BIFURCATION AND CHAOS ANALYSIS IN A DISCRETE-DELAY DYNAMIC MODEL FOR A STOCK MARKET

2013 ◽  
Vol 23 (09) ◽  
pp. 1350155 ◽  
Author(s):  
LORETTI DOBRESCU ◽  
MIHAELA NEAMTU ◽  
DUMITRU OPRIS
Keyword(s):  
Stock Market ◽  
Stochastic Model ◽  
Time Evolution ◽  
Deterministic Model ◽  
Chaotic Behavior ◽  
Market Price ◽  
Nonlinear Effects ◽  
Nonlinear Dynamic System ◽  
Acting Out ◽  
Discrete Delay

Using a discrete-delay nonlinear dynamic system, we model the time evolution of a stock market price index and net stock of savings in mutual funds. The proposed deterministic model has a unique steady-state, so its time evolution is determined by nonlinear effects acting out of equilibrium. For this model, we find the local stability properties and the local bifurcations conditions, given the parameter space. Specifically, we find that in both versions of the model (with and without delay) a Neimark–Sacker bifurcation can occur. Moreover, we show that the system without delay has a chaotic behavior. Finally, we formulate the associated discrete stochastic model and establish the conditions for asymptotic stability. Several numerical simulations are finally performed for both the deterministic and the stochastic model to justify the theoretical results.

Share Market Data Prediction Strategies using Deep Learning Algorithm

2019 ◽  
Vol 13 ◽  
Author(s):  
A John. ◽  
D. Praveen Dominic ◽  
M. Adimoolam ◽  
N. M. Balamurugan
Keyword(s):  
Neural Network ◽  
Deep Learning ◽  
Stock Market ◽  
Predictive Analytics ◽  
Learning Algorithm ◽  
Market Price ◽  
Stochastic Gradient ◽  
Stochastic Gradient Descent ◽  
Mining Machine ◽  
Gradient Descent Algorithm

Background:: Predictive analytics has a multiplicity of statistical schemes from predictive modelling, data mining, machine learning. It scrutinizes present and chronological data to make predictions about expectations or if not unexplained measures. Most predictive models are used for business analytics to overcome loses and profit gaining. Predictive analytics is used to exploit the pattern in old and historical data. Objective: People used to follow some strategies for predicting stock value to invest in the more profit-gaining stocks and those strategies to search the stock market prices which are incorporated in some intelligent methods and tools. Such strategies will increase the investor’s profits and also minimize their risks. So prediction plays a vital role in stock market gaining and is also a very intricate and challenging process. Method: The proposed optimized strategies are the Deep Neural Network with Stochastic Gradient for stock prediction. The Neural Network is trained using Back-propagation neural networks algorithm and stochastic gradient descent algorithm as optimal strategies. Results: The experiment is conducted for stock market price prediction using python language with the visual package. In this experiment RELIANCE.NS, TATAMOTORS.NS, and TATAGLOBAL.NS dataset are taken as input dataset and it is downloaded from National Stock Exchange site. The artificial neural network component including Deep Learning model is most effective for more than 100,000 data points to train this model. This proposed model is developed on daily prices of stock market price to understand how to build model with better performance than existing national exchange method.

Non-Linearity and Chaotic Behaviour in Cyprus Stock Market

2015 ◽  
Vol 5 (4) ◽  
Author(s):  
Athina Bougioukou
Keyword(s):  
Lyapunov Exponent ◽  
Stock Market ◽  
Chaos Theory ◽  
Linear Dependence ◽  
Chaotic Behavior ◽  
Efficient Market Hypothesis ◽  
Chaotic Behaviour ◽  
Maximum Lyapunov Exponent ◽  
Efficient Market ◽  
General Index

The intention of this research is to investigate the aspect of non-linearity and chaotic behavior of the Cyprus stock market. For this purpose, we use non-linearity and chaos theory. We perform BDS, Hinich-Bispectral tests and compute Lyapunov exponent of the Cyprus General index. The results show that existence of non-linear dependence and chaotic features as the maximum Lyapunov exponent was found to be positive. This study is important because chaos and efficient market hypothesis are mutually exclusive aspects. The efficient market hypothesis which requires returns to be independent and identically distributed (i.i.d.) cannot be accepted.

scholarly journals Stochastic and deterministic mathematical model of cholera disease dynamics with direct transmission

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Getachew Teshome Tilahun ◽  
Woldegebriel Assefa Woldegerima ◽  
Aychew Wondifraw
Keyword(s):  
Mathematical Model ◽  
Stochastic Model ◽  
Deterministic Model ◽  
Equilibrium Points ◽  
Invariant Solution ◽  
Stochastic Approach ◽  
Disease Dynamics ◽  
Treatment Rate ◽  
Invariant Region ◽  
Contact Transmission

AbstractIn this paper we develop a stochastic mathematical model of cholera disease dynamics by considering direct contact transmission pathway. The model considers four compartments, namely susceptible humans, infectious humans, treated humans, and recovered humans. Firstly, we develop a deterministic mathematical model of cholera. Since the deterministic model does not consider the randomness process or environmental factors, we converted it to a stochastic model. Then, for both types of models, the qualitative behaviors, such as the invariant region, the existence of a positive invariant solution, the two equilibrium points (disease-free and endemic equilibrium), and their stabilities (local as well as global stability) of the model are studied. Moreover, the basic reproduction numbers are obtained for both models and compared. From the comparison, we obtained that the basic reproduction number of the stochastic model is much smaller than that of the deterministic one, which means that the stochastic approach is more realistic. Finally, we performed sensitivity analysis and numerical simulations. The numerical simulation results show that reducing contact rate, improving treatment rate, and environmental sanitation are the most crucial activities to eradicate cholera disease from the community.

STOCHASTIC PREDATION MODEL WITH DEPLETION

1979 ◽  
Vol 111 (4) ◽  
pp. 465-470 ◽  
Author(s):  
Guy L. Curry ◽  
Richard M. Feldman
Keyword(s):  
Stochastic Model ◽  
Deterministic Model ◽  
Expected Number ◽  
Numerical Comparisons ◽  
Prey Depletion

AbstractA stochastic model is developed for the expected number of prey taken by a single predator when prey depletion is apparent. The so-called “random predator equation” with prey exploitation of Royama and Rogers is compared with the stochastic model. The numerical comparisons illustrate situations where the deterministic model provides adequate and inadequate approximations.

scholarly journals Fractional differencing in stock market price and online presence of global tourist corporations

2019 ◽  
Vol 24 (48) ◽  
pp. 194-204 ◽  
Author(s):  
Francisco Flores-Muñoz ◽  
Alberto Javier Báez-García ◽  
Josué Gutiérrez-Barroso
Keyword(s):  
Time Series ◽  
Stock Market ◽  
Market Price ◽  
Google Trends ◽  
Data Sets ◽  
Market Prices ◽  
Content Type ◽  
Search Results ◽  
Online Presence ◽  
Fractional Differencing

Purpose This work aims to explore the behavior of stock market prices according to the autoregressive fractional differencing integrated moving average model. This behavior will be compared with a measure of online presence, search engine results as measured by Google Trends. Design/methodology/approach The study sample is comprised by the companies listed at the STOXX® Global 3000 Travel and Leisure. Google Finance and Yahoo Finance, along with Google Trends, were used, respectively, to obtain the data of stock prices and search results, for a period of five years (October 2012 to October 2017). To guarantee certain comparability between the two data sets, weekly observations were collected, with a total figure of 118 firms, two time series each (price and search results), around 61,000 observations. Findings Relationships between the two data sets are explored, with theoretical implications for the fields of economics, finance and management. Tourist corporations were analyzed owing to their growing economic impact. The estimations are initially consistent with long memory; so, they suggest that both stock market prices and online search trends deserve further exploration for modeling and forecasting. Significant differences owing to country and sector effects are also shown. Originality/value This research contributes in two different ways: it demonstrate the potential of a new tool for the analysis of relevant time series to monitor the behavior of firms and markets, and it suggests several theoretical pathways for further research in the specific topics of asymmetry of information and corporate transparency, proposing pertinent bridges between the two fields.

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