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Yiwu Shang

Publications and source records attributed to Yiwu Shang.

5 recordsLinked to original sources
arXiv2026

Boundary Inference for Mixed Fractional Models under High-Frequency Observation Critical LAN and Score Tests at $H=3/4$

We study boundary inference at $H=3/4$ for mixed fractional Brownian motion and mixed fractional Ornstein--Uhlenbeck models under high-frequency observation. This boundary is economically important because it separates the critical and supercritical regimes of mixed fractional dynamics. We make three contributions. First, we identify the exact critical first-order scaling and show that, after removing the explicit linear component in the $H$-score, the transformed $(\sigma,H)$ block is already non-degenerate. Second, we establish critical score central limit theorems (CLT) and derive local asymptotic normality (LAN) with fully explicit leading information constants for both models. Third, we construct boundary-calibrated one-sided score tests for detecting entry into the supercritical region $H>3/4$ and discuss feasible implementation through restricted nuisance estimation. Monte Carlo evidence shows that the feasible statistic has the correct directional power but conservative null calibration. Finally, an intraday illustration on one-minute SPY data finds no persistent evidence in favor of $H>3/4$.

math.ST↗
arXiv2026

Local Asymptotic Normality for Mixed Fractional Brownian Motion Under High-Frequency Observation

In this paper we will consider the LAN property for both the Hurst parameter $H>3/4$ and the variance of the fractional Brownian motion plus an independent standard Brownian motion (called mixed fractional Brownian motion) with high-frequency observation. We will first remove the $H$-score linear term and orthogonalize the remainder through two non-diagonal transformations, then we can construct the CLT for the quadratic form base on $\| \cdot \|_{\mathrm{op}}/\|\cdot\|_F\to0$. At last we obtain a diagonal Gaussian LAN expansion with an explicit information matrix. Beyond the case of $H>3/4$, we also present that the $\| \cdot \|_{\mathrm{op}}/\|\cdot\|_F\to0$ method is also useful for the case of $H<3/4$ and the proof will be concise compared with the Whittle translation method. We consider that this method can be applied to this type of problem, including the fractional Ornstein-Uhlenbeck model and mixed fractional O-U process.

math.PR↗
arXiv2025

Parameter estimation for fractional autoregressive process with seasonal structure

This paper introduces a new kind of seasonal fractional autoregressive process (SFAR) driven by fractional Gaussian noise (fGn). The new model includes a standard seasonal AR model and fGn. {The estimation of the parameters of this new model has to solve two problems: nonstationarity from the seasonal structure and long memory from fGn. We innovatively solve these by getting a stationary subsequence, making a stationary additive sequence, and then obtaining their spectral density. Then, we use one-step procedure for Generalized Least Squares Estimator (GLSE) and the Geweke Porter-Hudak (GPH) method to get better results. We prove that both the initial and one-step estimators are consistent and asymptotically normal. Finally, we use Monte Carlo simulations with finite-sized samples to demonstrate the performance of these estimators. Moreover, through empirical analysis, it is shown that the SFAR model can simulate some real world phenomena better than general models.

stat.AP↗
arXiv2025

Parameter estimation for fractional autoregressive process with periodic structure

This paper introduces a new periodic fractional autoregressive process (PFAR) driven by fractional Gaussian noise (fGn) to model time series of precipitation evapotranspiration. Compared with the similar model in [\emph{Water Resources Research}, \textbf{20} (1984) 1898--1908], the new model incorporates a periodic structure via specialized varying coefficients and captures long memory and rough voltality through fGn for $0<H<1$, rather than via fractional differencing. In this work, Generalized Least Squares Estimation (GLSE) and the GPH method are employed to construct an initial estimator for the joint estimation of model parameters. A One-Step procedure is then used to obtain a more asymptotically efficient estimator. The paper proves that both estimators are consistent and asymptotically normal, and their performance is demonstrated via Monte Carlo simulations with finite-size samples. Simulation studies suggest that, while both estimation methods can accurately estimate the model parameters, the One-Step estimator outperforms the initial estimator.

math.ST↗