving from an international monetary regime based on flexible exchange rates toward one based on greater exchange rate fixity (McKinnon, 1988; Mundell, 1992; and Williamson, 1987) and is also one of the central arguments made by proponents of greater monetary integration in Europe. The volatility of nominal exchange rates has also had implications for the behavior of real exchange rates. In particular, because prices in goods markets are generally regarded as being sticky (certainly in the short run), volatility in nominal exchange rates is transferred into comparable real exchange rates. This violation of purchasing power parity (PPP) may be viewed as a second stylized fact in international finance. = LY ( , i

ABSTRACT: This paper examines whether output per capita in 126 countries is better described as trend or difference stationary using formal statistical tests. Appropriate finite-sample critical values are constructed to evaluate the test results. Depending upon whether one uses solely a test with a trend stationary null, or solely one with a difference stationary null, one obtains very different conclusions regarding the long run dynamics of GDP. This outcome suggests that it is useful to consider the tests complementary, rather than competing. Based on results from both tests, we find that when a definite characterization of GDP can be made, it is very likely to indicate a difference stationary process. However, the likelihood of making definite conclusions does vary positively with both the income level and the quality of data.

There has been serious suspicion of a spurious rejection of the unit roots in panel studies of PPP due to the failure to control for cross-sectional dependence. This article presents evidence of mean-reversion in industrial country real exchange rates in a set up that accounts naturally for cross-sectional dependence, is invariant to the benchmark currency and capable of detecting against regime changes, and actually tests for the null of interest, ie. the purchasing power parity. Our results are based on a KPSS test for the stationarity null generalized in a multivariate random walk plus noise model by Nyblom and Harvey (1998).

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In this paper, we investigate the persistence of British stock returns over the period 1962-98 using the Variance Ratio (VR) test to check for short-range dependence and the Modified Rescaled Range (MRS) test to check for long-range dependence. A central contribution of the paper is that we investigate the role of the great rebound in stock prices in January 1975 and the crash of October 1987. These shocks, which together represent less than 1% of the data fundamentally alter the time series properties of the data, with extreme skewness, excess kurtosis, and ARCH present in the unadjusted data, but absent from much of the shock-purged data. The VR and MRS tests reveal relatively little evidence of persistence in the original data. However, the VR tests exhibit systematic and significant reversals of sign as between the original and the shock-purged data. It appears that stock prices in Britain persistently stayed away from the mean, and then reverted back towards it in just two excepti...

Institut national de la planification et de la statistique (INPS) Since the paper of Rose (1988), a large literature has emerged on testing the stationarity of real interest rates using a variety of econometric procedures. In this study, we emphasize that the low power of standard unit root tests, especially with short data spans, may have caused researchers to incorrectly conclude that the rates are nonstationary. We present new unit root test results for four major ex-post and ex-ante real interest rates using monthly long-horizon data spanning the last century. The principal tenet of our analysis is that with the increased power of the tests, we are able to reject the unit root null hypothesis at the 1 % level of significance, although shocks impinging upon real interest rates are rather persistent, and the half-life is as much as 7.55 years.