The JLS model with ARMA/GARCH errors
Keywords:Graph operations, hierarchical diamond lattice, JLS model, financial bubbles and crashes, ARMA/GARCH errors
Prior to crashes, the stock index price time series is characterised by the Log-Periodic Power Law (LPPL) equation of the Johansen–Ledoit–Sornette (JLS) model, which leads to a critical point indicating a change to a new market regime. In this paper, we describe the hierarchical diamond lattice, upon which the JLS model is derived, using the diamond lattice operation Di and derive the recursion for the coefficients of the growth function in a diamond lattice rooted at the main root vertex rm. Further, to verify the adequacy of the JLS model, we analyse the model’s residuals and propose its generalization, using the ARMA/GARCH error model. We determine the ARMA/GARCH orders using the extended autocorrelation function (EACF) method and compare the results with those of the Akaike and Bayesian Information Criteria. Using the data for 33 major world stock indices we show, that proposed generalization of the JLS model in general performs better in predicting the market regime changes and has also the ability to recognise false bubble identification, indicated by the JLS model.