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Abstract: This study examines the martingale difference hypothesis (MDH) for the European emerging unit-linked insurance markets, using the automatic portmanteau (AQ) test of Escanciano and Lobato, 2009 for the three sub-periods of pre-crisis, crisis, and post-crisis. The martingale difference sequence is called conditional mean independence in the statistical literature, implying that the asset return is purely non-predictable from its own past. This study proposes a data-driven Box-Pierce for serial correlation. The automatic Portmanteau test for serial correlation test presents higher power in simulations than the existing ones for models commonly employed in empirical finance: the researcher does not need to specify the order of the autocorrelation tested, since the test automatically chooses this number; its asymptotic null distribution is chi-square with one degree of freedom, so there is no need of using a bootstrap procedure to estimate the critical values and the test is robust to the presence of conditional heteroskedasticity of unknown form. This paper examines return predictability of the daily ING unit-linked funds prices and aims at monitoring any improvement in the degree of efficiency in time. [Copyright &y& Elsevier]