Many key variablesin 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 . The approaches are based on robust inference methods exploiting conservativeness properties of t-statistics Ibragimov and Muller (2010,2016) and several new results on their applicability in the settings considered . In the approaches, estimates of parameters of interest 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 .
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 .
R
key variablesin finance, economics and risk management,
financial and economic variables,
D
and foreign exchange rates
R
of some usually largely unknown type. The presence of non-linear dependence (usually modelled using GARCH-type dynamics) and heavy-tailedness
. These properties
R
, volatility clustering and predictive regressions
and volatility clustering
D
(ACFs)
R
The paper presents several
This paper presents
R
, volatility clustering and nonlinear dependence
and volatility clustering
R
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
We further provide
R
them
the measures
A
time series, including
D
exhibiting heavy-tailedness properties
D
inference methods exploiting conservativeness properties of
R
Ibragimov and Muller (2010,2016) and several
tests and
R
in the settings considered
are presented
R
estimates of parameters of interest
parameter estimates (e.g., estimates of measures of nonlinear dependence)
A
,
A
the
D
a wide range of
R
financial and economic
real-world financial
R
advantages of the new approaches over existing ones and their wide applicability
the advantages and wide applicability of the proposed approaches