
Convergence rates of sums of αmixing triangular arrays: with an application to nonparametric drift function estimation of continuoustime processesConvergence rates of sums of αmixing triangular arrays: with an application to nonparametric drift function estimation of continuoustime processes 
"/Kanaya, Shin/"Kanaya, Shin
947201608 , Institute of Economic Research, Kyoto University
Description
The convergence rates of the sums of αmixing (or strongly mixing) triangular arrays of heterogeneous random variables are derived. We pay particular attention to the case where central limit theorems may fail to hold, due to relatively strong timeseries dependence and/or the nonexistence of higherorder moments. Several previous studies have presented various versions of laws of large numbers for sequences/triangular arrays, but their convergence rates were not fully investigated. This study is the first to investigate the convergence rates of the sums of αmixing triangular arrays whose mixing coefficients are permitted to decay arbitrarily slowly. We consider two kinds of asymptotic assumptions: one is that the time distance between adjacent observations is fixed for any sample size n; and the other, called the infill assumption, is that it shrinks to zero as n tends to infinity. Our convergence theorems indicate that an explicit tradeoff exists between the rate of convergence and the degree of dependence. While the results under the infill assumption can be seen as a direct extension of those under the fixeddistance assumption, they are new and particularly useful for deriving sharper convergence rates of discretization biases in estimating continuoustime processes from discretely sampled observations. We also discuss some examples to which our results and techniques are useful and applicable: a movingaverage process with long lasting past shocks, a continuoustime diffusion process with weak mean reversion, and a nearunitroot process.
FullText
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