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交易层面资产价格模型的极限规律AI 解读

We consider pure-jump transaction-level models for asset prices in continuous time, driven by point processes. In a bivariate model that admits cointegration, we allow for time deformations to account for such effects as intraday seasonal patterns in volatility and nontrading periods that may be different for the two assets. We also allow for asymmetries (leverage effects). We obtain the asymptotic distribution of the log-price process. For the weak fractional cointegration…

单调谱密度估计AI 解读

We propose two estimators of a monotone spectral density, that are based on the periodogram. These are the isotonic regression of the periodogram and the isotonic regression of the log-periodogram. We derive pointwise limit distribution results for the proposed estimators for short memory linear processes and long memory Gaussian processes and also that the estimators are rate optimal.

持续期记忆参数向计数与已实现波动率传递的条件AI 解读

We establish sufficient conditions on durations that are stationary with finite variance and memory parameter $d \in [0,{\textstyle{1 \over 2}})$ to ensure that the corresponding counting process N ( t ) satisfies Var N ( t ) ~ Ct 2 d +1 ( C > 0) as t → ∞, with the same memory parameter $d \in [0,{\textstyle{1 \over 2}})$ that was assumed for the durations. Thus, these conditions ensure that the memory parameter in durations propagates to the same memory parameter in the…

持续期驱动长程依赖过程的渐近理论AI 解读

We consider processes with second order long range dependence resulting from heavy tailed durations. We refer to this phenomenon as duration-driven long range dependence (DDLRD), as opposed to the more widely studied linear long range dependence based on fractional differencing of an iid process. We consider in detail two specific processes having DDLRD, originally presented in Taqqu and Levy (1986), and Parke (1999). For these processes, we obtain the limiting distribution…

存在平滑非参数趋势时的长记忆估计AI 解读

We consider semiparametric estimation of the long-memory parameter of a stationary process in the presence of an additive nonparametric mean function. We use a semiparametric Whittle-type estimator, applied to the tapered, differenced series. Because the mean function is not necessarily a polynomial of finite order, no amount of differencing will completely remove the mean. We establish a central limit theorem for the estimator of the memory parameter, assuming that a slowly…

波动率长记忆的估计AI 解读

We consider semiparametric estimation of the memory parameter in a model that includes as special cases both long-memory stochastic volatility and fractionally integrated exponential GARCH (FIEGARCH) models. Under our general model the logarithms of the squared returns can be decomposed into the sum of a long-memory signal and a white noise. We consider periodogram-based estimators using a local Whittle criterion function. We allow the optional inclusion of an additional…

波动率长记忆检验AI 解读

We consider the asymptotic behavior of log-periodogram regression estimators of the memory parameter in long-memory stochastic volatility models, under the null hypothesis of short memory in volatility. We show that in this situation, if the periodogram is computed from the log squared returns, then the estimator is asymptotically normal, with the same asymptotic mean and variance that would hold if the series were Gaussian. In particular, for the widely used GPH estimator…

长程依赖时间序列的宽频带对数周期图回归AI 解读

This paper discusses the properties of an estimator of the memory parameter of a stationary long-memory time-series originally proposed by Robinson. As opposed to ‘‘narrow-band’’ estimators of the memory parameter (such as the Geweke and Porter-Hudak or the Gaussian semiparametric estimators) which use only the periodogram ordinates belonging to an interval which degenerates to zero as the sample size $n$ increases, this estimator builds a model of the spectral density of…