This paper aims to test the finite sample properties of the automatic variance ratio (AVR) test and suggest suitable measure to improve its small sample properties under conditional heteroskedasticity and apply it to test the martingale hypothesis in the stock prices of the Portugal, Ireland, Italy, Greece and Spain (PIIGS economies) markets. This paper also seeks to investigate that “If the time series is not martingale, then what else?”
Monte Carlo experiments have been undertaken to test the small sample properties of automatic variance ratio (AVR) test. The study uses AVR test on daily and weekly data of the indices to investigate their martingale behaviour. It uses detrended fluctuation analysis (DFA) and BDS test statistics to answer, “If not martingale, then what else?”. The study also applies moving subsample approach to examine the dynamic behavior of stock prices and to obtain inferential findings robust to possible structural changes and presence of influential outliers.
The author finds that weighted bootstrap procedure significantly improves the small sample properties of AVR tests under conditional heteroskedasticity. The results provide evidence in support of the weak‐form efficiency of Italy and Spain. But Portugal, Ireland and Greece exhibit signs of long memory in the stock prices. All indices also exhibit chaotic characteristics.
This paper has both methodological and empirical originality. On the methodological aspect, the author proposes weighted bootstrap procedure on AVR test to improve its small sample properties. On the empirical side, the study finds that all stocks exhibit dynamic behavioral characteristics which change over time.
