arXiv subjects

Clifford Hurvich

Publications and source records attributed to Clifford Hurvich.

5 recordsLinked to original sources

arXiv2026

On the Expectation of the Local-to-Zero Cross-Validated Log Likelihood Criterion for Bandwidth Selection in Kernel Spectral Estimation

We consider data-driven bandwidth selection for a kernel spectral estimator at zero frequency based on a local-to-zero version of the cross validated log-likelihood (CVLL) criterion. The modified version is $\mbox{CVLL}_c$, based on a sum over Fourier frequencies from $1$ to $n^c$ with $0<c<1$, where $n$ is the sample size. We focus on the expectation of a key term in a Taylor series expansion for $\mbox{CVLL}_c$ and show that in the case $4/5 < c < 1$ it converges to the corresponding asymptotic mean squared error of the spectral estimator at zero frequency. This provides some justification for the use of the local CVLL criterion for Heteroskedasticity and Autocorrelation Consistent (HAC) standard error estimation. Our theoretical results do not follow from existing literature on CVLL because those results exploit the fact that CVLL is global, summing over all frequencies in $(0,\pi)$ rather than local-to-zero frequency, as is the case for $\mbox{CVLL}_c$.

stat.ME↗

arXiv2026

Binomial Smoothing for Inventory and Information Control in Supply Chains

In many decentralized supply chains, upstream firms do not observe market demand directly and instead infer downstream conditions from the order stream. A retailer's replenishment policy therefore plays a dual role: it governs inventory replenishment and shapes the information available for upstream forecasting. This creates a fundamental trade-off. Smoother orders improve upstream predictability, but delaying the response to demand can increase downstream inventory costs. We study how a retailer should optimally smooth demand in a two-tier supply chain with one retailer and one manufacturer when the manufacturer forecasts future orders from the retailer's order history. We propose Binomial Smoothing, a class of replenishment policies that implements delayed demand response by spreading each unit of demand over a finite horizon using binomial weights. The class is interpretable, easy to calibrate, and analytically tractable. Under weakly stationary Gaussian demand satisfying mild regularity conditions, we show that, for any fixed smoothing horizon, the Binomial policy minimizes the manufacturer's forecast error among all policies with the same degree of smoothing. It remains invertible, so the manufacturer can recover demand history from observed orders. More generally, Binomial Smoothing achieves a constant-factor approximation guarantee relative to an optimal policy. Our results yield a broader insight: replenishment policies should be designed not merely to reduce order variance, as in the traditional bullwhip measure, but to reduce the unpredictable component of orders. Carefully designed smoothing can improve supply-chain performance and partially substitute for information sharing, providing a concrete mechanism for coordination without collaboration.

stat.AP↗

arXiv2026

Designing Information Delays in Supply Chains

This paper studies how a downstream retailer in a decentralized two-tier supply chain can implicitly transmit demand information to an upstream supplier through the structure of its order stream in the absence of an explicit information-sharing mechanism. We distinguish our work from prior work by introducing the notion of information delay and by linking optimal implicit information sharing to the group delay of the retailer's ordering transfer function. We show that pure delay is strictly suboptimal, while fractional-delay mechanisms can reshape the order autocorrelation to improve supplier forecastability and reduce system-wide inventory costs. Using Hardy-space factorization, we develop a tractable family of invertible ARMA policies that approximates the theoretically optimal (but non-rational) limiting filter derived by Caldentey et al. (2025) and preserves its informational delay properties. This construction yields sharp guidance on how policy complexity, as measured by the degrees of the ARMA policies, impacts supply chain costs. We further extend the analysis to memory-constrained suppliers and characterize how the complexity of the retailer's policy should scale with the supplier's finite forecasting window, highlighting when, perhaps counterintuitively, increasing policy complexity can become counterproductive.

math.OC↗

arXiv2022

Long-Horizon Return Predictability from Realized Volatility in Pure-Jump Point Processes

We develop and justify methodology to consistently test for long-horizon return predictability based on realized variance. To accomplish this, we propose a parametric transaction-level model for the continuous-time log price process based on a pure jump point process. The model determines the returns and realized variance at any level of aggregation with properties shown to be consistent with the stylized facts in the empirical finance literature. Under our model, the long-memory parameter propagates unchanged from the transaction-level drift to the calendar-time returns and the realized variance, leading endogenously to a balanced predictive regression equation. We propose an asymptotic framework using power-law aggregation in the predictive regression. Within this framework, we propose a hypothesis test for long horizon return predictability which is asymptotically correctly sized and consistent.

econ.EM↗

arXiv2015

Drift in Transaction-Level Asset Price Models

We study the effect of drift in pure-jump transaction-level models for asset prices in continuous time, driven by point processes. The drift is as-sumed to arise from a nonzero mean in the efficient shock series. It follows that the drift is proportional to the driving point process itself, i.e. the cumulative number of transactions. This link reveals a mechanism by which properties of intertrade durations (such as heavy tails and long memory) can have a strong impact on properties of average returns, thereby poten-tially making it extremely difficult to determine long-term growth rates or to reliably detect an equity premium. We focus on a basic univariate model for log price, coupled with general assumptions on the point process that are satisfied by several existing flexible models, allowing for both long mem-ory and heavy tails in durations. Under our pure-jump model, we obtain the limiting distribution for the suitably normalized log price. This limiting distribution need not be Gaussian, and may have either finite variance or infinite variance. We show that the drift can affect not only the limiting dis-tribution for the normalized log price, but also the rate in the corresponding normalization. Therefore, the drift (or equivalently, the properties of dura-tions) affects the rate of convergence of estimators of the growth rate, and can invalidate standard hypothesis tests for that growth rate. As a rem-edy to these problems, we propose a new ratio statistic which behaves more

math.ST↗