The Statistics Seminar speaker for Wednesday, October 16, 2019, is Stoyan Stoyanov, a research professor of finance in the Center for Finance and the College of Business, Stony Brook University. Prior to joining Stony Brook University, Stoyan was a professor of finance at EDHEC Business School and head of research at EDHEC Risk Institute–Asia. He worked for over six years as head of quantitative research for FinAnalytica, a financial technology firm, currently a part of FactSet. His research focuses on probability theory, extreme risk modeling, and asset pricing. He has published over forty articles in leading academic and practitioner-oriented scientific journals such as Annals of Operations Research, Journal of Banking and Finance, and the Journal of Portfolio Management, contributed to many professional handbooks and co-authored five books on probability and stochastics, financial risk assessment and portfolio optimization. He holds a master in science in applied probability and statistics from Sofia University and a PhD in mathematical finance from Karlsruhe Institute of Technology.
Talk: Testing for Model Adequacy - A Metric Approach
Abstract: We propose a new method to assess model adequacy based on functionals with metric properties quantifying the deviation of the conditional expectation E(Y|X) of a response variable Y from a suggested parametric non-linear model m(X). We derive the asymptotic distribution of a test statistic under linear and non-linear specifications, when the parameter estimator is asymptotically linear and asymptotically normal. We find that the power of the test in misspecified linear models is better or similar to some of the most commonly used alternatives in the literature. The metric properties uniquely position the proposed method to study the impact of three types of aggregation on the specification error -- aggregation of observations across time, cross-sectional aggregation of variables, or aggregation of different models for the same variable. For example, neglected non-linearity in linear models is shown to be asymptotically negligible with a power-type rate of decay in the case of independent observations when data are aggregated across time. We provide an illustration from the field of finance with the capital asset pricing model (CAPM). The frequency of rejection of the linear specification of the CAPM can decline more than three times when the model is estimated with monthly rather than daily returns.