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This paper considers the problem of robust adaptive efficient estimating of a periodic function in a continuous time regression model with the dependent noises given by a general square integrable semimartingale with a conditionally…
Varying coefficient regression is a flexible technique for modeling data where the coefficients are functions of some effect-modifying parameter, often time or location in a certain domain. While there are a number of methods for variable…
We propose a new volatility model based on two stylized facts of the volatility in the stock market: clustering and leverage effect. We calibrate our model parameters, in the leading order, with 77 years Dow Jones Industrial Average data.…
Estimating conditional quantiles of financial time series is essential for risk management and many other applications in finance. It is well-known that financial time series display conditional heteroscedasticity. Among the large number of…
HYGARCH model is basically used to model long-range dependence in volatility. We propose Markov switch smooth-transition HYGARCH model, where the volatility in each state is a time-dependent convex combination of GARCH and FIGARCH. This…
We study quantitative large-time averages for Hamilton--Jacobi equations in a dynamic random environment that is stationary ergodic and has unit-range dependence in time. Our motivation comes from stochastic growth models related to the…
Maximum likelihood estimation of large Markov-switching vector autoregressions (MS-VARs) can be challenging or infeasible due to parameter proliferation. To accommodate situations where dimensionality may be of comparable order to or…
We introduce a new class of conditional autoregressive models for spatially dependent functional data, formulated through conditional means given neighboring functional observations and characterized by a covariance operator and a spatial…
High-dimensional time series data appear in many scientific areas in the current data-rich environment. Analysis of such data poses new challenges to data analysts because of not only the complicated dynamic dependence between the series,…
An efficient estimator is constructed for the quadratic covariation or integrated co-volatility matrix of a multivariate continuous martingale based on noisy and nonsynchronous observations under high-frequency asymptotics. Our approach…
Spatio-temporal areal data can be seen as a collection of time series which are spatially correlated according to a specific neighboring structure. Incorporating the temporal and spatial dimension into a statistical model poses challenges…
Existing theory of momentum assumes that gradients arrive at every parameter at a roughly constant rate, an assumption violated in practice by heavy-tailed data distributions and modern architectures. We theoretically analyze the dynamics…
Motivated by better modeling of intra-individual variability in longitudinal data, we propose a class of location-scale mixed effects models, in which the data of each individual is modeled by a parameter-varying generalized hyperbolic…
Using a large dataset on major FX rates, we test the robustness of the rough fractional volatility model over different time scales, by including smoothing and measurement errors into the analysis. Our findings lead to new stylized facts in…
This paper investigates the continuous-time limit of score-driven models with long memory. By extending score-driven models to incorporate infinite-lag structures with coefficients exhibiting heavy-tailed decay, we establish their weak…
We provide a simple method to estimate the parameters of multivariate stochastic volatility models with latent factor structures. These models are very useful as they alleviate the standard curse of dimensionality, allowing the number of…
This paper introduces a Bayesian vector autoregression (BVAR) with stochastic volatility-in-mean and time-varying skewness. Unlike previous approaches, the proposed model allows both volatility and skewness to directly affect macroeconomic…
HYGARCH process is the commonly used long memory process in modeling the long-rang dependence in volatility. Financial time series are characterized by transition between phases of different volatility levels. The smooth transition HYGARCH…
Strong consistency and asymptotic normality of the Gaussian pseudo-maximum likelihood estimate of the parameters in a wide class of ARCH$(\infty)$ processes are established. The conditions are shown to hold in case of exponential and…
Traditional credibility analysis of risks in insurance is based on the random effects model, where the heterogeneity across the policyholders is assumed to be time-invariant. One popular extension is the dynamic random effects (or…