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Full-Text Articles in Social and Behavioral Sciences
Glivenko-Cantelli Theorems For Integrated Functionals Of Stochastic Processes, Jia Li, Congshan Zhang, Yunxiao Liu
Glivenko-Cantelli Theorems For Integrated Functionals Of Stochastic Processes, Jia Li, Congshan Zhang, Yunxiao Liu
Research Collection School Of Economics
We prove a Glivenko-Cantelli theorem for integrated functionals of latent continuous-time stochastic processes. Based on a bracketing condition via random brackets, the theorem establishes the uniform convergence of a sequence of empirical occupation measures towards the occupation measure induced by underlying processes over large classes of test functions, including indicator functions, bounded monotone functions, Lipschitz-in-parameter functions, and Hölder classes as special cases. The general Glivenko-Cantelli theorem is then applied in more concrete high-frequency statistical settings to establish uniform convergence results for general integrated functionals of the volatility of efficient price and local moments of microstructure noise.
Generalized Jump Regressions For Local Moments, Tim Bollerslev, Jia Li, Leonardo Salim Saker Chaves
Generalized Jump Regressions For Local Moments, Tim Bollerslev, Jia Li, Leonardo Salim Saker Chaves
Research Collection School Of Economics
We develop new high-frequency-based inference procedures for analyzing the relationship between jumps in instantaneous moments of stochastic processes. The estimation consists of two steps: the nonparametric determination of the jumps as differences in local averages, followed by a minimum-distance type estimation of the parameters of interest under general loss functions that include both least-square and more robust quantile regressions as special cases. The resulting asymptotic distribution of the estimator, derived under an infill asymptotic setting, is highly nonstandard and generally not mixed normal. In addition, we establish the validity of a novel bootstrap algorithm for making feasible inference including bias-correction. …