An analytical comparison between Standard Johansen-Ledoit-Sornette (SJLS) Model and Generalized Johansen-Ledoit-Sornette (GJLS) model

Mustafa, Mamat and Nurfadhlina, Abdul Halim and Devendran, Indiran (2014) An analytical comparison between Standard Johansen-Ledoit-Sornette (SJLS) Model and Generalized Johansen-Ledoit-Sornette (GJLS) model. Applied Mathematical Sciences, 8 (45). pp. 2257-2267. ISSN 13147552 [P]

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Abstract

Economic bubbles can be defined as transient upward movements of prices above intrinsic value. The Standard Johansen-Ledoit-Sornette (SJLS) model and Generalized Johansen-Ledoit-Sornette (GJLS) models have been developed as flexible tools to detect bubble and forecasts the possible time of crash, tc. These models combines the economic theory of rational expectation bubbles with finite-time singular crash hazard rates, behavioural finance on imitation and herding of investors and traders as well as mathematical statistical physics of bifurcations and phase transitions. It has been employed successfully to a large variety of economic bubbles in many different markets. This study focused on the analytical differences between these two models to point out the best model to be used in forecasting time of crash and bubble detection. By doing so we are able to evaluate the differences and similarities of the methods and results in a practical way. The results appears that the two models are most appropriate to use for identify and predict financial bubbles and crash. But, the GJLS models selected as best model due to the limitation on the outputs of SJLS. The SJLS model only can detect and forecasts the financial bubble, but the GJLS models not only detect the time of crash but estimate the intrinsic value and the crash non-linearity as well. With the estimated intrinsic value, the unexplained problem which is differentiation between exponentially growing fundamental price and an exponentially growing bubble price are overcome. Moreover, the standard JLS model just describes the dynamics of the price during the bubble formation but the GJLS model can determines the dynamics of crash after the bubble by specifying how the price evolves towards the intrinsic value during crash.

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