In this work we employ a model based on the critical phenomena theory to explain the asset price formation associated to the pre- crash period. The evolution of the price is given by an over-all power law acceleration decorated by oscillations called log-periodic model. This growth is likely to be interrupted by a crash of prices that happen in a short and critical time interval. The purpose of this work is to investigate the log-periodic model within the econometric approach by suggesting guidelines to achieve its performance in order to accomplish reliable statistical inferences. Based on this analysis we here propose a stretching of the log-periodic model through the introduction of an autoregressive structure and an autoregressive conditional heteroskedasticity at the residual of the original model. The current model is applied to the study of financial index of the stock markets worldwide as: HANG SENG (Hong Kong), NASDAQ (USA), IBOVESPA (Brazil), MERVAL (Argentina), INDIA BSE NATIONAL (India) and FTSE100 (United Kingdom). The output of such work indicates that the use of the logperiodic model requires some care as far as its inference basis is fragile.