  Many financial and economic variables, including financial returns, exhibit
nonlinear dependence, heterogeneity and heavy-tailedness. These properties may
make problematic the analysis of (non-)efficiency and volatility clustering in
economic and financial markets using traditional approaches that appeal to
asymptotic normality of sample autocorrelation functions of returns and their
squares.
  This paper presents new approaches to deal with the above problems. We
provide the results that motivate the use of measures of market
(non-)efficiency and volatility clustering based on (small) powers of absolute
returns and their signed versions.
  We further provide new approaches to robust inference on the measures in the
case of general time series, including GARCH-type processes. The approaches are
based on robust $t-$statistics tests and new results on their applicability are
presented. In the approaches, parameter estimates (e.g., estimates of measures
of nonlinear dependence) are computed for groups of data, and the inference is
based on $t-$statistics in the resulting group estimates. This results in valid
robust inference under heterogeneity and dependence assumptions satisfied in
real-world financial markets. Numerical results and empirical applications
confirm the advantages and wide applicability of the proposed approaches.
