We introduce a general class of multifractional stochastic processes driven by a multifractional Brownian motion  and study estimation  of their pointwise H\"older exponents (PHE) using the localized generalized quadratic variation approach. By comparing it with the other two  benchmark estimation approaches  through a simulation study, we show that our estimator has better performance in the case where the observed process is some unknown bivariate function of time and multifractional Brownian motion . The time-varying PHE feature allows us to apply such class of multifractional processes to model stock prices under various market conditions . An empirical study on modeling cross-listed stocks provides new evidence that equity's path roughness varies via time and  price informativeness properties from global  markets.
We introduce a general class of stochastic processes driven by a multifractional Brownian motion (mBm) and study estimation problems of their pointwise H\"older exponents (PHE) based on a new localized generalized quadratic variation approach. By comparing our suggested approach with the other two existing benchmark estimation approaches (classicial LGQV and oscillation approach) through a simulation study, we show that our estimator has better performance in the case where the observed process is some unknown bivariate function of time and mBm . The time-varying feature of the PHE allows us to apply such class of multifractional processes to model stock prices under various market conditions , that are both time-dependent and region-dependent. As an application to finance, an empirical study on modeling cross-listed stocks provides new evidence that the equity path's roughness varies via time and stock price informativeness properties from global stock markets.
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multifractional
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(mBm)
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problems
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using the
based on a new
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it
our suggested approach
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existing
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(classicial LGQV and oscillation approach)
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multifractional Brownian motion
mBm
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PHE feature
feature of the PHE
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. An
, that are both time-dependent and region-dependent. As an application to finance, an
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equity's path
the equity path's
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stock
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stock