Search results for: Stock Price forecast

Authors: Laura Lukmanto, Harya Widiputra, Lukas

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Studies in economics domain tried to reveal the correlation between stock markets. Since the globalization era, interdependence between stock markets becomes more obvious. The Dynamic Interaction Network (DIN) algorithm, which was inspired by a Gene Regulatory Network (GRN) extraction method in the bioinformatics field, is applied to reveal important and complex dynamic relationship between stock markets. We use the data of the stock market indices from eight countries around the world in this study. Our results conclude that DIN is able to reveal and model patterns of dynamic interaction from the observed variables (i.e. stock market indices). Furthermore, it is also found that the extracted network models can be utilized to predict movement of the stock market indices with a considerably good accuracy.

Keywords: complex dynamic relationship, dynamic interaction network, interactive stock markets, stock market interdependence.

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Authors: Yaojun Wang, Yaoqing Wang

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Stock selection is an important decision-making problem. Many machine learning and data mining technologies are employed to build automatic stock-selection system. A profitable stock-selection system should consider the stock’s investment value and the market timing. In this paper, we present a hybrid system including both engage for stock selection. This system uses a case-based reasoning (CBR) model to execute the stock classification, uses a decision-tree model to help with market timing and stock selection. The experiments show that the performance of this hybrid system is better than that of other techniques regarding to the classification accuracy, the average return and the Sharpe ratio.

Keywords: Case-based reasoning, decision tree, stock selection, machine learning.

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Authors: Julian Becker, Wiebke Hartmann, Sebastian Bertsch, Johannes Nywlt, Matthias Schmidt

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In order to ensure a high service level industrial enterprises have to maintain safety-stock that directly influences the economic efficiency at the same time. This paper analyses established mathematical methods to calculate safety-stock. Therefore, the performance measured in stock and service level is appraised and the limits of several methods are depicted. Afterwards, a new dynamic approach is presented to gain an extensive method to calculate safety-stock that also takes the knowledge of future volatility into account.

Keywords: Inventory dimensioning, material requirement planning, safety-stock calculation.

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Authors: Katleho Daniel Makatjane, Diteboho Lawrence Xaba, Ntebogang Dinah Moroke

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The current study investigates the behaviour of time-varying parameters that are based on the score function of the predictive model density at time t. The mechanism to update the parameters over time is the scaled score of the likelihood function. The results revealed that there is high persistence of time-varying, as the location parameter is higher and the skewness parameter implied the departure of scale parameter from the normality with the unconditional parameter as 1.5. The results also revealed that there is a perseverance of the leptokurtic behaviour in stock returns which implies the returns are heavily tailed. Prior to model estimation, the White Neural Network test exposed that the stock price can be modelled by a GAS model. Finally, we proposed further researches specifically to model the existence of time-varying parameters with a more detailed model that encounters the heavy tail distribution of the series and computes the risk measure associated with the returns.

Keywords: Generalized autoregressive score model, stock returns, time-varying.

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Authors: Birol Yildiz, Abdullah Yalama, Metin Coskun

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Many studies have shown that Artificial Neural Networks (ANN) have been widely used for forecasting financial markets, because of many financial and economic variables are nonlinear, and an ANN can model flexible linear or non-linear relationship among variables. The purpose of the study was to employ an ANN models to predict the direction of the Istanbul Stock Exchange National 100 Indices (ISE National-100). As a result of this study, the model forecast the direction of the ISE National-100 to an accuracy of 74, 51%.

Keywords: Artificial Neural Networks, Istanbul StockExchange, Non-linear Modeling.

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Authors: Petr Seďa

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This paper deals with heterogeneous autoregressive models of realized volatility (HAR-RV models) on high-frequency data of stock indices in the USA. Its aim is to capture the behavior of three groups of market participants trading on a daily, weekly and monthly basis and assess their role in predicting the daily realized volatility. The benefits of this work lies mainly in the application of heterogeneous autoregressive models of realized volatility on stock indices in the USA with a special aim to analyze an impact of the global financial crisis on applied models forecasting performance. We use three data sets, the first one from the period before the global financial crisis occurred in the years 2006-2007, the second one from the period when the global financial crisis fully hit the U.S. financial market in 2008-2009 years, and the last period was defined over 2010-2011 years. The model output indicates that estimated realized volatility in the market is very much determined by daily traders and in some cases excludes the impact of those market participants who trade on monthly basis.

Keywords: Global financial crisis, heterogeneous autoregressive model, in-sample forecast, realized volatility, U.S. stock market.

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Authors: Taylan Kabbani, Ekrem Duman

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Deep Reinforcement Learning (DRL) algorithms can scale to previously intractable problems. The automation of profit generation in the stock market is possible using DRL, by combining  the financial assets price ”prediction” step and the ”allocation” step of the portfolio in one unified process to produce fully autonomous systems capable of interacting with its environment to make optimal decisions through trial and error. This work represents a DRL model to generate profitable trades in the stock market, effectively overcoming the limitations of supervised learning approaches. We formulate the trading problem as a Partially observed Markov Decision Process (POMDP) model, considering the constraints imposed by the stock market, such as liquidity and transaction costs. We then solved the formulated POMDP problem using the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm and achieved a 2.68 Sharpe ratio on the test dataset. From the point of view of stock market forecasting and the intelligent decision-making mechanism, this paper demonstrates the superiority of DRL in financial markets over other types of machine learning and proves its credibility and advantages of strategic decision-making.

Keywords: Autonomous agent, deep reinforcement learning, MDP, sentiment analysis, stock market, technical indicators, twin delayed deep deterministic policy gradient.

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Authors: Fazıl Gökgöz, Fahrettin Filiz

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Electricity prices have sophisticated features such as high volatility, nonlinearity and high frequency that make forecasting quite difficult. Electricity price has a volatile and non-random character so that, it is possible to identify the patterns based on the historical data. Intelligent decision-making requires accurate price forecasting for market traders, retailers, and generation companies. So far, many shallow-ANN (artificial neural networks) models have been published in the literature and showed adequate forecasting results. During the last years, neural networks with many hidden layers, which are referred to as DNN (deep neural networks) have been using in the machine learning community. The goal of this study is to investigate electricity price forecasting performance of the shallow-ANN and DNN models for the Turkish day-ahead electricity market. The forecasting accuracy of the models has been evaluated with publicly available data from the Turkish day-ahead electricity market. Both shallow-ANN and DNN approach would give successful result in forecasting problems. Historical load, price and weather temperature data are used as the input variables for the models. The data set includes power consumption measurements gathered between January 2016 and December 2017 with one-hour resolution. In this regard, forecasting studies have been carried out comparatively with shallow-ANN and DNN models for Turkish electricity markets in the related time period. The main contribution of this study is the investigation of different shallow-ANN and DNN models in the field of electricity price forecast. All models are compared regarding their MAE (Mean Absolute Error) and MSE (Mean Square) results. DNN models give better forecasting performance compare to shallow-ANN. Best five MAE results for DNN models are 0.346, 0.372, 0.392, 0,402 and 0.409.

Keywords: Deep learning, artificial neural networks, energy price forecasting, Turkey.

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Authors: Pei. P. Tan, Don. U.A. Galagedera, Elizabeth A.Maharaj

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This paper examines predictability in stock return in developed and emergingmarkets by testing long memory in stock returns using wavelet approach. Wavelet-based maximum likelihood estimator of the fractional integration estimator is superior to the conventional Hurst exponent and Geweke and Porter-Hudak estimator in terms of asymptotic properties and mean squared error. We use 4-year moving windows to estimate the fractional integration parameter. Evidence suggests that stock return may not be predictable indeveloped countries of the Asia-Pacificregion. However, predictability of stock return insome developing countries in this region such as Indonesia, Malaysia and Philippines may not be ruled out. Stock return in the Thailand stock market appears to be not predictable after the political crisis in 2008.

Keywords: Asia-Pacific stock market, long-memory, return predictability, wavelet

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Authors: LI qiu-min, TIAN yi-xiang, ZHANG gao-xun

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GMDH algorithm can well describe the internal structure of objects. In the process of modeling, automatic screening of model structure and variables ensure the convergence rate.This paper studied a new GMDH model based on polynomial spline  stimation. The polynomial spline function was used to instead of the transfer function of GMDH to characterize the relationship between the input variables and output variables. It has proved that the algorithm has the optimal convergence rate under some conditions. The empirical results show that the algorithm can well forecast Consumer Price Index (CPI).

Keywords: spline, GMDH, nonparametric, bias, forecast.

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Authors: Nabilah Filzah Mohd Radzuan, Andi Putra, Zalinda Othman, Azuraliza Abu Bakar, Abdul Razak Hamdan

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Precipitation forecast is important in avoid incident of natural disaster which can cause loss in involved area. This review paper involves three techniques from artificial intelligence namely logistic regression, decisions tree, and random forest which used in making precipitation forecast. These combination techniques through VAR model in finding advantages and strength for every technique in forecast process. Data contains variables from rain domain. Adaptation of artificial intelligence techniques involved on rain domain enables the process to be easier and systematic for precipitation forecast.

Keywords: Logistic regression, decisions tree, random forest, VAR model.

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Authors: Bin Mu, Site Li, Shijin Yuan

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Under the circumstance of environment deterioration, people are increasingly concerned about the quality of the environment, especially air quality. As a result, it is of great value to give accurate and timely forecast of AQI (air quality index). In order to simplify influencing factors of air quality in a city, and forecast the city’s AQI tomorrow, this study used MATLAB software and adopted the method of constructing a mathematic model of PCA-GABP to provide a solution. To be specific, this study firstly made principal component analysis (PCA) of influencing factors of AQI tomorrow including aspects of weather, industry waste gas and IAQI data today. Then, we used the back propagation neural network model (BP), which is optimized by genetic algorithm (GA), to give forecast of AQI tomorrow. In order to verify validity and accuracy of PCA-GABP model’s forecast capability. The study uses two statistical indices to evaluate AQI forecast results (normalized mean square error and fractional bias). Eventually, this study reduces mean square error by optimizing individual gene structure in genetic algorithm and adjusting the parameters of back propagation model. To conclude, the performance of the model to forecast AQI is comparatively convincing and the model is expected to take positive effect in AQI forecast in the future.

Keywords: AQI forecast, principal component analysis, genetic algorithm, back propagation neural network model.

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Authors: Tero Halme, Juho Kanniainen, Markus Nordberg

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According to the existing literature, companies manage analysts’ expectations of their future earnings by issuing pessimistic earnings guidance to meet the expectations. Consequently, one could expect that markets price this pessimistic bias in advance and penalize companies more for lowering the guidance than reward for beating the guidance. In this paper we confirm this empirically. In addition we show that although guidance revisions have a statistically significant relation to stock returns, that is not the case with the actual earnings surprise. Reason for this could be that, after the annual earnings report also information on future earnings power is given at the same time.

Keywords: Management guidance, earnings guidance, pessimistic bias

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Authors: Noor A. Auzairy, Rubi Ahmad, Catherine S.F. Ho, Ros Z. Z. Sapian

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This paper is to explore the relationship and the level of stock market integration of the Asian countries, primarily concentrating on Malaysia, Thailand, Indonesia, and South Korea, with the world from January 1997 to December 2009. The degree of short-run and long-run stock market integration of those Asian countries are analyzed in order to determine the significance of series of regional and world financial crises, liberalization policies and other financial reforms in influencing the level of stock market integration. To test for cointegration, this paper applies coefficient correlation, univariate regression analyses, cointegration tests, and vector autoregressive models (VAR) by using the four Asian stock markets main indices and the MSCI World index. The empirical findings from this work reveal that there is no long-run stock market integration for the four countries and the world market. However, there is short run integration.

Keywords: Asia, integration, relationship, stock market.

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Authors: R. Sammoura

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In Lebanon, public construction projects are awarded to the contractor submitting the lowest bid price based on a competitive bidding process. The contractor has to make a strategic decision in choosing the appropriate bid price that will offer a satisfactory profit with a greater probability to win. A simulation model for bid price decision making based on the lowest bid price evaluation is developed. The model, built using Crystal Ball decisionengineering software, considers two main factors affecting the bidding process: the number of qualified bidders and the size of the project. The validity of the model is tested on twelve separate projects. The study also shows how to use the model to conduct risk analysis and help any specific contractor to decide on his bid price with associated certainty level in a scientific method.

Keywords: Bid price, Competition, Decision making, Simulation.

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Authors: Chien-Hui Yang, Che-Yang Lin, Ya-Chen Hsu

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Gold passbook is an investing tool that is especially suitable for investors to do small investment in the solid gold. The gold passbook has the lower risk than other ways investing in gold, but its price is still affected by gold price. However, there are many factors can cause influences on gold price. Therefore, building a model to predict the price of gold passbook can both reduce the risk of investment and increase the benefits. This study investigates the important factors that influence the gold passbook price, and utilize the Group Method of Data Handling (GMDH) to build the predictive model. This method can not only obtain the significant variables but also perform well in prediction. Finally, the significant variables of gold passbook price, which can be predicted by GMDH, are US dollar exchange rate, international petroleum price, unemployment rate, whole sale price index, rediscount rate, foreign exchange reserves, misery index, prosperity coincident index and industrial index.

Keywords: Gold price, Gold passbook price, Group Method ofData Handling (GMDH), Regression.

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Authors: Oscar Javier Herrera, Manuel Ángel Camacho

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This paper addresses a cutting edge method of business demand forecasting, based on an empirical probability function when the historical behavior of the data is random. Additionally, it presents error determination based on the numerical method technique ‘propagation of errors.’ The methodology was conducted characterization and process diagnostics demand planning as part of the production management, then new ways to predict its value through techniques of probability and to calculate their mistake investigated, it was tools used numerical methods. All this based on the behavior of the data. This analysis was determined considering the specific business circumstances of a company in the sector of communications, located in the city of Bogota, Colombia. In conclusion, using this application it was possible to obtain the adequate stock of the products required by the company to provide its services, helping the company reduce its service time, increase the client satisfaction rate, reduce stock which has not been in rotation for a long time, code its inventory, and plan reorder points for the replenishment of stock.

Keywords: Demand Forecasting, Empirical Distribution, Propagation of Error.

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Authors: Chen-Yin Kuo

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This paper fist examines three set of bivariate cointegrations between any two of current accounts, stock markets, and currency exchange markets in ten Asian countries. Furthermore, we examined the effect of country characters on this bivariate cointegration. Our findings suggest that for three sets of cointegration test, each sample country at least exists one cointegration. India consistently exhibited a bi-directional causal relationship between any two of three indicators. Unlike Pan et al. (2007) and Phylaktis and Ravazzolo (2005), we found that such cointegration is influenced by three characteristics: capital control; flexibility in foreign exchange rates; and the ratio of trade to GDP. These characteristics are the result of liberalization in each Asian country. This implies that liberalization policies are effective on improving the cointegration between any two of financial markets and current account for ten Asian countries.

Keywords: Current account, stock price, foreign exchange rate, country characteristics, bivariate cointegration, bi-directional causal relationships.

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Authors: Bello Nurudeen Akinsola

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The study analyzed the risk and returns of commercial-property in Southwestern Nigeria and selected stocksmarket investment between 2000 and 2009; compared the inflation hedging characteristics and diversification potentials of investing in commercial-property and selected stock- market investment. Primary data were collected on characteristics, rental and capital values of commercial- properties from their property managers through the use of questionnaire. Secondary data on stock prices and dividends on banking, insurance and conglomerates sectors were sourced from the Nigerian Stock Exchange (2000-2009). The result showed that average return on all the selected stock- investments was higher than that of commercial-property. As regards risk, commercial-property indicated lower risk, compared to stocks. Also the stock-investment had better inflation hedging capacity than commercial-properties; combination of both had diversification potentials. The study concluded that stock-market investment offered attractive higher return than commercial-property although with higher risk and there could be diversification benefits in combining commercial-property with stock- investment.

Keywords: Commercial-Property, Return, Risk, Stock Market

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Authors: Zahra Amirhosseini, Alireza Bashiri

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The aim of this study was to examine and identify the type of Iranian financial market in terms of being symmetrical or asymmetrical and to measure relationship between type of market and the market's indices. In this study, daily information on the market-s Share Price Index, Industrial Index and Top Fifty Most Active Companies during the years 1999-2010 has been used. In addition, to determine type of the financial market, rate of return on Security is taken into account. In this research, by using logistic regression analysis methods, relationship of the market type with the above mentioned indices have been examined. The results showed that the type of the financial market has a positive significant association with market share price index and Industrial Index. Index of Top Fifty Most Active Companies is significantly associated with type of financial market, however this relationship is inverse.

Keywords: All Share Price Index, Asymmetrical Market, Industrial Index, Symmetrical Market, Top Fifty Most Active Companies Index

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Authors: Shih-Ching Lo

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Discrete choice model is the most used methodology for studying traveler-s mode choice and demand. However, to calibrate the discrete choice model needs to have plenty of questionnaire survey. In this study, an aggregative model is proposed. The historical data of passenger volumes for high speed rail and domestic civil aviation are employed to calibrate and validate the model. In this study, different models are compared so as to propose the best one. From the results, systematic equations forecast better than single equation do. Models with the external variable, which is oil price, are better than models based on closed system assumption.

Keywords: forecasting, passenger volume, dynamic competition model, external variable, oil price

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Authors: H. D. Ibrahim, H. C. Chinwenyi, T. Danjuma

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An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.

Keywords: Option price valuation, Partial Differential Equations, Black-Scholes PDEs, Ito process.

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Authors: Irwin Ma, Tony Wong, Thiagas Sankar

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By systematically applying different engineering methods, difficult financial problems become approachable. Using a combination of theory and techniques such as wavelet transform, time series data mining, Markov chain based discrete stochastic optimization, and evolutionary algorithms, this work formulated a strategy to characterize and forecast non-linear time series. It attempted to extract typical features from the volatility data sets of S&P100 and S&P500 indices that include abrupt drops, jumps and other non-linearity. As a result, accuracy of forecasting has reached an average of over 75% surpassing any other publicly available results on the forecast of any financial index.

Keywords: Discrete stochastic optimization, genetic algorithms, genetic programming, volatility forecast

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Authors: P. Kanakasabapathy, Radhika. S,

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In the competitive electricity market environment, the profit of the pumped-storage plant in the energy market can be maximized by operating it as a generator, when market clearing price is high and as a pump, to pump water from lower reservoir to upper reservoir, when the price is low. An optimal self-scheduling plan has been developed for a pumped-storage plant, carried out on weekly basis in order to maximize the profit of the plant, keeping into account of all the major uncertainties such as the sudden ancillary service delivery request and the price forecasting errors. For a pumped storage power plant to operate in a real time market successive self scheduling has to be done by considering the forecast of the day-ahead market and the modified reservoir storage due to the ancillary service request of the previous day. Sliding Window Technique has been used for successive self scheduling to ensure profit for the plant.

Keywords: Ancillary services, BPSO, Power System Economics (Electricity markets), Self-Scheduling, Sliding Window Technique.

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Authors: Muh. Hisjam, Nancy Oktyajati, Wakhid A. Jauhari, Wahyudi Sutopo

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This research is intended to develop a raw material allocation model in timber processing industry in Perum Perhutani Unit I, Central Java, Indonesia. The model can be used to determine the quantity of allocation of timber between chain in the supply chain to select supplier considering factors that are log price and the distance. In determining the quantity of allocation of timber between chains in the supply chain, the model considers the optimal inventory in each chain. Whilst the optimal inventory is determined based on demand forecast, the capacity and safety stock. Problem solving allocation is conducted by developing linear programming model that aims to minimize the total cost of the purchase, transportation cost and storage costs at each chain. The results of numerical examples show that the proposed model can generate savings of the purchase cost of 20.84% and select suppliers with mileage closer.

Keywords: Allocation model, linear programming, purchase costs, storage costs, suppliers, transportation costs.

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Authors: Jung-Hun Cho, Tae-Heon Moon, Jin-Hak Lee

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Land price contains the comprehensive characteristics of urban space, representing the social and economic features of the city. Accordingly, land price can be utilized as an indicator, which can identify the changes of spatial structure and socioeconomic variations caused by urban development. This study attempted to explore the changes in land price by a new road construction. Methodologically, it adopted Space Syntax, which can interpret urban spatial structure comprehensively, to identify the relationship between the forms of road networks and land price. The result of the regression analysis showed the ‘integration index’ of Space Syntax is statistically significant and has a strong correlation with land price. If the integration value is high, land price increases proportionally. Subsequently, using regression equation, it tried to predict the land price changes of each of the lots surrounding the roads that are newly opened. The research methods or study results have the advantage of predicting the changes in land price in an easy way. In addition, it will contribute to planners and project managers to establish relevant polices and smoothing urban regeneration projects through enhancing residents’ understanding by providing possible results and advantages in their land price before the execution of urban regeneration and development projects.

Keywords: Space syntax, urban regeneration, spatial structure, official land price.

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Authors: Mojtaba Rezaei, Elham Heydari

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This paper highlights the empirical results of analyzing the correlation between accounting information and systematic risk. This association is analyzed among financial ratios and systematic risk by considering the financial statement of 39 companies listed on the Tehran Stock Exchange (TSE) for five years (2014-2018). Financial ratios have been categorized into four groups and to describe the special features, as representative of accounting information we selected: Return on Asset (ROA), Debt Ratio (Total Debt to Total Asset), Current Ratio (current assets to current debt), Asset Turnover (Net sales to Total assets), and Total Assets. The hypotheses were tested through simple and multiple linear regression and T-student test. The findings illustrate that there is no significant relationship between accounting information and market risk. This indicates that in the selected sample, historical accounting information does not fully reflect the price of stocks.

Keywords: Accounting information, market risk, systematic risk, efficient market hypothesis, EMH, Tehran Stock Exchange, TSE.

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Authors: M’hamed Outanoute, Mohamed Baslam, Belaid Bouikhalene

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The customers use the best compromise criterion between price and quality of service (QoS) to select or change their Service Provider (SP). The SPs share the same market and are competing to attract more customers to gain more profit. Due to the divergence of SPs interests, we believe that this situation is a non-cooperative game of price and QoS. The game converges to an equilibrium position known Nash Equilibrium (NE). In this work, we formulate a game theoretic framework for the dynamical behaviors of SPs. We use Genetic Algorithms (GAs) to find the price and QoS strategies that maximize the profit for each SP and illustrate the corresponding strategy in NE. In order to quantify how this NE point is performant, we perform a detailed analysis of the price of anarchy induced by the NE solution. Finally, we provide an extensive numerical study to point out the importance of considering price and QoS as a joint decision parameter.

Keywords: Pricing, QoS, Market share game, Genetic algorithms, Nash equilibrium, Learning, Price of anarchy.

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Authors: Tahseen A. Jilani, Aqil S. Burney, C. Ardil

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Time series models have been used to make predictions of academic enrollments, weather, road accident, casualties and stock prices, etc. Based on the concepts of quartile regression models, we have developed a simple time variant quantile based fuzzy time series forecasting method. The proposed method bases the forecast using prediction of future trend of the data. In place of actual quantiles of the data at each point, we have converted the statistical concept into fuzzy concept by using fuzzy quantiles using fuzzy membership function ensemble. We have given a fuzzy metric to use the trend forecast and calculate the future value. The proposed model is applied for TAIFEX forecasting. It is shown that proposed method work best as compared to other models when compared with respect to model complexity and forecasting accuracy.

Keywords: Quantile Regression, Fuzzy time series, fuzzy logicalrelationship groups, heuristic trend prediction.

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Authors: Nadira Kaimova

Abstract:

In this paper it was examined the influence of margin regulation on stock market volatility in EU 1993 – 2014. Regulating margin requirements or haircuts for securities financing transactions has for a long time been considered as a potential tool to limit the build-up of leverage and dampen volatility in financial markets. The margin requirement dictates how much investors can borrow against these securities. Margin can be an important part of investment. Using daily and monthly stock returns and there is no convincing evidence that EU Regulation margin requirements have served to dampen stock market volatility. In this paper was detected the expected negative relation between margin requirements and the amount of margin credit outstanding. Also, it confirmed that changes in margin requirements by the EU regulation have tended to follow than lead changes in market volatility. For the analysis have been used the modified Levene statistics to test whether the standard deviation of stock returns in the 25, 50 and 100 days preceding margin changes is the same as that in the succeeding 25, 50 and 100 days. The analysis started in May 1993 when it was first empowered to set the initial margin requirement and the last sample was in May 2014. To test whether margin requirements influence stock market volatility over the long term, the sample of stock returns was divided into 14 periods, according to the 14 changes in margin requirements.

Keywords: Levene statistic, Margin Regulation, Stock Market, Volatility.

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