Predicting Stock Market Crashes Using LPPL Model and Machine Learning

A problem of crash forecasting is highly important as the ability to foreseen crashes can allow the users of this information to earn high profits, influence the corporate decisions about investments and the governmental policies concerning business cycle regulations. Now there are a lot of papers dedicated to the problem of crash forecasting; a number of different models were invented and among them there is a log-periodic power law and model, based on this law (LPPL). The majority of papers consider time of crash as the main parameter to estimate and much less attention was paid to the values of other parameters. In this research we are going to apply a different approach to the LPPL parameters estimation and obtain vectors of parameters estimation by continuously fitting the model on a set of rolling subsamples always shifting one day ahead an assuming the crash to occur the next day. The main goal of this research is to check whether the LPPL parameters estimates influence significantly the probability of crash and if they do, check if these parameters estimates have the predictive power by using them as an input data for machine learning classifiers. The thesis we are going to check is that the LPPL parameters significantly influence the probability of crash and can be used as an input data for classifiers to do future crash predictions. The LPPL fitting is to be done in this paper using SANN method; to check if the parameters estimates influence the probability of crash simple logits are to be used; as classifiers to predict crashes we will use the following 4 models: random forest, support vector machine, gradient boosting machine, stepwise logit with AIC criterion. As an empirical result in this paper we were not able to reject the hypothesis about significant influence of the LPPL parameters values on crash probability for both DJIA and MICEX indices. Classification confirmed that the LPPL parameters estimates have strong enough predictive power.