Random Walk Process Research Articles

A Comparative Study on the Efficiency of Korean Stock Markets: KOSPI and KOSDAQ

Purpose - This study aims to examine and compare the weak-form efficiency of the KOSPI and KOSDAQ markets in Korea based upon the random walk process framework. Design/Methodology/Approach - This study uses multiple variance ratio tests with the purpose of testing the random walk process for daily returns of stocks to investigate the efficiency of stock markets in Korea. Chow-Denning and Richardson-Smith multiple variance ratio tests have been employed in order to find out the level of the efficiency of Korea’s stock markets. Findings - First, the daily return of both market indexes did not follow the random walk process for the sampling period, indicating that the Korean stock market indexes are not weak-form efficient. Second, all the individual stocks used for the analysis are shown to be inefficient in the weak form. Only three sample stocks in KOSPI market out of ten stocks accept the null hypothesis under the heteroscedasticity assumption, but the null hypothesis in these stocks is rejected under the homoscedasticity assumption. Research Implications - This study suggests that under the random walk hypothesis framework, the market index and individual stocks in Korean stock market show the informational inefficiency in a weak form. Accordingly, it seems that domestic and foreign investors may still be able to get the yield better than market average, or market index, in the Korea’s stock markets including KOSDAQ market by doing fundamental and technical analysis on the stock markets.

Comment on the paper by R. Maniar and A. Bhattacharyay, [Random walk model for coordinate-dependent diffusion in a force field, Physica A 584 (2021) 126348

Paper (Maniar and Bhattacharyay, 2021) introduces a discrete random-walk (RW) model with a site dependent waiting time and an external force i.e. a site dependent drift. The RW is compared with a Smoluchowski equation in continuous space and time with space dependent diffusivity and space dependent damping. Using numerical simulations in Maniar and Bhattacharyay (2021) it is shown that the equilibrium distribution satisfies locally the Stokes–Einstein relation i.e. there is a constant temperature in the whole system. Here we show that the result can be recovered analytically with a continuous limit in the RW master equation. Moreover, we evidence that the RW model should be carefully defined in order to satisfy locally Stokes–Einstein relation, indeed a different definition of the discrete RW process describes a system that satisfies the Smoluchowski equation with constant damping, where the temperature is not uniform.

Hubs-biased resistance distances on graphs and networks

We define and study two new kinds of “effective resistances” based on hubs-biased – hubs-repelling and hubs-attracting – models of navigating a graph/network. We prove that these effective resistances are squared Euclidean distances between the vertices of a graph. They can be expressed in terms of the Moore–Penrose pseudoinverse of the hubs-biased Laplacian matrices of the graph. We define the analogous of the Kirchhoff indices of the graph based of these resistance distances. We prove several results for the new resistance distances and the Kirchhoff indices based on spectral properties of the corresponding Laplacians. After an intensive computational search we conjecture that the Kirchhoff index based on the hubs-repelling resistance distance is not smaller than that based on the standard resistance distance, and that the last is not smaller than the one based on the hubs-attracting resistance distance. We also observe that in real-world brain and neural systems the efficiency of standard random walk processes is as high as that of hubs-attracting schemes. On the contrary, infrastructures and modular software networks seem to be designed to be navigated by using their hubs.

Exchange rate forecasting with real-time data: Evidence from Western offshoots

This study explores the out-of-sample forecasting ability of exchange rate models using real-time macroeconomic data with bilateral exchange rates and short-term interest rates from the U.K. and Western Offshoot countries, that is, Australia, Canada, New Zealand, and the U.S. We employ the Taylor rule with monetary policy inertia to forecast the out-of-sample exchange rate changes across these economies using various methods, such as ordinary least squares, non-linear least squares, and generalized method of moments. Our findings show that the exchange rate forecasting performance of the relative Taylor rule model is mostly superior to that of a naïve random walk process even after utilizing real-time macroeconomic data. By comparing them to the results obtained from ex post revised data, we confirm the desirability of real-time data for estimating the model. Our results also present the invalidity of the assumptions concerning the homogeneous coefficient and symmetric reaction of real exchange rates. Furthermore, we split the sample at the point where some structural breaks occur through a policy interest rate’s deviation from its forecast obtained from the original Taylor rule model and estimate the exchange rate model in each subsample. The superiority of the model persists in terms of its predictability during relatively moderate deviation periods for each of the currency pairs. Using forward-looking inflation/output gaps, including stock prices, and employing alternative econometric approaches, we also corroborate the desirable forecasting abilities for several model specifications.

Random Walk Hypothesis for Stock Prices in Fiji

The main goal of this paper is to investigate the random walk hypothesis in Fiji using monthly data from January 2000 to October 2017. Applying augmented Dickey Fuller (ADF 1979, 1981) and Phillips-Perron (1988), Zivot-Andrews (1992), and Narayan and Popp (2010) unit root tests, this study finds that stock prices is best characterized as non-stationary. The estimated multiple structural break dates in the stock prices corresponds with devaluation of Fijian dollar by 20 percent in 2009 and General Elections in September 2014, which Fiji First Party won by majority votes. The empirical results indicate that stock prices are best characterized as a unit root (random walk) process, indicating that the weak-form efficient market hypothesis holds in Fiji’s stock market. Hence, it will be difficult to predict future returns based on historical movement of stock prices in Fiji’s stock market.

Distance-aware optimization model for influential nodes identification in social networks with independent cascade diffusion

Influence maximization (IM) is a challenge in social networks, which depends on the spreader selection. We propose a quadratic programming model to identify a fixed number of initial spreaders to affect the maximum nodes within the minimum diffusion time. We solve this model using a new Distance Aware Spreader Finding (DASF) algorithm independent of the community detection problem. On large-scale social networks, DASF selects anchor nodes by a novel threshold. Then a social distance is defined between anchor nodes via random walk processes. This distance is regularized by the neighborhood degree. Our model finds influential spreaders under the Independent Cascade (IC) diffusion model. It implicitly maximizes the local coverage of spreaders and minimizes the global overlap. We extract the solution of this bi-objective model by finding the principal eigenvector of the regularized distance matrix. Comparing DASF with nine algorithms on various large-scale social networks indicates that DASF performs well based on the influence spread and diffusion rate criteria. The robustness of DASF is also acceptable dealing with different noisy scenarios.

How Li diffusion in spinel Li[Ni1/2Mn3/2]O4 is seen with μ ±SR

Abstract The diffusive behavior in a spinel-type Li+ ion battery material, Li[Ni1/2Mn3/2]O4, has been studied with positive and negative muon spin rotation and relaxation (μ ±SR) measurements in the temperature range between 200 and 400 K using a powder sample. The implanted μ + locates at an interstitial site near O2− ion so as to form a O–H like bond, while the implanted μ − is mainly captured by an oxygen nucleus, resulting in the formation of muonic oxygen. This means that local magnetic environments in Li[Ni1/2Mn3/2]O4 were investigated from the two different sites in the lattice, i.e., one is an interstitial site for μ +SR and the other is an oxygen site for μ −SR. Since both μ +SR and μ −SR detected an increase in the fluctuation rate of a nuclear magnetic field for temperatures above 200 K, the origin of this increase is clearly confirmed as Li diffusion. Assuming a random walk process with the hopping of thermally activated Li+ between a regular Li site and the nearest neighboring vacant octahedral sites, a self-diffusion coefficient of Li+ was found to range above 10−11 cm2/s at temperatures above 250 K with an activation energy of about 0.06 eV.

The Bluest Changing-Look QSO SDSS J224113-012108

Abstract In this manuscript, we report a new changing-look QSO (CLQSO) SDSS J2241 at z = 0.059. Based on the multi-epoch Sloan Digital Sky Survey spectra from 2011 to 2017, the flux ratio of broad Hα to broad Hβ has changed from 7 in 2011 to 2.7 in 2017, leading SDSS J2241 with a spectral index α λ ∼ −5.21 ± 0.02 (λ < 4000) in 2017 to be, so far, the bluest CLQSO. Based on the SDSS spectrum in 2011, the host galaxy contribution with a stellar velocity dispersion of ∼86 km s−1 can be well determined, leading to the M–sigma relation expected central black hole (BH) mass of ∼3 × 106 M ⊙. However, based on properties of the broad Hα emission, the virial BH mass is ∼108 M ⊙, about two magnitudes larger than the mass found through the M–sigma relation. The different BH masses found using different methods indicate that SDSS J2241 is one unique CLQSO. The long-term photometric light curve shows interesting variability that is not expected assuming the Damped Random Walk process commonly applied to active galactic nuclei but probably connected to a central tidal disruption event. Furthermore, based on continuum emission properties in 2017 with no dust obscuration, the moving dust clouds scenario alone cannot be preferred to explain the CLQSO SDSS J2241, because the expected intrinsic reddening-corrected continuum emission was unreasonably higher than the unobscured continuum emission in 2017.

From continuous-time random walks to the fractional Jeffreys equation: Solution and properties

Jeffreys equation provides an increasingly popular extension of the diffusive laws of Fourier and Fick for heat and particle transport. Similar to generalisations of the diffusion equation, we here investigate the connection between a time-fractional generalisation of the Jeffreys equation and a continuous-time random walk process based on a generalised waiting time density with diverging mean. We demonstrate that the mean squared displacement exhibits a variety of anomalous behaviors, such as retarding and accelerating subdiffusion, as well as a crossover from superdiffusion to subdiffusion. Moreover, we provide two alternative approaches, namely, a fractional Taylor series and distributed-order derivatives, that transform Fourier’s or Fick’s law into the time-fractional Jeffreys equation. Our discussion provides physics-based support for the fractional Jeffreys equation and shows its versatility for practical applications.

Improving the Stochastic Model of Ionospheric Delays for BDS Long-Range Real-Time Kinematic Positioning

Although ionosphere-free (IF) combination is usually employed in long-range precise positioning, in order to employ the knowledge of the spatiotemporal ionospheric delays variations and avoid the difficulty in choosing the IF combinations in case of triple-frequency data processing, using uncombined observations with proper ionospheric constraints is more beneficial. Yet, determining the appropriate power spectral density (PSD) of ionospheric delays is one of the most important issues in the uncombined processing, as the empirical methods cannot consider the actual ionosphere activities. The ionospheric delays derived from actual dual-frequency phase observations contain not only the real-time ionospheric delays variations, but also the observation noise which could be much larger than ionospheric delays changes over a very short time interval, so that the statistics of the ionospheric delays cannot be retrieved properly. Fortunately, the ionospheric delays variations and the observation noise behave in different ways, i.e., can be represented by random-walk and white noise process, respectively, so that they can be separated statistically. In this paper, we proposed an approach to determine the PSD of ionospheric delays for each satellite in real-time by denoising the ionospheric delay observations. Based on the relationship between the PSD, observation noise and the ionospheric observations, several aspects impacting the PSD calculation are investigated numerically and the optimal values are suggested. The proposed approach with the suggested optimal parameters is applied to the processing of three long-range baselines of 103 km, 175 km and 200 km with triple-frequency BDS data in both static and kinematic mode. The improvement in the first ambiguity fixing time (FAFT), the positioning accuracy and the estimated ionospheric delays are analysed and compared with that using empirical PSD. The results show that the FAFT can be shortened by at least 8% compared with using a unique empirical PSD for all satellites although it is even fine-tuned according to the actual observations and improved by 34% compared with that using PSD derived from ionospheric delay observations without denoising. Finally, the positioning performance of BDS three-frequency observations shows that the averaged FAFT is 226 s and 270 s, and the positioning accuracies after ambiguity fixing are 1 cm, 1 cm and 3 cm in the East, North and Up directions for static and 3 cm, 3 cm and 6 cm for kinematic mode, respectively.

Testing the Efficiency of Globally Listed Private Equity Markets

This study is the first to investigate the efficient market hypothesis in its weak form and the random walk behaviour of globally listed private equity (LPE) markets represented by nine global, regional, and style indices based on weekly data covering the period from January 2004 to December 2020. Autocorrelation tests, variance ratio tests, and a non-parametric runs test are employed. The results of the autocorrelation tests and the variance ratio tests tend to correspond for all indices, and they reject the random walk hypothesis for the returns of all LPE indices under investigation. In contrast, the runs test for direct weak-form market efficiency cannot reject the null hypothesis of a random walk process for almost all LPE indices under investigation. Furthermore, there is no evidence that the market efficiency of globally listed private equity markets has improved after the global financial crisis. Due to the fact that the rapidly growing asset class of LPE as a form of private equity is still relatively unknown, the implications of the results of our paper are relevant for investors, policy makers, and academics alike. In addition, the results provide valuable insights to better understand the emerging asset class of LPE.

Design of a recommendation system based on the transition graph

A recommendation system has been built for a web resource’s users that applies statistics about user activities to provide recommendations. The purpose of the system operation is to provide recommendations in the form of an orderly sequence of HTML pages of the resource suggested for the user. The ranking procedure uses statistical information about user transitions between web resource pages. The web resource model is represented in the form of a web graph; the user behavior model is shown as a graph of transitions between resource pages. The web graph is represented by an adjacency matrix; for the transition graph, a weighted matrix of probabilities of transitions between the vertices of the graph has been constructed. It was taken into consideration that user transitions between pages of a web resource may involve entering a URL in the address bar of a browser or by clicking on a link in the current page. The user’s transition between vertices in a finite graph according to probabilities determined by the weight of the graph’s edges is represented by a homogeneous Markov chain and is considered a process of random walk on the graph with the possibility of moving to a random vertex. Random Walk with Restarts was used to rank web resource pages for a particular user. Numerical analysis has been performed for an actual online store website. The initial data on user sessions are divided into training and test samples. According to the training sample, a weighted matrix of the probability of user transitions between web resource pages was constructed. To assess the quality of the built recommendation system, the accuracy, completeness, and Half-life Utility metrics were used. On the elements of the test sample, the accuracy value of 65‒68 % was obtained, the optimal number of elements in the recommendation list was determined. The influence of model parameters on the quality of recommendation systems was investigated.

The Relationship between Stock Price Index and Industrial Production Index in Construction Industry

This paper investigates the relation between stock price index and industrial production index in construction industry, namely, the relation between stock market and real economy activity. Because stock price is the leading indicator, stock price may be related to industrial production. Previous studies have been studied on the relation between released stock price index and IPI. However, this study is distinguishable in that released stock price index is decomposed into fundamental component and transitory component. The first step in this empirical analysis is to decompose released stock price index. In state-space model, fundamental component is set up as a random walk process and transitory component is modeled as a stationary AR(2) process. In the second step, to check the stationarity, the ADF unit root test is used. In the third step, to elucidate the relationship between stock price index and IPI, Granger causality test is applied. The findings are as follows. The results reveal that released stock price index Granger causes IPI. The fundamental component of stock price index Granger causes IPI, and the transitory component of stock price index Granger causes IPI. The increase in released stock price index and the fundamental component of stock price index causes IPI to increase after one month. This paper indicates that the analysis of stock price index helps to predict IPI in construction industry.

Open Relation Extraction for Chinese Noun Phrases

Relation Extraction (RE) aims at harvesting relational facts from texts. A majority of existing research targets at knowledge acquisition from sentences, where subject-verb-object structures are usually treated as the signals of existence of relations. In contrast, relational facts expressed within noun phrases are highly implicit. Previous works mostly relies on human-compiled assertions and textual patterns in English to address noun phrase-based RE. For Chinese, the corresponding task is non-trivial because Chinese is a highly analytic language with flexible expressions. Additionally, noun phrases tend to be incomplete in grammatical structures, where clear mentions of predicates are often missing. In this article, we present an unsupervised Noun Phrase-based Open RE system for the Chinese language (NPORE), which employs a three-layer data-driven architecture. The system contains three components, i.e., Modifier-sensitive Phrase Segmenter, Candidate Relation Generator and Missing Relation Predicate Detector. It integrates with a graph clique mining algorithm to chunk Chinese noun phrases, considering how relations are expressed. We further propose a probabilistic method with knowledge priors and a hypergraph-based random walk process to detect missing relation predicates. Experiments over Chinese Wikipedia show NPORE outperforms state-of-the-art, capable of extracting 55.2 percent more relations than the most competitive baseline, with a comparable precision at 95.4 percent.

One-step random-walk process of nanoparticles in cement-based materials

Efficient modelling approaches capable of predicting the behavior and effects of nanoparticles in cement-based materials are required for conducting relevant experiments. From the microstructural characterization of a cement-nanoparticle system, this paper investigates the potential of cell-based weighted random-walk method to establish statistically significant relationships between chemical bonding and diffusion processes of nanoparticles within cement matrix. LaSr0.5C0.5O3 (LSCO) nanoparticles were employed to develop a discrete event system that accounts for the behavior of individual cells where nanoparticles and cement components were expected to interact. The stochastic model is based on annihilation (loss) and creation (gain) of a bond in the cell. The model considers both chemical reactions and transport mechanism of nanoparticles from cementitious cells, along with cement hydration process. This approach may be useful for simulating nanoparticle transport in complex 2D cement-based materials systems.

Detecting Abrupt Changes in the Presence of Local Fluctuations and Autocorrelated Noise

While there are a plethora of algorithms for detecting changes in mean in univariate time-series, almost all struggle in real applications where there is autocorrelated noise or where the mean fluctuates locally between the abrupt changes that one wishes to detect. In these cases, default implementations, which are often based on assumptions of a constant mean between changes and independent noise, can lead to substantial over-estimation of the number of changes. We propose a principled approach to detect such abrupt changes that models local fluctuations as a random walk process and autocorrelated noise via an AR(1) process. We then estimate the number and location of changepoints by minimizing a penalized cost based on this model. We develop a novel and efficient dynamic programming algorithm, DeCAFS, that can solve this minimization problem; despite the additional challenge of dependence across segments, due to the autocorrelated noise, which makes existing algorithms inapplicable. Theory and empirical results show that our approach has greater power at detecting abrupt changes than existing approaches. We apply our method to measuring gene expression levels in bacteria. Supplementary materials for this article are available online.

Bayesian estimation of instantaneous frequency reduction on cracked concrete railway bridges under high-speed train passage

When a train passes along prestressed concrete (PC) bridges, crack opening reduces the girder stiffness, providing important indicators for the practical evaluation of bridge performance. However, this phenomenon is difficult to detect in the free vibrations induced by trains or via hammer tests as these vibrations have very small amplitudes. Moreover, although the bridge under a passing train vibrates with large amplitude, the vibrational state is forced, and the girder stiffness induced by crack opening occurs only in the downward displacement. To estimate this complex but valuable system, this study establishes a time-varying autoregressive with eXogenous (TV-ARX) model and a hierarchical Bayesian estimation (Bayesian TV-ARX) method. The exogenous variables in the TV-ARX model are the modal-transformed moving loads, which constitute the main excitation frequency of the running train. The variation of the autoregressive (AR) coefficient includes the modal characteristic as a random walk process. When a train passes, the Bayesian TV-ARX estimates the instantaneous amplitude-dependent drop of the bridge frequency from the displacement response. After formulating the Bayesian TV-ARX, the effects of the vehicle–bridge interaction (VBI), train speed, and track irregularity on the accuracy of the instantaneous stiffness decrease estimated via the Bayesian TV-ARX were verified using VBI simulations of a nonlinear beam, in which the bending stiffness decreased only during a downward displacement. Even when the VBI effects overlapped, the model accurately estimated the reduced bridge stiffness due to crack opening. Next, the Bayesian TV-ARX was applied to two PC bridges on a real high-speed railway. On one of the bridges, the estimated stiffness decreased by ~ 12% when the bridge was downward-displaced by crack opening during the train passage. Such results on a real bridge under operation have not been previously reported. Four months later, the amplitude-dependent decrease in the bridge frequency was amplified by crack propagation. These results are important evidences of a nonlinear and nonstationary system. Besides solving real problems, the proposed method is expected to significantly contribute to condition-based maintenance and structure-health monitoring of PC bridges. In particular, it enables early detection of damage and deterioration in addition to bridge performance evaluation over time.

Criticality and conformality in the random dimer model.

In critical systems, the effect of a localized perturbation affects points that are arbitrarily far from the perturbation location. In this paper, we study the effect of localized perturbations on the solution of the random dimer problem in two dimensions. By means of an accurate numerical analysis, we show that a local perturbation of the optimal covering induces an excitation whose size is extensive with finite probability. We compute the fractal dimension of the excitations and scaling exponents. In particular, excitations in random dimer problems on nonbipartite lattices have the same statistical properties of domain walls in spin glass. Excitations produced in bipartite lattices, instead, are compatible with a loop-erased self-avoiding random walk process. In both cases, we find evidence of conformal invariance of the excitations that is compatible with SLE_{κ} with parameter κ depending on the bipartiteness of the underlying lattice only.

A random walk Monte Carlo simulation study of COVID-19-like infection spread

Recent analysis of early COVID-19 data from China showed that the number of confirmed cases followed a subexponential power-law increase, with a growth exponent of around 2.2 (Maier and Brockmann, 2020). The power-law behavior was attributed to a combination of effective containment and mitigation measures employed as well as behavioral changes by the population. In this work, we report a random walk Monte Carlo simulation study of proximity-based infection spread. Control interventions such as lockdown measures and mobility restrictions are incorporated in the simulations through a single parameter, the size of each step in the random walk process. The step size l is taken to be a multiple of 〈r〉, which is the average separation between individuals. Three temporal growth regimes (quadratic, intermediate power-law and exponential) are shown to emerge naturally from our simulations. For l=〈r〉, we get intermediate power-law growth exponents that are in general agreement with available data from China. On the other hand, we obtain a quadratic growth for smaller step sizes l≲〈r〉∕2, while for large l the growth is found to be exponential. We further performed a comparative case study of early fatality data (under varying levels of lockdown conditions) from three other countries, India, Brazil and South Africa. We show that reasonable agreement with these data can be obtained by incorporating small-world-like connections in our simulations.

Temporal oscillations in preference strength provide evidence for an open system model of constructed preference

The decision process is often conceptualized as a constructive process in which a decision maker accumulates information to form preferences about the choice options and ultimately make a response. Here we examine how these constructive processes unfold by tracking dynamic changes in preference strength. Across two experiments, we observed that mean preference strength systematically oscillated over time and found that eliciting a choice early in time strongly affected the pattern of preference oscillation later in time. Preferences following choices oscillated between being stronger than those without prior choice and being weaker than those without choice. To account for these phenomena, we develop an open system dynamic model which merges the dynamics of Markov random walk processes with those of quantum walk processes. This model incorporates two sources of uncertainty: epistemic uncertainty about what preference state a decision maker has at a particular point in time; and ontic uncertainty about what decision or judgment will be observed when a person has some preference state. Representing these two sources of uncertainty allows the model to account for the oscillations in preference as well as the effect of choice on preference formation.