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.

In biological suspensions, the forward light scattering is done mainly by the contribution of the suspended cells. The multiple scattering is almost always unavoidable, its contribution being described by Monte Carlo simulations or by approximate analytical formula. The Monte Carlo approach we propose moves one photon at a time and checks all scattering centers to find, at each simulation step, which one will scatter the photon. The validation of the simulation results is performed by comparing the obtained angular distribution with the predictions of the effective phase function theory reported recently in the literature and with the angle resolved experimental measurements performed on human red blood cells (RBCs) in suspensions at different hematocrits. The results show a good agreement in the small concentration range.

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 ...

We investigate the survival probability ⌽(n,c) of particles performing a random walk on a two-dimensional lattice that contains static traps, which are randomly distributed with a concentration c, as a function of the number of steps n. ⌽(n,c) is analyzed in terms of a scaling ansatz, which allows us to locate quantitatively the crossover between the Rosenstock approximation ͑valid only at early times͒ and the asymptotic Donsker-Varadhan behavior ͑valid only at long times͒. While the existence of the crossover has been postulated before, its exact location has not been known. Our scaling hypothesis is based on the mean value of the quantity S n , the number of sites visited in an n-step walk. We make use of the idea of self-interacting random walks, and a ''slithering'' snake algorithm, available in the literature, and we are thus able to obtain accurate survival probability data indirectly by Monte Carlo simulation techniques. The crossover can now be determined by our method, and it is found to depend on a combination of c and n. It occurs at small ⌽(n,c) values, which is typically the case for large values of n.

Problem statement: The stock exchange market has been one of the most popular investments in the recent past due to its high returns. The market has become an integral part of the global economy to the extent that any fluctuation in this market influences personal and corporate financial lives and the economic health of a country. The daily behavior of the market prices revealed that the future stock prices cannot be predicted based on past movements. Approach: In this study, we analyzed the behavior of daily return of Nigerian stock market prices. The sample included daily market prices of all securities listed in the Nigeria Stock Exchange (NSE). Results: The result from the study provided evidence that the Nigerian stock exchange is not efficient even in weak form and that NSE follow the random walk model. The idealized stock price in the Nigerian stock exchange is a martingale. Conclusion: Martingale defines the fairness or unfairness of the investment and no investor can alter the stock price as defined by expectation.

Using Monte Carlo simulations we examine the diffusive properties of the greedy algorithm in the d-dimensional traveling salesman problem. Our results show that for d = 3 and 4 the average squared distance from the origin r 2 is proportional to the number of steps t. In the d = 2 case such a scaling is modified with some logarithmic corrections, which might suggest that d = 2 is the critical dimension of the problem. The distribution of lengths also shows marked differences between d = 2 and d > 2 versions. A simple strategy adopted by the salesman might resemble strategies chosen by some foraging and hunting animals, for which anomalous diffusive behavior has recently been reported and interpreted in terms of Lévy flights. Our results suggest that broad and Lévy-like distributions in such systems might appear due to dimension-dependent properties of a search space.

Based on reinforced urn process introduced by Muliere, Secchi and Walker we propose a Bayesian nonparametric approach to analyse a design determining the maximum tolerated dose in Phase I clinical trials for new drug development when intrapatient dose escalation is allowed. A predictive distribution of maximum tolerated dose is obtained and its point estimation may consist in the corresponding expected value.

Asymptotic forms for the expected number of distinct sites visited by an n-step random walk, being calculable for many random walks, have been used in a number of analyses of physical models. We describe three recent extensions of the problem, the first replacing the single random walker by N+ m random walkers, the second to the study of a random walk in the presence of a trapping site, and the third to a random walk in the presence of a trapping hyperplane.

This paper presents a chip-level charged device model (CDM) electrostatic discharge (ESD) simulation method. The chiplevel simulation is formulated as a DC analysis problem. A network reduction algorithm based on random walks is proposed for rapid analysis, and to support incremental design. A benchmark with a 2.3M-node VDD net and 1000 I/O pads is checked in 13 minutes, and 10 re-simulations for incremental changes take a total of 9 minutes.

We introduce solvable stochastic dealer models, which can reproduce basic empirical laws of financial markets such as the power law of price change. Starting from the simplest model that is almost equivalent to a Poisson random noise generator, the model becomes fairly realistic by adding only two effects, the self-modulation of transaction intervals and a forecasting tendency, which uses a moving average of the latest market price changes. Based on the present microscopic model of markets, we find a quantitative relation with market potential forces, which has recently been discovered in the study of market price modeling based on random walks.

This paper presents the SILAM dispersion modelling system that has been developed for solving various forward and inverse dispersion problems. The current operational version is based on a Lagrangian dispersion model that applies an iterative advection algorithm and a Monte Carlo random-walk diffusion representation. The system can utilize meteorological data from either the HIRLAM or ECMWF numerical weather prediction models. We present an evaluation of SILAM against the data of the European Tracer Experiment (ETEX). The model showed an overall time correlation coefficient of 0.6 (over 150 stations), with specific values for the two ETEX measurement arcs of 0.75 and 0.74, respectively. The number of well-reproduced observation sites are 55, 37, and 40-for a Figure of Merit in Time of 40.2, a correlation coefficient of 40.7, and mean observed and modelled values being within a factor of 2, respectively. We have also investigated the sensitivity of the model to the meteorological input data and model setup. The most important factors with regard to the model performance were (i) the selection of the meteorological input data set and (ii) the method used for the atmospheric boundary layer height estimation. The study allowed selection of the optimum setup for the operational model configuration. We also tried to find explanations for the successes and failures of the specific methodologies in order to facilitate broader conclusions on their applicability in emergency dispersion modelling. r

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.

Collaborative Filtering is one of the most widely used approaches in recommendation systems which predicts user preferences by learning past user-item relationships. In recent years, item-oriented collaborative filtering methods came into prominence as they are more scalable compared to useroriented methods. Item-oriented methods discover itemitem relationships from the training data and use these relations to compute predictions. In this paper, we propose a novel item-oriented algorithm, Random Walk Recommender, that first infers transition probabilities between items based on their similarities and models finite length random walks on the item space to compute predictions. This method is especially useful when training data is less than plentiful, namely when typical similarity measures fail to capture actual relationships between items. Aside from the proposed prediction algorithm, the final transition probability matrix computed in one of the intermediate steps can be used as an item similarity matrix in typical item-oriented approaches. Thus, this paper suggests a method to enhance similarity matrices under sparse data as well. Experiments on Movie-Lens data show that Random Walk Recommender algorithm outperforms two other item-oriented methods in different sparsity levels while having the best performance difference in sparse datasets.

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.

This paper examines whether stock prices for a sample of 22 OECD countries can be best represented as mean reversion or random walk processes. A sequential trend break test proposed by Zivot and Andrews is implemented, which has the advantage that it can take account of a structural break in the series, as well as panel data unit root tests proposed by Im et al., which exploits the extra power in the panel properties of the data. Results provide strong support for the random walk hypothesis.

The fundamental design choices in an evolutionary algorithm are its representation of candidate solutions and the operators that will act on that representation. We propose representing spanning trees in evolutionary algorithms for network design problems directly as sets of their edges, and we describe initialization, recombination, and mutation operators for this representation. The operators offer locality, heritability, and computational efficiency. Initialization and recombination depend on an underlying random spanning tree algorithm; three choices for this algorithm, based on the minimum spanning tree algorithms of Prim and Kruskal and on random walks, respectively, are examined analytically and empirically. We demonstrate the usefulness of the edge-set encoding in an evolutionary algorithm for the NP-hard degree-constrained minimum spanning tree problem. The algorithm's operators are easily extended to generate only feasible spanning trees and to incorporate local, problem-specific heuristics. Comparisons of this algorithm to others that encode candidate spanning trees via the Blob Code, with network random keys, and as strings of weights indicate the superiority of the edge-set encoding, particularly on larger instances.

We present a new approach for conformance testing of protocols specified as a collection of communicating finite state machines (FSM's). Our approach uses a guided random walk procedure. This procedure attempts to cover all transitions in the component FSM's. We also introduce the concept of observers that check some aspect of protocol behavior. We present the result of applying our method to two example protocols: full-duplex alternating bit protocol and the ATM-adaptationlayer-convergence protocol. Applying our procedure to the ATM adaptation layer, 99% of component FSM's edges can be covered in a test with 11692 input steps. Previous approaches cannot do conformance test generation for standard protocols (such as asynchronous transfer mode (ATM) adaptation layer) specified as a collection of communicating FSM's.

We present an adaptive method for the automatic scaling of Random-Walk Metropolis-Hastings algorithms, which quickly and robustly identifies the scaling factor that yields a specified overall sampler acceptance probability. Our method relies on the use of the Robbins-Monro search process, whose performance is determined by an unknown steplength constant. We give a very simple estimator of this constant for proposal distributions that are univariate or multivariate normal, together with a sampling algorithm for automating the method. The effectiveness of the algorithm is demonstrated with both simulated and real data examples. This approach could be implemented as a useful component in more complex adaptive Markov chain Monte Carlo algorithms, or as part of automated software packages.

We investigate the random walk properties of a class of two-dimensional lattices with two different types of columns and discuss the dependence of the properties on the densities and detailed arrangements of the columns. We show that the row and column components of the mean square displacement are asymptotically independent of the details of the arrangement of columns. We reach the same conclusion for some other random walk properties (return to the origin and number of distinct sites visited) for various periodic arrangements of a given relative density of the two types of columns. We also derive exact asymptotic results for the occupation probabilities of the two types of distinct sites on our lattices which validate the basic conjecture on bond and step ratios made in the preceding paper in this series.

... 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. ...

Random walks are gaining much attention from the networks research community. They are the basis of many proposals aimed to solve a variety of network-related problems such as resource location, network construction, nodes sampling, etc. This interest on random walks is justified by their inherent properties. They are very simple to implement as nodes only require local information to take routing decisions. Also, random walks demand little processing power and bandwidth. Besides, they are very resilient to changes on the network topology.

Hypothesis of Market Efficiency is an important concept for the investors who wish to hold internationally diversified portfolios. With increased movement of investments across international boundaries owing to the integration of world economies, the understanding of efficiency of the emerging markets is also gaining greater importance. In this paper we test the weak form efficiency in the framework of random walk hypothesis for the two major equity markets in India for the period 1991 to 2006. The evidence suggests that the series do not follow random walk model and there is an evidence of autocorrelation in both markets rejecting the weak form efficiency hypothesis.

This paper describes an approximate approach to evaluating the performance, including the probability of loss-of-power (or loss-of-load, as some would have it) of stand-alone photovoltaic solar energy systems. The method treats the energy capture, storage and disbursement process as a random walk in the storage domain. To apply the technique, one must know the variance, as well as the mean, of the probability density of the daily solar insolation impinging onto the photovoltaic array. Analytical expressions are obtained for the probability of depleting the system's storage, as well as how much auxiliary energy, on the average, would be required to cover the load in that event.

This work introduces a new family of link-based dissimilarity measures between nodes of a weighted, directed, graph that generalizes both the shortest-path and the commute-time (or resistance) distances. This measure, called the randomized shortest-path (RSP) dissimilarity, depends on a parameter θ and has the interesting property of reducing, on one end, to the standard shortest-path distance when θ is large and, on the other end, to the commute-time distance when θ is small (near zero). Intuitively, it corresponds to the expected cost incurred by a random walker in order to reach a destination node from a starting node, while maintaining a constant entropy (related to θ) spread in the graph. The parameter θ is therefore biasing gradually the simple random walk on the graph towards the shortest-path policy. By adopting a statistical physics approach and computing a sum over all the possible paths, it is shown that the RSP dissimilarity from every node to a particular node of interest can be computed efficiently by solving two linear systems of n equations, where n is the number of nodes. On the other hand, the dissimilarity between every couple of nodes is obtained by inverting an n × n matrix. The proposed measure could be used for various graph mining tasks such as computing betweenness centrality, finding dense communities, etc, as shown in the experimental section.

The main objective of a hedge strategy is to generate positive returns irrespective of market conditions. This paper presents a classic hedge fund strategy: an investment vehicle whose key objective is to minimize investment risk in an attempt to deliver profits under all market circumstances. The hedge is designed to have minimal correlation with the market and, irrespective of market direction, the fund seeks to generate positive alpha. A significant difference between this model and more traditional hedge fund strategies is that portfolio optimization is based upon the cointegration of prices rather than the correlation of returns.

A bivariate inverse Gaussian (IG) density function is constructed. Relations of the bivariate IG distribution to the normal and Z ~ distributions are established. The corresponding bivariate random walk (RW) density function is obtained. The properties and behaviour of bivariate IG distribution are studied for large parametric values. Moment estimates of the five parameters are given and applications are pointed out. A generalization to the multivariate IG distribution is proposed.

While detection of acute cardiac disorders such as myocardial infarction (MI) from electrocardiogram (ECG) and vectorcardiogram (VCG) has been widely reported, identification of MI locations from these signals, pivotal for timely therapeutic and prognostic interventions, remains a standing issue. We present an approach for MI localization based on representing complex spatiotemporal patterns of cardiac dynamics as a randomwalk network reconstructed from the evolution of VCG signals across a 3-D state space. Extensive tests with signals from the PTB database of the PhysioNet databank suggest that locations of MI can be determined accurately (sensitivity of ∼88% and specificity of ∼92%) from tracking certain consistently estimated invariants of this random-walk representation.

Random walks have been created using the pseudo-random generators in di erent computer language compilers (BASIC, PASCAL, FORTRAN, C++) using a Pentium processor. All the obtained paths have apparently a random behavior for short walks (∼2 14 steps). From long random walks (2 33 steps) di erent periods have been found, the shortest being 2 18 for PASCAL and the longest 2 31 for FORTRAN and C++, while BASIC had a 2 24 steps period. The BASIC, PASCAL and FORTRAN long walks had even (2 or 4) symmetries. The C++ walk systematically roams away from the origin. Using deviations from the mean-distance rule for random walks, d 2 ∝ N, a more severe criterion is found, e.g. random walks generated by a PASCAL compiler fulÿlls this criterion to N ¡ 10 000.

The monograph presents new probabilistic representations for classical boundary value problems of mathematical physics. When comparing with the well known probabilistic representations in the form of Wiener and diffusion path integrals, the trajectories of random walks in our representations are simulated on the boundary of the domain as Markov chains generated by the kernels of the boundary integral equations equivalent to the original boundary value problem. The Monte Carlo methods based on the walk on boundary processes have a series of advantages: (1) high-dimensional problems can be solved, (2) the method is grid-free and gives the solution simultaneously in arbitrary points, (3) external and internal boundary value problems are solved using one and the same random walk on boundary process, (4) when comparing with the classical probabilistic representations, there is no ε-error generated by the approximations in the ε-boundary, and (5) parallel implementation of the walk on boundary algorithms is straightforward and much easier. This is the first book devoted to the walk on boundary algorithms. First introduced by K. Sabelfeld for solving the interior and exterior boundary value problems for the Laplace and heat equations, the method was then extended to all the main boundary value problems of the potential and elasticity theories.

It is well known that there is no analytic expression for the electrical capacitance of the unit cube. However, there are several Monte Carlo methods that have been used to numerically estimate this capacitance to high accuracy. These include a Brownian dynamics algorithm [HA Brownian dynamics algorithm for calculating the hydrodynamic friction and the electrostatic capacitance of an arbitrarily shaped object, J. Chem. Phys. 100 3821-3826] coupled to the "walk on spheres" (WOS) method [M.E. Müller, Some continuous Monte Carlo methods for the Dirichlet problem, Ann. Math. Stat. 27 (1956) 569-589]; the Green's function first-passage (GFFP) algorithm [J.A. Given, J.B. Hubbard, J.F. Douglas, A firstpassage algorithm for the hydrodynamic friction and diffusion-limited reaction rate of macromolecules, J. Chem. Phys. 106 (9) (1997) 3721-3771]; an error-controlling Brownian dynamics algorithm [C.-O. Hwang, M. Mascagni, Capacitance of the unit cube, J. Korean Phys. Soc. 42 (2003) L1-L4]; an extrapolation technique coupled to the WOS method [C.-O. Hwang, Extrapolation technique in the "walk on spheres" method for the capacitance of the unit cube, J. Korean Phys. Soc. 44 (2) (2004) 469-470]; the "walk on planes" (WOP) method [M.L. Mansfield, J.F. Douglas, E.J. Garboczi, Intrinsic viscosity and the electrical polarizability of arbitrarily shaped objects, Phys. Rev. E 64 (6) (2001) 061401:1-061401:16; C.-O. Hwang, M. Mascagni, Electrical capacitance of the unit cube, J. Appl. Phys. 95 (7) (2004) 3798-3802]; and the random "walk on the boundary" (WOB) method [M. Mascagni, N.A. Simonov, The random walk on the boundary method for calculating capacitance, J. Comp. Phys. 195 (2004) 465-473]. Monte Carlo methods are convenient and efficient for problems whose solution includes singularities. In the calculation of the unit cube capacitance, there are edge and corner singularities in the charge density distribution. In this paper, we review the above Monte Carlo methods for computing the electrical capacitance of a cube and compare their effectiveness. We also provide a new result. We will focus our attention particularly on two Monte Carlo methods: WOP [M.L. Mansfield, J.F. Douglas, E.J. Garboczi, Intrinsic viscosity and the electrical polarizability of arbitrarily shaped objects, Phys. Rev. E 64 (6) (2001) 061401:1-061401:16; C.-O. Hwang, M. Mascagni, Electrical capacitance of the unit cube, J. Appl. Phys. 95 (7) (2004) 3798-3802; C.-O. Hwang, T. Won, Edge charge singularity of conductors, J. Korean Phys. Soc. 45 (2004) S551-S553] and the random WOB [M. Mascagni, N.A. Simonov, The random walk on the boundary method for calculating capacitance, J. Comp. Phys. 195 (2004) 465-473] methods.

This paper investigates the properties of Dickey-Fuller tests for seasonally unadjusted quarterly data when deterministic seasonality is present but it is neglected in the test regression. While for the random walk case the answer is straightforward, an extensive Monte Carlo study has to be performed for more realistic processes and testing strategies. The most important conclusion is that the common perception that deterministic seasonality has nothing to do with testing for the long-run properties of the data is incorrect. Further numerical evidence on the shortcomings of the general-to-specific t-sig lag selection method is also presented.

This study addresses the question of whether the adaptive market hypothesis provides a better description of the behaviour of emerging stock market like India. We employed linear and nonlinear methods to evaluate the hypothesis empirically. The linear tests show a cyclical pattern in linear dependence suggesting that the Indian stock market switched between periods of efficiency and inefficiency. In contrast, the results from nonlinear tests reveal a strong evidence of nonlinearity in returns throughout the sample period with a sign of tapering magnitude of nonlinear dependence in the recent period. The findings suggest that Indian stock market is moving towards efficiency. The results provide additional insights on association between financial crises, foreign portfolio investments and inefficiency.

This paper focuses on the problem of wind turbine fatigue load reduction by means of individual pitch control (IPC). The control approach has a two-degree-of-freedom structure, consisting of an optimal multivariable LQG controller and a feedforward disturbance rejection controller based on estimated wind speed signals. To make the control design problem time invariant, all signals are transformed to the non-rotating reference frame using the Coleman transformation. In the Coleman domain, the LQG control objective is minimization of the rotor tilt and yaw moments, whereas the feedforward controller tries to achieve even further improvement by rejecting the influence of the low-frequency components of the wind on the rotor moments. To this end, the tilt-and yaw-oriented components of the blade-effective wind speeds are approximated using stochastic random walk models, the states of which are then augmented with the turbine states and estimated using a Kalman filter. The effects of these (estimated) disturbances on the controlled outputs are then reduced using stable dynamic model inversion. The approach is tested and compared with the conventional IPC method in simulation studies with models of different complexities. The results demonstrate very good load reduction at not only low frequencies (1p blade fatigue load reduction) but also at the 3p frequency, giving rise to fatigue load reduction of the non-rotating turbine components.

This study assesses the forecast bias and accuracy of the three commonly used forecast methods for 12 different emerging market currencies. We find that each forecast method commonly exhibits a forecast bias. The random walk method outperformed the forward rate and ARIMA methods for some emerging market currencies, and was not outperformed by these alternative methods. In general, it appears that the incorporation of expectation components by the implicit forward and ARIMA methods do not improve the forecast, and actually reduce forecast accuracy in some cases. Furthermore, the Latin American currencies were typically forecast with more error.

The few existing studies on equity price dynamics and market efficiency for Latin American emerging equity markets show conflicting results. This study uses multiple varianceratio and auto-regressive fractionally integrated moving-average tests and new data (U.S. dollar-based national equity indices for the 1987-1997 period) to clarify these results. Documented evidence shows that equity prices in major Latin American emerging equity markets-Argentina, Brazil, Chile and Mexico-follow a random walk, and that they are, generally, weak-form efficient. In sum, therefore, the evidence suggests that international investors in these markets cannot use historical information to design systematically profitable trading schemes because future long-term returns are not dependent on past returns.

A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with user-defined (or pre-defined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the pre-labeled pixels. By assigning each pixel to the label for which the greatest probability is calculated, a high-quality image segmentation may be obtained. Theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits. This algorithm is formulated in discrete space (i.e., on a graph) using combinatorial analogues of standard operators and principles from continuous potential theory, allowing it to be applied in arbitrary dimension on arbitrary graphs.

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.