Applications of linear ordinary differential equations and dynamic system to economics - an example of Taiwan stock index TAIEX

Chen, Nien Ping; Li, Meng Rong; Lin, Tsung Jui Chiang; Lee, Young Shiuan; Miao, Daniel Wei Chung

doi:10.1504/ijdsde.2017.085824

Cited by 3 publications

(7 citation statements)

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“…Li et al [17] also applied the same methods to model German DAX and tried to develop a risk detecting instrument of approaching financial catastrophe. Chen et al [2] further combined Newton's law of cooling and dynamic integration to explain the phenomenon of mean reversion by modelling TAIEX. On the basis of existing researches, we try to transform the logistic model into some models by considering the stock price, the velocity of the stock price, and the stock return as the subject, respectively.…”

Section: Literature Reviewmentioning

confidence: 99%

“…The dynamic models above are built on the work of Chen et al [2]. But all of them consist of two coefficients instead of one as in their study.…”

Section: Model C (Dynamic Relative Growth Rate Transformed Logistic Mmentioning

confidence: 99%

“…The solution can be found in the article of Chen et al [2]. As applying these dynamic models, we discretize and convert them into difference equations since the time interval between the two given points at times 0 and 1 is relatively short compared to the interval of the complete data.…”

Section: Model D (Dynamic General Newton Model)mentioning

confidence: 99%

“…Fama's 1965 article [1] is one of the most commonly known ones. Among massive researches of modelling stock prices, Chen et al [2] have investigated and modelled the mean reversion of stock prices. They characterized the phenomenon by three dynamic models derived from the concept of Newton's law of cooling.…”

Section: Introductionmentioning

confidence: 99%

“…In order to depict the movement with respect to time, we attempt to modify the logistic growth model and bring in the technique of dynamic integration to construct some models. Furthermore, the models describing the mean reversion in the existing study only consist one time related coefficient [2]. We include two time-varying coefficients for constructing new models to increase the accuracy.…”

Section: Introductionmentioning

confidence: 99%

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Applications of Parameterized Nonlinear Ordinary Differential Equations and Dynamic Systems: An Example of the Taiwan Stock Index

Chiang-Lin

Lee

2018

International Journal of Differential Equations

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Considering the phenomenon of the mean reversion and the different speeds of stock prices in the bull market and in the bear market, we propose four dynamic models each of which is represented by a parameterized ordinary differential equation in this study. Based on existing studies, the models are in the form of either the logistic growth or the law of Newton's cooling. We solve the models by dynamic integration and apply them to the daily closing prices of the Taiwan stock index, Taiwan Stock Exchange Capitalization Weighted Stock Index. The empirical study shows that some of the models fit the prices well and the forecasting ability of the best model is acceptable even though the martingale forecasts the prices slightly better. To increase the forecasting ability and to broaden the scope of applications of the dynamic models, we will model the coefficients of the dynamic models in the future. Applying the models to the market without the price limit is also our future work.

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Section: Literature Reviewmentioning

confidence: 99%

“…The dynamic models above are built on the work of Chen et al [2]. But all of them consist of two coefficients instead of one as in their study.…”

Section: Model C (Dynamic Relative Growth Rate Transformed Logistic Mmentioning

confidence: 99%

Section: Model D (Dynamic General Newton Model)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Applications of Parameterized Nonlinear Ordinary Differential Equations and Dynamic Systems: An Example of the Taiwan Stock Index

Chiang-Lin

Lee

2018

International Journal of Differential Equations

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Introduction

Nwogugu¹

2018

Indices, Index Funds and ETFs

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Study of Asian indexes by a newly derived dynamic model

et al. 2022

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We take the stock prices as a dynamic system and characterize its movements by a newly derived dynamic model, called the new Price Reversion Model (nPRM), for which the solution is derived and carefully analyzed under different circumstances. We also develop a procedure of applying the nPRM to real daily closing prices of a stock index. This proposed procedure brings a different perspective to the study of stock prices based on thermodynamics, and the time varying coefficients in the nPRM offer economic meanings of the stock movements. More specifically, the average of smoothed historical data A in the nPRM, analogous to the environment temperature in the Newton’s law of cooling, represent an implied equilibrium price. The heat transfer coefficient κ is adapted to be either negative or positive, which illustrates the speed of convergence or divergence of stock prices, respectively. The empirical study of ten Asian stock indexes shows that the nPRM accurately characterizes and forecasts the market values.

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Applications of linear ordinary differential equations and dynamic system to economics - an example of Taiwan stock index TAIEX

Cited by 3 publications

References 0 publications

Applications of Parameterized Nonlinear Ordinary Differential Equations and Dynamic Systems: An Example of the Taiwan Stock Index

Applications of Parameterized Nonlinear Ordinary Differential Equations and Dynamic Systems: An Example of the Taiwan Stock Index

Introduction

Study of Asian indexes by a newly derived dynamic model

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