This paper investigates the nonparametric estimation problem for some periodic stochastic differential equation driven by fractional G-Brownian motion (fGBm), which generalizes the concepts of the standard Brownian motion, fractional Brownian motion and G-Brownian motion in the framework of sublinear expectation. The fGBm can exhibit long-range dependence and feature the volatility uncertainty simultaneously. Thus it can be a better alternative stochastic process in real applications. First, some probability density function (pdf) called H-G-normal pdf associated with the fGBm is defined, the Volterra representation for fGBm and its Wiener integral are established. Then, the nonparametric estimator for the drift function of the periodic stochastic differential equation is defined by some kernel function, and its consistency and asymptotic distribution are investigated. Finally, some numerical experiments are carried out to illustrate the theoretical results. This study generalizes some well-known existing results of nonparametric estimation.
This paper addresses the problem of global parameter estimation for the AD (1,n) model, where n is a positive integer. The AD (1,n) model is a subclass of affine diffusions introduced by Duffie, Filipovi?, and Schachermayer in Duffie et al. (2003). Affine diffusion models are widely used in the pricing of bonds and stock options, including the Vasicek, Cox-Ingersoll-Ross, and Heston models. Our main results concern the conditional least squares estimation of the drift parameters of the AD (1,n) model, based on high-frequency discrete-time observations over an infinite horizon. We then analyze the asymptotic properties of the estimators in both ergodic and non-ergodic cases. Additionally, this paper presents some moment results related to the AD (1,n) model.
We consider the estimation of the marginal expected shortfall 𝔼( X_h | Y_0>U_Y(1/p)) at extreme levels, when ((X_t, Y_t))_t∈ℤ is a strictly stationary β - mixing time series with marginal distributions of Pareto-type, U_Y is the tail quantile function associated to Y_t , h is a positive integer and p∈ (0, 1) is such that p→ 0 . We propose an estimator for this risk measure based on a Weissman-type construction. First, in case of a non-negative time series, we establish the weak convergence of our estimator by using empirical processes arguments combined with the cluster method of Drees and Rootzén (2010). Then, we extend our result to the case of real-valued time series by using the decomposition of the original time series into the positive and negative parts, and we also propose a bootstrap procedure. The performance of our estimator is illustrated on a simulation experiment. Finally, the method is applied on river flow data.
This study examines the intricate process of estimating nonparametrically in expectile regression models for functional time series data that exhibit strong mixing properties within the context of a random right-censoring model. Specifically, we establish the almost complete consistency and asymptotic normality of the kernel-based expectile regression estimator. Notably, these results are derived in an asymptotic setting and are applicable under reasonably broad assumptions about the underlying model. Furthermore, we explore the practical implications of our theoretical findings in analyzing financial time series. To evaluate the performance of the proposed estimator on finite samples, we conducted comprehensive Monte Carlo simulations. These simulations provide a quantitative assessment of the estimator’s accuracy and efficiency under various scenarios, allowing for a thorough understanding of its practical utility.
We deal with a model selection problem for structural equation modeling (SEM) for diffusion processes. Based on the asymptotic expansion of the marginal quasi-log likelihood, we propose two types of quasi-Bayesian information criteria of the SEM. It is shown that the information criteria have model selection consistency. Furthermore, we examine the finite-sample performance of the proposed information criteria by numerical experiments.
