Are gold markets weak form efficient? Evidence from China, India and Russia

The main purpose of this study is to determine the weak form efficiency of the emerging gold markets such as China, India and Russia with the special focus on testing random walks (RWS) and martingale difference sequence (MDS) hypotheses during different periods of time. This study uses biased free statistical techniques such as runs test, parametric variance ratio tests and recent modified non-parametric variance ratio tests based on ranks and signs by using daily spot gold prices from January 12, 1993 to October 28, 2016. Findings of the study suggest that Russian gold market is weak form efficient throughout the period whereas other two markets are found weak form efficient during second sub period only that is, January 2000 to December 2005.

Exponential Inequalities for Bounded Random Variables

In the paper, several precise exponential inequalities for the sums of bounded or semi-bounded random variables are established, which involve independent random variables, martingale difference sequence, negatively associated random variables, Markov chains.

Operator Fractional Brownian Motion and Martingale Differences

It is well known that martingale difference sequences are very useful in applications and theory. On the other hand, the operator fractional Brownian motion as an extension of the well-known fractional Brownian motion also plays an important role in both applications and theory. In this paper, we study the relation between them. We construct an approximation sequence of operator fractional Brownian motion based on a martingale difference sequence.

Convergence Rates in the Strong Law of Large Numbers for Martingale Difference Sequences

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).

ON THE CENTRAL AND LOCAL LIMIT THEOREM FOR MARTINGALE DIFFERENCE SEQUENCES

Let [Formula: see text] be a Lebesgue space and T: Ω→Ω an ergodic measure-preserving automorphism with positive entropy. We show that there is a bounded and strictly stationary martingale difference sequence defined on Ω with a common nondegenerate lattice distribution satisfying the central limit theorem with an arbitrarily slow rate of convergence and not satisfying the local limit theorem. A similar result is established for martingale difference sequences with densities provided the entropy is infinite. In addition, the martingale difference sequence may be chosen to be strongly mixing.