The log-periodic-AR(1)-GARCH(1,1) model for financial crashes

TL;DR

This paper introduces a new econometric model combining log-periodic, AR(1), and GARCH(1,1) components to improve the statistical analysis and forecasting of financial crashes, applied to US market indices.

Contribution

It develops and applies a novel log-periodic-AR(1)-GARCH(1,1) model for better inference of crash timing and residual properties in financial data.

Findings

Enhanced residual statistical properties with the new model

Improved accuracy in estimating crash timing

Better fit to US market index data

Abstract

This paper intends to meet recent claims for the attainment of more rigorous statistical methodology within the econophysics literature. To this end, we consider an econometric approach to investigate the outcomes of the log-periodic model of price movements, which has been largely used to forecast financial crashes. In order to accomplish reliable statistical inference for unknown parameters, we incorporate an autoregressive dynamic and a conditional heteroskedasticity structure in the error term of the original model, yielding the log-periodic-AR(1)-GARCH(1,1) model. Both the original and the extended models are fitted to financial indices of U. S. market, namely S&P500 and NASDAQ. Our analysis reveal two main points: (i) the log-periodic-AR(1)-GARCH(1,1) model has residuals with better statistical properties and (ii) the estimation of the parameter concerning the time of the financial crash has been improved.