每日简报

高维向量误差修正模型的贝叶斯分析AI 解读

Vector Error Correction Model (VECM) is a classic method to analyse cointegration relationships amongst multivariate non-stationary time series. In this paper, we focus on high dimensional setting and seek for sample-size-efficient methodology to determine the level of cointegration. Our investigation centres at a Bayesian approach to analyse the cointegration matrix, henceforth determining the cointegration rank. We design two algorithms and implement them on simulated…

Welch 谱密度估计方法的去偏AI 解读

Welch's method provides an estimator of the power spectral density that is statistically consistent. This is achieved by averaging over periodograms calculated from overlapping segments of a time series. For a finite length time series, while the variance of the estimator decreases as the number of segments increase, the magnitude of the estimator's bias increases: a bias-variance trade-off ensues when setting the segment number. We address this issue by providing a novel…

参数不稳定下的高维线性回归变量选择AI 解读

This paper considers the problem of variable selection allowing for parameter instability. It distinguishes between signal and pseudo-signal variables that are correlated with the target variable, and noise variables that are not, and investigate the asymptotic properties of the One Covariate at a Time Multiple Testing (OCMT) method proposed by Chudik et al. (2018) under parameter insatiability. It is established that OCMT continues to asymptotically select an approximating…

提高时空数据贝叶斯非参数因子分析的可扩展性AI 解读

This article introduces novel and practicable Bayesian factor analysis frameworks that are computationally feasible for moderate to large spatiotemporal data. Previous Bayesian analysis of spatiotemporal data has utilized a Bayesian factor model with separable temporal latent factors and spatial factor loadings, along with stick-breaking process priors on the loadings to enable clustering of spatial locations. Such a flexible Bayesian model, however, faces a prohibitively…

网络计数时间序列的新方法AI 解读

The original generalized network autoregressive models are poor for modelling count data as they are based on the additive and constant noise assumptions, which is usually inappropriate for count data. We introduce two new models (GNARI and NGNAR) for count network time series by adapting and extending existing count-valued time series models. We present results on the statistical and asymptotic properties of our new models and their estimates obtained by conditional least…

通过噪声正则化实现经济预测中的良性过拟合AI 解读

This paper studies linear overparameterized models in economic forecasting and highlights that including noise variables (regressors with no predictive power) regularizes the estimator. We consider a setting where both the outcome variable and the high-dimensional predictors are driven by a small number of latent factors, and show that the linear forecast model is dense rather than sparse. It turns out that a ridgeless regression augmented with noise predictors attains the…

混合矩阵值自回归模型AI 解读

Time series of matrix-valued data are increasingly available in various areas including economics, finance, social science, among others. These data may shed light on the inter-dynamical relationships between two sets of attributes, for instance, countries and economic indices. The matrix autoregressive (MAR) model provides a parsimonious approach for analyzing such data. However, the MAR model, being a linear model with parametric constraints, cannot capture the nonlinear…

基于广义协方差的综合序列相关检验AI 解读

We study nonlinear serial dependence tests for non-Gaussian time series and residuals of dynamic models based on portmanteau statistics involving nonlinear autocovariances. A new test with an asymptotic $χ^2$ distribution is introduced for testing nonlinear serial dependence (NLSD) in time series. This test is inspired by the Generalized Covariance (GCov) residual-based specification test, recently proposed as a diagnostic tool for semi-parametric dynamic models with i.i.d.…

函数型时间序列共同趋势的统计推断AI 解读

We study statistical inference on unit roots and cointegration for time series in a Hilbert space. We develop statistical inference on the number of common stochastic trends embedded in the time series, i.e., the dimension of the nonstationary subspace. We also consider tests of hypotheses on the nonstationary and stationary subspaces themselves. The Hilbert space can be of an arbitrarily large dimension, and our methods remain asymptotically valid even when the time series…

一般线性约束多元时间序列的点预测与概率预测协调AI 解读

Forecast reconciliation is the post-forecasting process aimed to revise a set of incoherent base forecasts into coherent forecasts in line with given data structures. Most of the point and probabilistic regression-based forecast reconciliation results ground on the so called "structural representation" and on the related unconstrained generalized least squares reconciliation formula. However, the structural representation naturally applies to genuine hierarchical/grouped…

非线性网络自回归AI 解读

We study general nonlinear models for time series networks of integer and continuous valued data. The vector of high dimensional responses, measured on the nodes of a known network, is regressed non-linearly on its lagged value and on lagged values of the neighboring nodes by employing a smooth link function. We study stability conditions for such multivariate process and develop quasi maximum likelihood inference when the network dimension is increasing. In addition, we…

PromptCast：基于提示的时间序列预测范式AI 解读

This paper presents a new perspective on time series forecasting. In existing time series forecasting methods, the models take a sequence of numerical values as input and yield numerical values as output. The existing SOTA models are largely based on the Transformer architecture, modified with multiple encoding mechanisms to incorporate the context and semantics around the historical data. Inspired by the successes of pre-trained language foundation models, we pose a…

时间序列预测：利用分数差分保留长期依赖AI 解读

This study introduces a novel forecasting strategy that leverages the power of fractional differencing (FD) to capture both short- and long-term dependencies in time series data. Unlike traditional integer differencing methods, FD preserves memory in series while stabilizing it for modeling purposes. By applying FD to financial data from the SPY index and incorporating sentiment analysis from news reports, this empirical analysis explores the effectiveness of FD in…

因子模型结构变化的似然比检验AI 解读

A factor model with a break in its factor loadings is observationally equivalent to a model without changes in the loadings but a change in the variance of its factors. This effectively transforms a structural change problem of high dimension into a problem of low dimension. This paper considers the likelihood ratio (LR) test for a variance change in the estimated factors. The LR test implicitly explores a special feature of the estimated factors: the pre-break and…

不依赖维度选择的变点检测AI 解读

Change point testing for high-dimensional data has attracted a lot of attention in statistics and machine learning owing to the emergence of high-dimensional data with structural breaks from many fields. In practice, when the dimension is less than the sample size but is not small, it is often unclear whether a method that is tailored to high-dimensional data or simply a classical method that is developed and justified for low-dimensional data is preferred. In addition, the…

亚稳态金融市场AI 解读

Metastability is a phenomenon observed in stochastic systems which stay in a false-equilibrium within a region of its state space until the occurrence of a sequence of rare events that leads to an abrupt transition to a different region. This paper presents financial markets as metastable systems and shows that, under this assumption, financial time series evolve as hidden Markov models. In special, we propose a theory that outlines an explicit causal relation between a…

流形上多分数阶函数型时间序列的长程依赖谱分析AI 解读

This paper addresses the estimation of the second-order structure of a manifold cross-time random field (RF) displaying spatially varying Long Range Dependence (LRD), adopting the functional time series framework introduced in Ruiz-Medina (2022). Conditions for the asymptotic unbiasedness of the integrated periodogram operator in the Hilbert-Schmidt operator norm are derived beyond structural assumptions. Weak-consistent estimation of the long-memory operator is achieved…

协整向量自回归过程的一致有效推断AI 解读

Uniformly valid inference for cointegrated vector autoregressive processes has so far proven difficult due to certain discontinuities arising in the asymptotic distribution of the least squares estimator. We extend asymptotic results from the univariate case to multiple dimensions and show how inference can be based on these results. Furthermore, we show that lag augmentation and a recent instrumental variable procedure can also yield uniformly valid tests and confidence…

最优因果滤波器有限截段的渐近行为AI 解读

We establish an $L_1$-bound between the coefficients of the optimal causal filter applied to the data-generating process and its finite sample approximation. Here, we assume that the data-generating process is a second-order stationary time series with either short or long memory autocovariances. To derive the $L_1$-bound, we first provide an exact expression for the coefficients of the causal filter and their approximations in terms of the absolute convergent series of the…

基于非高斯非齐次时间序列观测重建二值空间随机场AI 解读

We develop a new model for spatial random field reconstruction of a binary-valued spatial phenomenon. In our model, sensors are deployed in a wireless sensor network across a large geographical region. Each sensor measures a non-Gaussian inhomogeneous temporal process which depends on the spatial phenomenon. Two types of sensors are employed: one collects point observations at specific time points, while the other collects integral observations over time intervals.…

基于评分规则的多元预测分布校准检验AI 解读

Calibration tests based on the probability integral transform (PIT) are routinely used to assess the quality of univariate distributional forecasts. However, PIT-based calibration tests for multivariate distributional forecasts face various challenges. We propose two new types of tests based on proper scoring rules, which overcome these challenges. They arise from a general framework for calibration testing in the multivariate case, introduced in this work. The new tests…

利用代理变量从低频采样时间序列发现因果结构AI 解读

Inferring causal structures from time series data is the central interest of many scientific inquiries. A major barrier to such inference is the problem of subsampling, i.e., the frequency of measurement is much lower than that of causal influence. To overcome this problem, numerous methods have been proposed, yet either was limited to the linear case or failed to achieve identifiability. In this paper, we propose a constraint-based algorithm that can identify the entire…