Authors: Anton Skrobotov, Rasmus Pedersen and Rustam Ibragimov
Abstract: Many key variables in finance, economics and risk management, including financial returns and foreign exchange rates, exhibit nonlinear dependence, heterogeneity and heavy-tailedness of some usually largely unknown type. The presence of non-linear dependence (usually modelled using GARCH-type dynamics) and heavy-tailedness may make problematic the analysis of (non-)efficiency, volatility clustering and predictive regressions in economic and financial markets using traditional approaches that appeal to asymptotic normality of sample autocorrelation functions (ACFs) of returns and their squares. The paper presents several new approaches to deal with the above problems. We provide the results that motivate the use of measures of market (non-)efficiency, volatility clustering and nonlinear dependence based on (small) powers of absolute returns and their signed versions. The paper provides asymptotic theory for sample analogues of the above measures in the case of general time series, including GARCH-type processes. It further develops new approaches to robust inference on them in the case of general GARCH-type processes exhibiting heavy-tailedness properties typical for real-world financial markets. The approaches are based on robust inference methods exploiting conservativeness properties of t-statisticsIbragimov and Muller (2010,2016) and several new results on their applicability in the settings considered. In the approaches, estimates of parameters of interest (e.g., measures of nonlinear dependence given by sample autocorrelations of powers of the returns' absolute values) are computed for groups of data and the inference is based on t-statistics in resulting group estimates. This results in valid robust inference under a wide range of heterogeneity and dependence assumptions satisfied in financial and economic markets. Numerical results and empirical applications confirm advantages of the new approaches over existing ones and their wide applicability in the study of market (non-)efficiency, volatility clustering, nonlinear dependence, and other areas.