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非平稳时间序列的图模型AI 解读

We propose NonStGM, a general nonparametric graphical modeling framework, for studying dynamic associations among the components of a nonstationary multivariate time series. It builds on the framework of Gaussian graphical models (GGM) and stationary time series graphical models (StGM) and complements existing works on parametric graphical models based on change point vector autoregressions (VAR). Analogous to StGM, the proposed framework captures conditional noncorrelations…

协调高斯似然与 Whittle 似然：频域估计的应用AI 解读

In time series analysis there is an apparent dichotomy between time and frequency domain methods. The aim of this paper is to draw connections between frequency and time domain methods. Our focus will be on reconciling the Gaussian likelihood and the Whittle likelihood. We derive an exact, interpretable, bound between the Gaussian and Whittle likelihood of a second order stationary time series. The derivation is based on obtaining the transformation which is biorthogonal to…

多变量时间序列的二阶平稳性检验AI 解读

It is well known that the discrete Fourier transforms (DFTs) of a second order stationary time series between two distinct Fourier frequencies are asymptotically uncorrelated. In contrast for a large class of second order nonstationary time series, including locally stationary time series, this property does not hold. In this paper these starkly differing properties are used to define a global test for stationarity based on the DFT of a vector time series. It is shown that…

时变 ARCH 模型中的归一化最小二乘估计AI 解读

We investigate the time-varying ARCH (tvARCH) process. It is shown that it can be used to describe the slow decay of the sample autocorrelations of the squared returns often observed in financial time series, which warrants the further study of parameter estimation methods for the model. Since the parameters are changing over time, a successful estimator needs to perform well for small samples. We propose a kernel normalized-least-squares (kernel-NLS) estimator which has a…

时变 ARCH 过程的统计推断AI 解读

In this paper the class of ARCH(∞) models is generalized to the nonstationary class of ARCH(∞) models with time-varying coefficients. For fixed time points, a stationary approximation is given leading to the notation “locally stationary ARCH(∞) process.” The asymptotic properties of weighted quasi-likelihood estimators of time-varying ARCH(p) processes (p<∞) are studied, including asymptotic normality. In particular, the extra bias due to nonstationarity of the process is…