Forecasting crashes of the stock markets model-based log-periodic law and machine learning methods

The best predictions, despite the overfitting cases were obtained using rf model. This, in accordance with theory should make the results less accurate and the chance of an error should increase. However, overfitting just means that on the training sample the model managed to define for each crash and non crash case a set of parameter values in such way that the trees can correctly define in a unique way a crash and no crash situation from each other orienting only on the parameters values.

Excluding crisis and turning on data preprocessing both influenced positive on our predictions. This means that models gave the best results and work better if they were not trained through crisis years, where great daily drops occurred very often. Also models are better trained and give better results if not all the variables are included in analysis, but only those that explain 70% of variance. The last thing is especially important for the most powerful rf classifier.

From Table 6 it can be noticed that for deeper than 2% crashes retrospective predictions can be obtained only for MICEX; working with DJIA classifiers were not able to detect such a powerful crashes even on validation sample. However, the power and the potential of the models themselves can be seen from the predictions done on MICEX validation sample. This situation we explain with the absence of the necessary number of deep crashes on DJIA as to the relatively stable growth of this index during the period of validation and test samples.

Conclusion

In conclusion we want to summarize the results and match them with our hypothesis and then suggest a field for the future research.

Now we can say that the LPPL parameters do influence the probability of crash as we supposed in our hypothesis. We could see it using simple logit regressions and this was true for both indices. Moreover, machine-learning classifiers gave us pretty good predictions and managed to distinct crashes from no crash cases with high . For classification on the test sample for the period from 2014 to 2016 years (positive predictive value) used to reach . This means that if the model classifies an event as a crash than it is really crash with probability equal to . This results remain true for both indices, however are slightly better for MICEX index.

However, during the period from 2014 to 2016 DJIA and MICEX were growing predominantly sustainably and the volatility rate was low, which resulted in low number of crashes for crash level more than 1.5%. This in turn caused poor predictions for this crash power levels, because crash were not just recognized being too rear events. For lower crash levels the results were more encouraging.

All in all, the answer to the research question for now seems to be positive, or the LPPL parameters seem to have a predictive power and can be used as crash precursors at least on Russian stock exchange (MICEX) and DJIA on subsample sizes from 20 to 200 days and to predict crashes from to daily drop in price.

As a suggested field for future research, more markets have to be tested and probably more machine learning techniques applied. There have to be tested some other indices for longer periods in order to train the models and predict on the subsamples with higher number of powerful crashes. Moreover, we can test if we can use these crash predictions to extract profits acting as bears and construct bearish trading strategy. Finally, the LPPL model modifications sometimes are used to predict ant bubbles, so we can apply the models and methods described here to anti bubbles and construct full scalping trading strategy for sell and buy together.

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