Markov Dependency Research Articles

Application of Markov chain to share price movement in Nigeria (1985–2019)

The study evaluates the movement of share prices in the Nigerian stock market. Markov chain approach provides a successful analysis and prediction of time-series data (1985–2019) which reflects Markov dependency. The probability alpha and beta was estimated, and the expectation of the monthly increase (E(I)) and decrease (E(D)) of the share price index was obtained as 5 months and 3 months, respectively. The steady-state probabilities π1 and π2 were obtained as 0.335 and 0.665, respectively, independent of the initial conditions. The results observed that as the years rolled, the monthly share prices continued to increase due to increased activity in the stock market. In addition, further investigation shows that share price movement and stock market performance influence economic performance. Based on the findings, the Nigerian government and the market authorities should initiate policies that reduce arbitragers' ability to forecast and beat the markets to forestall investors' confidence. Hence, investor property rights protection, discouragement of insider trading, and ensuring that local or domestic investors are enlightened about the stock market and the inherent benefits in Nigeria will enhance stock market efficiency and growth.

Hidden Markov Pólya Trees for High-Dimensional Distributions

The Pólya tree (PT) process is a general-purpose Bayesian nonparametric model that has found wide application in a range of inference problems. It has a simple analytic form and the posterior computation boils down to beta-binomial conjugate updates along a partition tree over the sample space. Recent development in PT models shows that performance of these models can be substantially improved by (i) allowing the partition tree to adapt to the structure of the underlying distributions and (ii) incorporating latent state variables that characterize local features of the underlying distributions. However, important limitations of the PT remain, including (i) the sensitivity in the posterior inference with respect to the choice of the partition tree, and (ii) the lack of scalability with respect to dimensionality of the sample space. We consider a modeling strategy for PT models that incorporates a flexible prior on the partition tree along with latent states with Markov dependency. We introduce a hybrid algorithm combining sequential Monte Carlo (SMC) and recursive message passing for posterior sampling that can scale up to 100 dimensions. While our description of the algorithm assumes a single computer environment, it has the potential to be implemented on distributed systems to further enhance the scalability. Moreover, we investigate the large sample properties of the tree structures and latent states under the posterior model. We carry out extensive numerical experiments in density estimation and two-group comparison, which show that flexible partitioning can substantially improve the performance of PT models in both inference tasks. We demonstrate an application to a mass cytometry dataset with 19 dimensions and over 200,000 observations. Supplementary Materials for this article are available online.

Activity discovery using Dirichlet multinomial mixture models from discrete sensor data in smart homes

To develop smart home technology designed to analyze the activity of residents based on the logs of installed sensors, an activity model tailored to individuals must be constructed from less privacy-invasive sensors to avoid interference in daily life. Unsupervised machine learning techniques are desirable to automatically construct such models without costly data annotation, but their application has not yet been sufficiently successful. In this study, we show that an activity model can be effectively estimated without activity labels via the Dirichlet multinomial mixture (DMM) model. The DMM model assumes that sensor signals are generated according to a Dirichlet multinomial distribution conditioned on a single unobservable activity and can capture the burstiness of sensors, in which even sensors that rarely fire may fire repeatedly after being triggered. We demonstrate the burstiness phenomenon in real data using passive infrared ray motion sensors. For such data, the assumptions of the DMM model are more suitable than the assumptions employed in models used in previous studies. Moreover, we extend the DMM model so that each activity depends on the preceding activity to capture the Markov dependency of activities, and a Gibbs sampler used in the model estimation algorithm is also presented. An empirical study using publicly available data collected in real-life settings shows that the DMM models can discover activities more correctly than the other models and expected to be used as a primitive activity extraction tool in activity analysis.

Hidden Markov models with binary dependence

Hidden Markov models are widely used to model the probabilistic structures with latent variables. The main assumption of hidden Markov models is that; observation symbols are conditionally independent and identically distributed random variables. There exist some cases where this assumption may not be valid in practice. That is, an observation symbol that occurs in the current state may depend on the previous observation symbol that occurred in the previous state. In this study, a new type of hidden Markov model is introduced in which the current pair of hidden state-emitted observation symbol and the previous pair of those have a first-order Markov dependency. The proposed model is capable of capturing a possible first-order Markov dependency between the last and the previous steps of the system. In addition, it provides a better representation for the appropriate real-life problems where, if the observation symbols have conditional dependence. It is an alternative model to the classical hidden Markov model for revealing the Markov dependency between the current and the previous binary information of the system. An experimental study is conducted to show the performance of the proposed model compared to the classical hidden Markov model. Besides, two different case studies are conducted namely the occurrences of strong earthquakes and daily stock prices are modeled with both the classical hidden Markov model and the proposed model, and the results are compared.

Forecasting the Long-Run Behavior of the Stock Price of Some Selected Companies in the Malaysian Construction Sector: A Markov Chain Approach

The fluctuations in stock prices produce a high risk that makes investors uncertain about their investment decisions. The present paper provides a methodology to forecast the long-term behavior of five randomly selected equities operating in the Malaysian construction sector. The method used in this study involves Markov chains as a stochastic analysis, assuming that the price changes have the proparty of Markov dependency with their transition probabilities. We identified a three-state Markov model (i.e., increase, stable, fall) and a two-state Markov model (i.e., increase and fall). The findings suggested that the chains had limiting distributions. The mean return time was computed for respective equities as well as to determine the average duration to return to a stock price increase. The analysis might aid investors in improving their investment knowledge, and they will be able to make better decisions when an equity portfolio possesses higher transition probabilities, higher limiting distribution, and lowest mean return time in response to a price increase. Finally, our investigations suggest that investors are more likely to invest in the GKent based on the three-state model, while VIZIONE seems to be a better investment choice based on a two-state model.

Modeling Stock Index Using Finite State Markov Chain

Existing stock price models are based on time series methodologies which are hard to estimate and involves lots of assumptions. This study, in contrast, assumes that the stock prices follow stochastic process that possesses Markov dependency with finite state transition probabilities. For this purpose, daily stock index data from Pakistan Stock Exchange (PSE) is collected from 2010-2015 and categorized in to 10 state spaces. Based on the results of state transition model, the study highlights the most probable state of return and also its transition into another state. Further, the study used Monte Carlo method of stock index simulations both Markov chain and original stock index. The analysis shows that it is possible to model and forecast stock index by capturing Markov process. The results of the study are helpful for investors in selecting right time of making investment and for academician to think about more sophisticated methods of state identification.

Automated Cell Tracking Using Motion Prediction-Based Matching and Event Handling.

Automated cell segmentation and tracking enables the quantification of static and dynamic cell characteristics and is significant for disease diagnosis, treatment, drug development, and other biomedical applications. This paper introduces a method for fully automated cell tracking, lineage construction, and quantification. Cell detection is performed in the joint spatio-temporal domain by a motion diffusion-based Partial Differential Equation (PDE) combined with energy minimizing active contours. In the tracking stage, we adopt a variational joint local-global optical flow technique to determine the motion vector field. We utilize the predicted cell motion jointly with spatial cell features to define a maximum likelihood criterion to find inter-frame cell correspondences assuming Markov dependency. We formulate cell tracking and cell event detection as a graph partitioning problem. We propose a solution obtained by minimization of a global cost function defined over the set of all cell tracks. We construct a cell lineage tree that represents the cell tracks and cell events. Finally, we compute morphological, motility, and diffusivity measures and validate cell tracking against manually generated reference standards. The automated tracking method applied to reference segmentation maps produces an average tracking accuracy score ( TRA) of 99 percent, and the fully automated segmentation and tracking system produces an average TRA of 89 percent.

Independent attributes control chart for Markov-dependent processes

ABSTRACTStatistical process monitoring (SPM) is a very efficient tool to maintain and to improve the quality of a product. In many industrial processes, end product has two or more attribute-type quality characteristics. Some of them are independent, but the observations are Markovian dependent. It is essential to develop a control chart for such situations. In this article, we develop an Independent Attributes Control Chart for Markov Dependent Processes based on error probabilities criterion under the assumption of one-step Markov dependency. Implementation of the chart is similar to that of Shewhart-type chart. Performance of the chart has been studied using probability of detecting shift criterion. A procedure to identify the attribute(s) responsible for out-of-control status of the process is given.

Profust reliability of linear and circular type F and G systems having two failure criteria under Markov dependency

ABSTRACTIn this study, the profust reliabilities of (n, f, k): F(G) and < n, f, k > : F(G) systems for Markov dependent components are investigated. Having two failure criteria are the common features of these four systems. The usage of both fuzzy approach and two failure criteria in the same system provides us more realistic approach to evaluate the reliability of more complex systems. The component configurations are examined for both linear and circular sequences and the working principle of systems are studied for both F and G systems. Under all these assumptions, the profust reliabilities of (n, f, k): F(G) and < n, f, k > : F(G) systems are obtained using the distribution of run statistics. Also a new membership function different from the linear membership function which is generally used in the literature is proposed. Some numerical results which allow the comparison of the systems from various perspectives and various figures for both linear and circular type systems are presented. Some special cases (between Markov – iid assumption, conventional – profust reliability) are also considered.

Robust statistical recognition and reconstruction scheme based on hierarchical Bayesian learning of HRR radar target signal

A hierarchical Bayesian model is developed to characterize the complex-valued high range resolution (HRR) radar target signal, motivated by the problem of radar automatic target recognition (RATR) robust to low signal-to-noise ratio (SNR) or narrowband interference. Here we assume a sparseness-promoting prior on the complex echoes and a Markov dependency for the location of the dominant scattering center between consecutive HRR signals. The number of the dominant scattering centers can be automatically determined, while the posterior distributions of their complex coefficients and locations can be inferred via such Bayesian model. In the training stage, based on the proposed Bayesian model, the statistical aspect-frame template can be learned for HRR complex training samples from each target-aspect sector under high SNR and without any interference. Considering the low SNR or narrowband interference problem for a test sample, the aspect-frame templates can be updated to make a robust recognition decision for the noised and interfered test sample. Simultaneously, the test sample can be denoised and recovered via the analytically posterior estimation for the reconstruction, which is referred to as the statistical compressive sensing (CS) inversion. In contrast to the traditional CS methods that only utilize the underlying sparse property of a measurement (here a measurement is a test sample), our statistical CS inversion also exploits the statistical information of the training samples, which are under high SNR and without any interference. Therefore, the better recognition and reconstruction performances can be obtained via our method. Efficient inference is performed via variational Bayesian (VB) for the proposed Bayesian model. To validate the formulation, we present our experimental results on the measured HRR dataset, with comparisons to some state-of-the-art methods.

A methodology for stochastic analysis of share prices as Markov chains with finite states

Price volatilities make stock investments risky, leaving investors in critical position when uncertain decision is made. To improve investor evaluation confidence on exchange markets, while not using time series methodology, we specify equity price change as a stochastic process assumed to possess Markov dependency with respective state transition probabilities matrices following the identified state pace (i.e. decrease, stable or increase). We established that identified states communicate, and that the chains are aperiodic and ergodic thus possessing limiting distributions. We developed a methodology for determining expected mean return time for stock price increases and also establish criteria for improving investment decision based on highest transition probabilities, lowest mean return time and highest limiting distributions. We further developed an R algorithm for running the methodology introduced. The established methodology is applied to selected equities from Ghana Stock Exchange weekly trading data.Electronic supplementary materialThe online version of this article (doi:10.1186/2193-1801-3-657) contains supplementary material, which is available to authorized users.

Bayesian Robust Principal Component Analysis

A hierarchical Bayesian model is considered for decomposing a matrix into low-rank and sparse components, assuming the observed matrix is a superposition of the two. The matrix is assumed noisy, with unknown and possibly non-stationary noise statistics. The Bayesian framework infers an approximate representation for the noise statistics while simultaneously inferring the low-rank and sparse-outlier contributions; the model is robust to a broad range of noise levels, without having to change model hyperparameter settings. In addition, the Bayesian framework allows exploitation of additional structure in the matrix. For example, in video applications each row (or column) corresponds to a video frame, and we introduce a Markov dependency between consecutive rows in the matrix (corresponding to consecutive frames in the video). The properties of this Markov process are also inferred based on the observed matrix, while simultaneously denoising and recovering the low-rank and sparse components. We compare the Bayesian model to a state-of-the-art optimization-based implementation of robust PCA; considering several examples, we demonstrate competitive performance of the proposed model.

Estimating time-to-event from longitudinal ordinal data using random-effects Markov models: application to multiple sclerosis progression

Longitudinal ordinal data are common in many scientific studies, including those of multiple sclerosis (MS), and are frequently modeled using Markov dependency. Several authors have proposed random-effects Markov models to account for heterogeneity in the population. In this paper, we go one step further and study prediction based on random-effects Markov models. In particular, we show how to calculate the probabilities of future events and confidence intervals for those probabilities, given observed data on the ordinal outcome and a set of covariates, and how to update them over time. We discuss the usefulness of depicting these probabilities for visualization and interpretation of model results and illustrate our method using data from a phase III clinical trial that evaluated the utility of interferon beta-1a (trademark Avonex) to MS patients of type relapsing-remitting.

Subsample distribution distance and McMC convergence

Abstract. A new measure based on comparison of empirical distributions for sub sequences or parallel runs and the full sequence of Markov chain Monte Carlo simulations, is proposed as a criterion of stability or convergence. The measure is also put forward as a loss function when the design of a Markov chain is optimized. The comparison is based on a Kullback–Leibler (KL) type distance over value sets defined by the output data. The leading term in a series expansion gives an interpretation in terms of the relative uncertainty of cell frequencies. The validity of this term is studied by simulation in two analytically tractable cases with Markov dependency. The agreement between the leading term and the KL-measure is close, in particular when the simulations are extensive enough for stable results. Comparisons with established criteria turn out favourably in examples studied.

Sample size for a two-group comparison of repeated binary measurements using GEE

Controlled clinical trials often randomize subjects to two treatment groups and repeatedly evaluate them at baseline and intervals across a treatment period of fixed duration. A popular primary objective in these trials is to compare the change rates in the repeated measurements between treatment groups. Repeated measurements usually involve missing data and a serial correlation within each subject. The generalized estimating equation (GEE) method has been widely used to fit the time trend in repeated measurements because of its robustness to random missing and mispecification of the true correlation structure. In this paper, we propose a closed form sample size formula for comparing the change rates of binary repeated measurements using GEE for a two-group comparison. The sample size formula is derived incorporating missing patterns, such as independent missing and monotone missing, and correlation structures, such as AR(1) model. We also propose an algorithm to generate correlated binary data with arbitrary marginal means and a Markov dependency and use it in simulation studies.

Markov dependency based on Shannon's entropy and its application to neural spike trains

A measure of simplified dependency is introduced representing Markovian characteristics based on Shannon's entropy and conditional entropy under the Gaussian assumption. It is considered to be the most concise measure for expressing the higher order statistical properties of a time series and, in this regard, to be superior to a correlation or spectral measure. Simplified dependency is shown to be closely related to the prediction error in the autoregressive analysis of a time series and to be applicable also to non-Gaussian processes. Both the truncation method of distribution and the ensemble dependency analysis are informative for clarifying the statistical characteristics of interval sequence of a skewed distribution in a heterogeneous time series. These techniques serve to clarify the neural modulation mechanism.

Quantitative analysis of the sympathetic efferent activity to characterize the integrative function of the sympathetic ganglion.

Using the concept of the Markov dependency, we analyzed the spontaneous activity in the pre- and postganglionic nerve trunks of the feline superior cervical ganglion. The time structure (order and value of time dependency) of the sequence of compound action potentials was determined. The analysis revealed that the time dependency of the postganglionic activity is of higher order and is generally more consistent than that of the preganglionic one. The difference in orders and values between the pre- and postganglionic activities was found to be a measure of the integrative function of the ganglion. A transformation by the ganglion of some additional information, inaccessible in the time structure of the preganglionic activity, seems to underlie this difference.

Microcomputer-based spike train analysis

A system has been developed to analyse statistically the information contained within neuronal spike trains in the central neurvous system. The system consists of a microprocessor development system, together with the peripheral components and transducers. Suitable software packages have been developed to analyse statistical parameters including the mean, variance, entropy, conditional entropy, serial correlation coefficients, Markov dependency and Markov order. By linking up the required routines, the system is capable of responding in real-time and plotting the desired results from the spike train obtained. Such system has been used to study the neuronal spike trains recorded from central vestibular neurons which could be affected by positional changes, anaesthetics and various drugs for the relief of motion sickness.

Performance Comparison Between a Simplified and the Optimal Decoder for Minimizing Symbol Error Rate

The probability of error of the optimal decoder, based on the criterion of minimizing bit-error rate, is calculated for a Markov source imbedded in additive Gaussian noise for several specific cases. The tradeoff between bit-error rate and complexity of a simplified decoder is presented for various signal-to-noise ratios and Markov dependency.

Procedures for determining the order of dependence in streamflow records

As will be documented in detail, a common feature of all the streamflow models in the literature is that they assume some known order of Markov dependency to be available prior to calibration of the model parameters. Yet the statistical methods for finding this order are subtle and perhaps may themselves need refinement. In brief, the problem of finding the minimum order of Markov dependence is a difficult one and yet one that must be faced no matter what streamflow model is selected. This study is devoted in the main to setting forth the extant statistical techniques available for this problem of determining Markov order and applying the stated techniques to finding the order of records of particular rivers in the Tucson basin. Care is taken in describing the hydrologic properties of the rivers studied, since these properties may ultimately be crucial in establishing some a priori feelings for the range of likely orders.