Analysis of the conditional stock-return distribution under incomplete specification

The analysis of the distribution of the stock-returns plays an important role in financial theory since a distributional assumption is required for mean–variance portfolio theory, theoretical models of capital asset prices, determining the price of derivative products, efficient estimation by maximum likelihood procedure and establishing forecasting confidence intervals. Up to now, most of the studies analyze the unconditional distribution of the stock-returns using the likelihood ratio test, the Schwarz Information Criterion or by graphical analysis. However, the analysis of the conditional distribution is very important since most of the empirical financial studies use high-frequency data and these data present dynamic structure. In this paper, we focus on the conditional distribution. We design different bootstrap mechanisms for comparing the goodness-of-fit of several functional forms postulated under the null hypothesis for individual Spanish stocks and for the General Index of the Madrid Stock Market. We use the Crámer–von Mises test statistic, based on the standardized residuals and assuming that the null distribution can depend on some unknown parameters.