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时间序列数据的高维 Knockoffs 推断AI 解读

We make some initial attempt to establish the theoretical and methodological foundation for the model-X knockoffs inference for time series data. We suggest the method of time series knockoffs inference (TSKI) by exploiting the ideas of subsampling and e-values to address the difficulty caused by the serial dependence. We also generalize the robust knockoffs inference in Barber, Candès, and Samworth to the time series setting to relax the assumption of known covariate…

具有高维协变量的多臂老虎机自适应算法AI 解读

This article studies an important sequential decision making problem known as the multi-armed stochastic bandit problem with covariates. Under a linear bandit framework with high-dimensional covariates, we propose a general multi-stage arm allocation algorithm that integrates both arm elimination and randomized assignment strategies. By employing a class of high-dimensional regression methods for coefficient estimation, the proposed algorithm is shown to have near optimal…

ARFIMA 过程的一致阶数选择AI 解读

Estimating the orders of the autoregressive fractionally integrated moving average (ARFIMA) model has been a long-standing problem in time series analysis. This paper tackles this challenge by establishing the consistency of the Bayesian information criterion (BIC) for ARFIMA models with independent errors. Since the memory parameter of the model can be any real number, this consistency result is valid for short memory, long memory and nonstationary time series. This paper…

依赖观测下高维线性回归的模型选择AI 解读

We investigate the prediction capability of the orthogonal greedy algorithm (OGA) in high-dimensional regression models with dependent observations. The rates of convergence of the prediction error of OGA are obtained under a variety of sparsity conditions. To prevent OGA from overfitting, we introduce a high-dimensional Akaike’s information criterion (HDAIC) to determine the number of OGA iterations. A key contribution of this work is to show that OGA, used in conjunction…

具有时间序列与异方差误差的高维回归变量选择AI 解读

Although existing literature on high-dimensional regression models is rich, the vast majority of studies have focused on independent and homogeneous error terms. In this article, we consider the problem of selecting high-dimensional regression models with heteroscedastic and time series errors, which have broad applications in economics, quantitative finance, environmental science, and many other fields. The error term in our model is the product of two components: one time…

从有限个可能误设的时间序列模型中进行模型选择AI 解读

Consider finite parametric time series models. “I have $n$ observations and $k$ models, which model should I choose on the basis of the data alone” is a frequently asked question in many practical situations. This poses the key problem of selecting a model from a collection of candidate models, none of which is necessarily the true data generating process (DGP). Although existing literature on model selection is vast, there is a serious lacuna in that the above problem does…

基于分组正交贪婪算法的阈值估计AI 解读

A threshold autoregressive (TAR) model is an important class of nonlinear time series models that possess many desirable features such as asymmetric limit cycles and amplitude-dependent frequencies. Statistical inference for the TAR model encounters a major difficulty in the estimation of thresholds, however. This article develops an efficient procedure to estimate the thresholds. The procedure first transforms multiple-threshold detection to a regression variable selection…

具有时间序列误差的回归模型最优模型平均AI 解读

Consider a regression model with infinitely many parameters and time series errors. We are interested in choosing weights for averaging across generalized least squares (GLS) estimators obtained from a set of approximating models. However, GLS estimators, depending on the unknown inverse covariance matrix of the errors, are usually infeasible. We therefore construct feasible generalized least squares (FGLS) estimators using a consistent estimator of the unknown inverse…

地统计回归模型选择中广义信息准则的渐近理论AI 解读

Information criteria, such as Akaike’s information criterion and Bayesian information criterion are often applied in model selection. However, their asymptotic behaviors for selecting geostatistical regression models have not been well studied, particularly under the fixed domain asymptotic framework with more and more data observed in a bounded fixed region. In this article, we study the generalized information criterion (GIC) for selecting geostatistical regression models…

正误差自回归过程的预测器选择AI 解读

Let observations y1, …, yn be generated from a first-order autoregressive (AR) model with positive errors. In both the stationary and unit root cases, we derive moment bounds and limiting distributions of an extreme value estimator, , of the AR coefficient. These results enable us to provide asymptotic expressions for the mean squared error (MSE) of and the mean squared prediction error (MSPE) of the corresponding predictor, , of yn + 1. Based on these expressions, we…

长记忆时间序列的矩界与均方预测误差AI 解读

A moment bound for the normalized conditional-sum-of-squares (CSS) estimate of a general autoregressive fractionally integrated moving average (ARFIMA) model with an arbitrary unknown memory parameter is derived in this paper. To achieve this goal, a uniform moment bound for the inverse of the normalized objective function is established. An important application of these results is to establish asymptotic expressions for the one-step and multi-step mean squared prediction…

Fisher 信息的一致矩界及其时间序列应用AI 解读

In this paper, a uniform (over some parameter space) moment bound for the inverse of Fisher’s information matrix is established. This result is then applied to develop moment bounds for the normalized least squares estimate in (nonlinear) stochastic regression models. The usefulness of these results is illustrated using time series models. In particular, an asymptotic expression for the mean squared prediction error of the least squares predictor in autoregressive moving…

无限阶非平稳自回归的预测误差AI 解读

Assume that observations are generated from nonstationary autoregressive (AR) processes of infinite order. We adopt a finite-order approximation model to predict future observations and obtain an asymptotic expression for the mean-squared prediction error (MSPE) of the least squares predictor. This expression provides the first exact assessment of the impacts of nonstationarity, model complexity, and model misspecification on the corresponding MSPE. It not only provides a…

累积预测误差、信息准则与自回归时间序列的最优预测AI 解读

The predictive capability of a modification of Rissanen’s accumulated prediction error (APE) criterion, APEδn, is investigated in infinite-order autoregressive (AR(∞)) models. Instead of accumulating squares of sequential prediction errors from the beginning, APEδn is obtained by summing these squared errors from stage nδn, where n is the sample size and 1/n≤δn≤1−(1/n) may depend on n. Under certain regularity conditions, an asymptotic expression is derived for the…

自回归过程中同一实现预测的阶数选择AI 解读

Assume that observations are generated from an infinite-order autoregressive [AR(∞)] process. Shibata [Ann. Statist. 8 (1980) 147–164] considered the problem of choosing a finite-order AR model, allowing the order to become infinite as the number of observations does in order to obtain a better approximation. He showed that, for the purpose of predicting the future of an independent replicate, Akaike’s information criterion (AIC) and its variants are asymptotically…

未知阶自回归过程的最优多步预测器选择AI 解读

We consider the problem of choosing the optimal (in the sense of mean-squared prediction error) multistep predictor for an autoregressive (AR) process of finite but unknown order. If a working AR model (which is possibly misspecified) is adopted for multistep predictions, then two competing types of multistep predictors (i.e., plug-in and direct predictors) can be obtained from this model. We provide some interesting examples to show that when both plug-in and direct…

自回归过程中的多步预测AI 解读

In this paper, two competing types of multistep predictors, i.e., plug-in and direct predictors, are considered in autoregressive (AR) processes. When a working model AR(k) is used for the h-step prediction with h > 1, the plug-in predictor is obtained from repeatedly using the fitted (by least squares) AR(k) model with an unknown future value replaced by their own forecasts, and the direct predictor is obtained by estimating the h-step prediction model's coefficients…