Martingale difference sequence variance - The Variance Ratio Statistic at Large Horizons

We study the complete convergence and complete moment convergence for martingale difference sequence. Especially, we get the Baum-Katz-type Theorem and Hsu-Robbins-type Theorem for martingale difference sequence. As a result, the Marcinkiewicz-Zygmund strong law of large numbers for martingale difference sequence is obtained. Our results generalize the corresponding ones of Stoica (2007, 2011).

Abstract. 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.

An MDS is just a discrete-time martingale with mean zero. In particular, its increments are uncorrelated. (The martingale assumption is an intermediate condition between serially uncorrelated and independence.) So a rejection by a serial correlation test would also reject the MDS assumption.

Martingale Difference Sequences. In the last discussion, we saw that the partial sum process associated with a sequence of independent, mean 0 variables is a martingale. Conversely, every martingale in discrete time can be written as a partial sum process of uncorrelated mean 0 variables. This representation gives some significant insight into.

This paper addresses the following classical question: Given a sequence of identically distributed random variables in the domain of attraction of a normal law, does the associated linear process.

For example, the efficient market hypothesis implies that asset returns are an martingale difference sequence (m.d.s.), and so are serially uncorrected. More generally, rational expectations theory implies that the expectational errors of the economic agent are serially uncorrelated. In this article we first discuss various tests for serial correlation, for both estimated model residuals and.

Perhaps the most popular empirical technique used in checking the existence of a martingale difference sequence in an observed realization of a time series is the so-called variance ratio test.

We show this by estimating these models and deriving expected returns from them and then testing whether the difference between observed and expected returns is a martingale difference sequence. We use variance ratio and rescaled range tests which we modify to account for the expected returns being functions of estimated parameters. We also use a weighted quantilogram test based on a bootstrap.

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.

STAT331 Martingale Central Limit Theorem and Related Results In this unit we discuss a version of the martingale central limit theorem, which states that under certain conditions, a sum of orthogonal martingales con-verges weakly to a zero-mean Gaussian process with independent increments. In subsequent units we will use this key result to nd the asymptotic behavior of estimators and tests.

This study empirically re-examines the weak form efficient markets hypothesis of the Ghana Stock Market using a new robust non-parametric variance-ratios test in addition to its parametric alternative. The main finding is that stock returns are conclusively not efficient in the weak form, neither from the perspective of the strict random walk nor in the relaxed martingale difference sequence.

This article proposes using variance-ratio tests based on the ranks and signs of a time series to test the null that the series is a martingale difference sequence. Unlike conventional variance-ratio tests, these tests can be exact. In Monte Carlo simulations, I find that they can also be more powerful than conventional variance-ratio tests. I apply the proposed tests to five exchange-rate.

Testing the martingale difference hypothesis in CO2.

Are exchange rate movements predictable in Asia-Pacific.