## Are exchange rate movements predictable in Asia-Pacific.

This article extends and generalizes the variance-ratio (VR) statistic by employing an estimator of the asymptotic covariance matrix of the sample autocorrelations. The estimator is consistent under the null for general classes of innovations exhibiting statistical dependence including exponential generalized autoregressive conditional heteroskedasticity and non-martingale difference sequence.

We show that these residuals form a martingale difference sequence and that the unconditional variance of these residuals is strictly positive and bounded by the expected value of its conditional variance. We compare the class of MAR Models to the class of GARCH models and observed that both the GARCH type models andMAR models can be cast into.

In probability theory, a martingale difference sequence (MDS) is related to the concept of the martingale.A stochastic series X is an MDS if its expectation with respect to the past is zero. Formally, consider an adapted sequence on a probability space. is an MDS if it satisfies the following two conditions:, and, for all .By construction, this implies that if is a martingale, then will be an.

On the central and local limit theorem for martingale difference sequences Let.that the rate of convergence in this central limit theorem is of order n. On Berry--Esseen bounds for non-instantaneous filte. martingale decomposition to prove the central limit theorem for instantaneous .the rate of convergence, we shall combine the martingale method proposed in.Convergence dans le Th.

The hypothesis that stock index returns form a martingale difference sequence (MDS) is tested for 10 European emerging stock markets: the Czech Republic, Estonia, Hungary, Malta, Poland, Russia, the Slovak Republic, Slovenia, Turkey and the Ukraine, using joint variance ratio tests based on signs and the wild bootstrap, for the period beginning in January 1998 and ending in September 2007.

This paper examines the weak-form efficiency of the global gold markets with specific focus on the random walks (RWS) and martingale difference sequence (MDS) hypotheses, and consequently, investigates the extent to which predictability or non-predictability of global daily spot gold price return series behaviour can be explained by volatilities in macroeconomic fundamentals.

Traditional autocorrelation and variance ratio tests are based on serial uncorrelatedness rather than martingale difference. As such, they do not capture potential nonlinearity-in-mean behavior, which could lead to misleading inferences in favor of the martingale hypothesis. This paper employs various parametric and nonparametric nonlinear models as well as several model comparison criteria to.