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函数型线性回归斜率算子的统计推断AI 解读

In this paper we consider the linear regression model $Y =S X+\varepsilon $ with functional regressors and responses. We develop new inference tools to quantify deviations of the true slope $S$ from a hypothesized operator $S_0$ with respect to the Hilbert--Schmidt norm $\| S- S_0\|^2$, as well as the prediction error $\mathbb{E} \| S X - S_0 X \|^2$. Our analysis is applicable to functional time series and based on asymptotically pivotal statistics. This makes it…

具有一般独立列的数据矩阵的奇异值AI 解读

In this paper, we analyse singular values of a large $p\times n$ data matrix $\mathbf{X}_n= (\mathbf{x}_{n1},\ldots,\mathbf{x}_{nn})$ where the column $\mathbf{x}_{nj}$'s are independent $p$-dimensional vectors, possibly with different distributions. Such data matrices are common in high-dimensional statistics. Under a key assumption that the covariance matrices $\mathbfΣ_{nj}=\text{Cov}(\mathbf{x}_{nj})$ can be asymptotically simultaneously diagonalizable, and appropriate…

降维与状态空间系统：用频率学派及贝叶斯 VAR 预测美国国债收益率AI 解读

Using a state-space system, I forecasted the US Treasury yields by employing frequentist and Bayesian methods after first decomposing the yields of varying maturities into its unobserved term structure factors. Then, I exploited the structure of the state-space model to forecast the Treasury yields and compared the forecast performance of each model using mean squared forecast error. Among the frequentist methods, I applied the two-step Diebold-Li, two-step principal…

Ornstein–Uhlenbeck 过程的推广：理论、模拟与参数估计AI 解读

In this work, we study the class of stochastic process that generalizes the Ornstein-Uhlenbeck processes, hereafter called by \emph{Generalized Ornstein-Uhlenbeck Type Process} and denoted by GOU type process. We consider them driven by the class of noise processes such as Brownian motion, symmetric $α$-stable Lévy process, a Lévy process, and even a Poisson process. We give necessary and sufficient conditions under the memory kernel function for the time-stationary and the…

用于多重变化点识别的多分割模型AI 解读

Among the main goals in multiple change point problems are the estimation of the number and positions of the change points, as well as the regime structure in the clusters induced by those changes. The product partition model (PPM) is a widely used approach for the detection of multiple change points. The traditional PPM assumes that change points split the set of time points in random clusters that define a partition of the time axis. It is then typically assumed that…

多重协整系统中的完全修正最小二乘协整参数估计AI 解读

Multicointegration is traditionally defined as a particular long run relationship among variables in a parametric vector autoregressive model that introduces additional cointegrating links between these variables and partial sums of the equilibrium errors. This paper departs from the parametric model, using a semiparametric formulation that reveals the explicit role that singularity of the long run conditional covariance matrix plays in determining multicointegration. The…

局部格兰杰因果关系的统计推断AI 解读

Granger causality has been employed to investigate causality relations between components of stationary multiple time series. We generalize this concept by developing statistical inference for local Granger causality for multivariate locally stationary processes. Our proposed local Granger causality approach captures time-evolving causality relationships in nonstationary processes. The proposed local Granger causality is well represented in the frequency domain and estimated…

基于极端依赖的时间序列模型设定检验AI 解读

We propose a specification test for conditional location--scale models based on extremal dependence properties of the standardized residuals. We do so comparing the left-over serial extremal dependence -- as measured by the pre-asymptotic tail copula -- with that arising under serial independence at different lags. Our main theoretical results show that the proposed Portmanteau-type test statistics have nuisance parameter-free asymptotic limits. The test statistics are easy…

异质缺失下的高维变点估计AI 解读

We propose a new method for changepoint estimation in partially-observed, high-dimensional time series that undergo a simultaneous change in mean in a sparse subset of coordinates. Our first methodological contribution is to introduce a 'MissCUSUM' transformation (a generalisation of the popular Cumulative Sum statistics), that captures the interaction between the signal strength and the level of missingness in each coordinate. In order to borrow strength across the…

稀疏高维时间序列模型估计方法综述AI 解读

High-dimensional time series datasets are becoming increasingly common in many areas of biological and social sciences. Some important applications include gene regulatory network reconstruction using time course gene expression data, brain connectivity analysis from neuroimaging data, structural analysis of a large panel of macroeconomic indicators, and studying linkages among financial firms for more robust financial regulation. These applications have led to renewed…

厚尾非平稳多元时间序列中的推断AI 解读

We study inference on the common stochastic trends in a non-stationary, $N$-variate time series $y_{t}$, in the possible presence of heavy tails. We propose a novel methodology which does not require any knowledge or estimation of the tail index, or even knowledge as to whether certain moments (such as the variance) exist or not, and develop an estimator of the number of stochastic trends $m$ based on the eigenvalues of the sample second moment matrix of $y_{t}$. We study…

大量弱依赖数据短序列的单步超学习及自然灾害成本预测AI 解读

Suppose that we observe a short time series where each time-t-specific data-structure consists of many slightly dependent data indexed by a and that we want to estimate a feature of the law of the experiment that depends neither on t nor on a. We develop and study an algorithm to learn sequentially which base algorithm in a user-supplied collection best carries out the estimation task in terms of excess risk and oracular inequalities. The analysis, which uses dependency…

高维马尔可夫状态转换向量自回归的估计AI 解读

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 exceeds the sample size, we adopt a sparse framework and propose two penalized maximum likelihood estimators with either the Lasso or the smoothly clipped absolute deviation (SCAD) penalty. We show that both estimators are estimation consistent,…

Whittle 估计量的自助法AI 解读

Fitting parametric models by optimizing frequency domain objective functions is an attractive approach of parameter estimation in time series analysis. Whittle estimators are a prominent example in this context. Under weak conditions and the (realistic) assumption that the true spectral density of the underlying process does not necessarily belong to the parametric class of spectral densities fitted, the distribution of Whittle estimators typically depends on difficult to…

新冠疫情后的宏观经济变动建模AI 解读

The coronavirus is a global event of historical proportions and just a few months changed the time series properties of the data in ways that make many pre-covid forecasting models inadequate. It also creates a new problem for estimation of economic factors and dynamic causal effects because the variations around the outbreak can be interpreted as outliers, as shifts to the distribution of existing shocks, or as addition of new shocks. I take the latter view and use covid…

借助外生变量改进新冠疫情预测AI 解读

In this work, we study the pandemic course in the United States by considering national and state levels data. We propose and compare multiple time-series prediction techniques which incorporate auxiliary variables. One type of approach is based on spatio-temporal graph neural networks which forecast the pandemic course by utilizing a hybrid deep learning architecture and human mobility data. Nodes in this graph represent the state-level deaths due to COVID-19, edges…

贝叶斯分位数回归中收缩与变量选择的解耦AI 解读

This paper extends the idea of decoupling shrinkage and sparsity for continuous priors to Bayesian Quantile Regression (BQR). The procedure follows two steps: In the first step, we shrink the quantile regression posterior through state of the art continuous priors and in the second step, we sparsify the posterior through an efficient variant of the adaptive lasso, the signal adaptive variable selection (SAVS) algorithm. We propose a new variant of the SAVS which automates…

近不稳定整数值ARCH过程与单位根检验AI 解读

This paper introduces a Nearly Unstable INteger-valued AutoRegressive Conditional Heteroskedasticity (NU-INARCH) process for dealing with count time series data. It is proved that a proper normalization of the NU-INARCH process endowed with a Skorohod topology weakly converges to a Cox-Ingersoll-Ross diffusion. The asymptotic distribution of the conditional least squares estimator of the correlation parameter is established as a functional of certain stochastic integrals.…

共轭贝叶斯向量自回归中的子空间收缩AI 解读

Macroeconomists using large datasets often face the choice of working with either a large Vector Autoregression (VAR) or a factor model. In this paper, we develop methods for combining the two using a subspace shrinkage prior. Subspace priors shrink towards a class of functions rather than directly forcing the parameters of a model towards some pre-specified location. We develop a conjugate VAR prior which shrinks towards the subspace which is defined by a factor model. Our…

使用EM算法估计的正态逆高斯自回归模型AI 解读

In this article, normal inverse Gaussian (NIG) autoregressive model is introduced. The parameters of the model are estimated using Expectation Maximization (EM) algorithm. The efficacy of the EM algorithm is shown using simulated and real world financial data. It is shown that NIG autoregressive model fit very well the considered financial data and hence could be useful in modeling of various real life time-series data.

广义协方差估计量AI 解读

We consider a class of semi-parametric dynamic models with strong white noise errors. This class of processes includes the standard Vector Autoregressive (VAR) model, the nonfundamental structural VAR, the mixed causal-noncausal models, as well as nonlinear dynamic models such as the (multivariate) ARCH-M model. For estimation of processes in this class, we propose the Generalized Covariance (GCov) estimator, which is obtained by minimizing a residual-based multivariate…

时间局部最大似然估计及其在SIS模型中的应用AI 解读

The parametric estimators applied by rolling are commonly used in the analysis of time series with nonlinear features, such as structural change due to time varying parameters and local trends. This paper examines the properties of rolling estimators in the class of Temporally Local Maximum Likelihood (TLML) estimators. We study the TLML estimators of constant parameters, stochastic and stationary parameters and parameters with the Ultra Long Run (ULR) dynamics bridging the…

双变量时间序列因果性指标：性能比较综述AI 解读

Inferring nonlinear and asymmetric causal relationships between multivariate longitudinal data is a challenging task with wide-ranging application areas including clinical medicine, mathematical biology, economics and environmental research. A number of methods for inferring causal relationships within complex dynamic and stochastic systems have been proposed but there is not a unified consistent definition of causality in this context. We evaluate the performance of ten…

用含外生变量的广义网络自回归预测采购经理指数：COVID-19防控与死亡率的经济响应AI 解读

Knowledge of the current state of economies, how they respond to COVID-19 mitigations and indicators, and what the future might hold for them is important. We use recently-developed generalised network autoregressive (GNAR) models, using trade-determined networks, to model and forecast the Purchasing Managers' Indices for a number of countries. We use networks that link countries where the links themselves, or their weights, are determined by the degree of export trade…