Random Walk

Most of economic and financial time series have a nonstationary behavior. There are different types of nonstationary processes, such as those with stochastic trend and those with deterministic trend. In practice, it can be quite difficult to distinguish between the two processes. In this paper, we compare random walk and determinist trend processes using sample autocorrelation, sample partial autocorrelation and periodogram based metrics.

We survey the current status of the list of questions related to the favourite (or: most visited) sites of simple random walk on Z, raised by Pál Erd˝os and Pál Révész in the early eighties. ... Let (S(n), n ∈ Z+) be a simple symmetric random walk on Z with S(0) = 0. Define

We present a continuous extension of the recent Monte Carlo entropic method for sampling a density of states restricted in dimensionless macroscopic parameters. The method performs a random walk through a two-dimensional macrostate space and provides complete ...

In this paper we examine four different approaches in trading rules for stock returns. More specifically we examine the popular procedures in technical analysis, which are the moving average and the Moving Average Convergence-Divergence (MACD) oscillator. The third approach is the simple random walk autoregressive model and the fourth model we propose is a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) regression with wavelets decomposition and Monte- Carlo simulations algorithm developed in MATLAB. We examine five major stock market index returns for a testing forecasting period of 10 days ahead. We conclude that moving average and MACD might lead to net profits, but not in all cases, therefore are not consistent procedures. Furthermore, moving average 1-30 provides the best results. On the other hand random walk autoregressive model leads in all cases to net losses. Finally, the model we propose not only leads always to net profits, but also to significant highe...

The purpose of this paper is to investigate random walk in HongKong stock exchange. The unit root, autocorrelation and the variance ratio tests are applied, using daily data on returns of two indexes in the period 1997:7 to 2012:12. For two indexes, the null hypothesis of random walk is rejected and therefore the markets are no weak-form efficiency.

Manifold learning has been successfully used for finding dominant factors (low-dimensional manifold) in a high-dimensional data set. However, most existing manifold learning algorithms only consider one manifold based on one dissimilarity matrix. For utilizing multiple manifolds, a key question is how different pieces of information can be integrated when multiple measurements are available. Amari proposed α-integration for stochastic model integration, which is a generalized averaging method that includes as a special case arithmetic, geometric, and harmonic averages. In this paper, we propose a new generalized manifold integration algorithm equipped with α-integration, manifold α -integration (MAI). Interestingly, MAI can be shown to be a generalization of other integration methods (that may or may not use manifolds) like kernel fusion or mixture of random walk. Our experimental results also confirm that integration of multiple sources of information on individual manifolds is superior to the use of individual manifolds separately, in tasks including classification and sensorimotor integration.

... Although this approach has been very successful, up to now the related ideas (multifractality ... shown in (b)]. De-pending on the parameters b, different structures with arbitrary ... proper-ties can be investigated by the corresponding methods developed for such geometrical objects. ...

ABSTRACT
The responsiveness of the market financial instruments in terms of prices to reflect market information and the inability of information privileged market participant(s) to out-perform other counterparts pose the quest to test whether the strong form of market efficiency prevail in the Nigerian capital market or not. With the extraction of the returns on 240 stocks from the database of the Nigerian Stock Exchange (NSE), a comparison was made between a constructed random portfolio and a 3-year annualized average return on the portfolios of the mutual fund industry. In this empirical study, the analysis deduced that mutual funds were unable to out-perform the random portfolios created from the index stocks, which thus implies that the strong form of market efficiency holds in the Nigerian Capital Market. Nonetheless, profound analysis on stock volatility risk is essential to avoid substantial loss in the stock market.
Keywords: Market Efficiency, Capital Market, Nigerian Stock Exchange (NSE) Stocks, Information, Portfolio, Random Walk, Mutual Funds.