Estimation on Rational Speculative Bubbles in Stock Market by Using Generalised Johansen-Ledoit-Sornette Model

IF 0.5 Q3 MATHEMATICS

Malaysian Journal of Mathematical Sciences Pub Date : 2022-12-23 DOI:10.47836/mjms.16.4.05

N. Borhan, N. Halim

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引用次数: 0

Abstract

This paper discusses the generalized Johansen-Ledoit-Sornette (GJLS) model in determining and predicting the size of rational speculative bubbles in stock market. In this study, the GJLS model is used as an approach to detect the presence and prediction of rational speculative bubble sizes of the stock market. The stock markets chosen in this study are Hang Seng, Nikkei 225 and S\&P 500. This is because China, Japan and United States are countries that pioneers the world economy. This paper presents step by step on finding the linear and non-linear parameters in the generalized Johansen-Ledoit-Sornette model using the Ordinary Least Squares method for the linear parameters and formulas for the non-linear parameters. There are 7 parameters that need to be identified which are A,B and C for linear parameter and ω, φ, β and t for the non-linear parameter. Then, the size of speculative rational bubbles is determined and predict using the GJLS model. The size of speculative rational bubbles for future cycle is forecasted. Then, the effect of the presence of rational speculative bubbles towards the economy is discussed.

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用广义Johansen-Ledoit-Sornette模型估计股票市场的理性投机泡沫

本文讨论了广义Johansen-Ledoit-Sornette (GJLS)模型在股票市场理性投机泡沫大小的确定和预测中的应用。本文采用GJLS模型来检测股票市场是否存在理性投机泡沫，并对其规模进行预测。本研究选择的股票市场是恒生、日经225和标准普尔500。这是因为中国、日本和美国是世界经济的先行者。本文给出了用普通最小二乘法求解广义Johansen-Ledoit-Sornette模型的线性参数和非线性参数的公式。需要识别的参数有7个，线性参数为A、B和C，非线性参数为ω、φ、β和t。然后，利用GJLS模型确定和预测投机理性泡沫的规模。预测了未来周期投机理性泡沫的大小。然后，讨论了理性投机泡沫的存在对经济的影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Malaysian Journal of Mathematical Sciences MATHEMATICS-

CiteScore

1.10

自引率

20.00%

发文量

期刊介绍： The Research Bulletin of Institute for Mathematical Research (MathDigest) publishes light expository articles on mathematical sciences and research abstracts. It is published twice yearly by the Institute for Mathematical Research, Universiti Putra Malaysia. MathDigest is targeted at mathematically informed general readers on research of interest to the Institute. Articles are sought by invitation to the members, visitors and friends of the Institute. MathDigest also includes abstracts of thesis by postgraduate students of the Institute.