10h30 - 12h10
Monte Carlo Methods for Testing Statistical Hypotheses
In most applications of statistics, particularly in financial engineering, dynamic stochastic models are assumed to satisfy certain hypotheses, mainly related to their probabilistic distribution. For example, in time series, random error terms (innovations) are often assumed to be independent and/or have a distribution belonging to a specific family of distributions. The problem is then to test these statistical hypotheses. To make things worse, the asymptotic distribution of the tests statistics generally depends on unknown parameters, so it is impossible to construct tables of critical values. The solution to that problem is to use Monte Carlo methods to estimate the p-value of test statistics. In this tutorial, I will focus on several interesting methods to estimate p-values: bootstrap, parametric bootstrap and multipliers methodology. Examples of applications in actuarial science, econometrics, and financial engineering will be given.