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Estimation and inference for precision matrices of nonstationary time series

非平稳时间序列精度矩阵的估计与推断

We consider the estimation of and inference on precision matrices of a rich class of univariate locally stationary linear and nonlinear time series, assuming that only one realization of the time series is observed. Using a Cholesky decomposition technique, we show that the precision matrices can be directly estimated via a series of least squares linear regressions with smoothly time-varying coefficients. The method of sieves is utilized for the estimation and is shown to…

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Extending the validity of frequency domain bootstrap methods to general stationary processes

将频域自助法的有效性扩展至一般平稳过程

Existing frequency domain methods for bootstrapping time series have a limited range. Essentially, these procedures cover the case of linear time series with independent innovations, and some even require the time series to be Gaussian. In this paper we propose a new frequency domain bootstrap method—the hybrid periodogram bootstrap (HPB)—which is consistent for a much wider range of stationary, even nonlinear, processes and which can be applied to a large class of…

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Empirical risk minimization and complexity of dynamical models

经验风险最小化与动力系统模型的复杂度

A dynamical model consists of a continuous self-map $T:\mathcal{X}\to \mathcal{X}$ of a compact state space $\mathcal{X}$ and a continuous observation function $f:\mathcal{X}\to \mathbb{R}$. This paper considers the fitting of a parametrized family of dynamical models to an observed real-valued stochastic process using empirical risk minimization. The limiting behavior of the minimum risk parameters is studied in a general setting. We establish a general convergence theorem…

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ASYMPTOTIC THEORY FOR KERNEL ESTIMATORS UNDER MODERATE DEVIATIONS FROM A UNIT ROOT, WITH AN APPLICATION TO THE ASYMPTOTIC SIZE OF NONPARAMETRIC TESTS

单位根中度偏离下核估计的渐近理论与非参数检验的水平

We provide new asymptotic theory for kernel density estimators, when these are applied to autoregressive processes exhibiting moderate deviations from a unit root. This fills a gap in the existing literature, which has to date considered only nearly integrated and stationary autoregressive processes. These results have applications to nonparametric predictive regression models. In particular, we show that the null rejection probability of a nonparametric t test is controlled…

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TRUNCATED SUM OF SQUARES ESTIMATION OF FRACTIONAL TIME SERIES MODELS WITH DETERMINISTIC TRENDS

含确定性趋势的分数阶时间序列模型:截断平方和估计

We consider truncated (or conditional) sum of squares estimation of a parametric model composed of a fractional time series and an additive generalized polynomial trend. Both the memory parameter, which characterizes the behavior of the stochastic component of the model, and the exponent parameter, which drives the shape of the deterministic component, are considered not only unknown real numbers but also lying in arbitrarily large (but finite) intervals. Thus, our model…

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Predicting interest rates using shrinkage methods, real‐time diffusion indexes, and model combinations

用收缩方法、实时扩散指数与模型组合预测利率

Summary In the context of predicting the term structure of interest rates, we explore the marginal predictive content of real‐time macroeconomic diffusion indexes extracted from a “data rich” real‐time data set, when used in dynamic Nelson–Siegel (NS) models of the variety discussed in Svensson (NBER technical report, 1994; NSS) and Diebold and Li ( Journal of Econometrics , 2006, 130 , 337–364; DNS). Our diffusion indexes are constructed using principal component analysis…

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Model simplification and variable selection: A replication of the UK inflation model by Hendry (2001)

模型简化与变量选择:复现 Hendry 的英国通胀模型

Summary In this paper, we revisit the well‐known UK inflation model by Hendry ( Journal of Applied Econometrics , 2001, 16 , 255–275. We replicate the results in a narrow sense using the gretl and PcGive programs. In a wide sense, we extend the study of model uncertainty using the Bayesian averaging of classical estimates (BACE) approach as an automatic model reduction strategy. We consider three different specifications to compare BACE variable selection with Hendry's…

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Forecasting stock returns with model uncertainty and parameter instability

模型不确定性与参数不稳定性下的股票收益预测

Summary We compare several representative sophisticated model averaging and variable selection techniques of forecasting stock returns. When estimated traditionally, our results confirm that the simple combination of individual predictors is superior. However, sophisticated models improve dramatically once we combine them with the historical average and take parameter instability into account. An equal weighted combination of the historical average with the standard…

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Time Series Clustering and Classification

时间序列聚类与分类

As we enter the big data era, the amount of time-series data is growing especially fast, originating from various sources like web traffic, healthcare sensors, etc. To understand how these time ser...

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Multivariate Bayesian Predictive Synthesis in Macroeconomic Forecasting

宏观经济预测中的多变量贝叶斯预测综合

We present new methodology and a case study in use of a class of Bayesian predictive synthesis (BPS) models for multivariate time series forecasting. This extends the foundational BPS framework to the multivariate setting, with detailed application in the topical and challenging context of multistep macroeconomic forecasting in a monetary policy setting. BPS evaluates—sequentially and adaptively over time—varying forecast biases and facets of miscalibration of individual…

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Tests for Scale Changes Based on Pairwise Differences

基于成对差分的尺度变化检验

In many applications it is important to know whether the amount of fluctuation in a series of observations changes over time. In this article, we investigate different tests for detecting changes in the scale of mean-stationary time series. The classical approach, based on the CUSUM test applied to the squared centered observations, is very vulnerable to outliers and impractical for heavy-tailed data, which leads us to contemplate test statistics based on alternative, less…

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A Likelihood Ratio Approach to Sequential Change Point Detection for a General Class of Parameters

一般参数序贯变点检测的似然比方法

In this article, we propose a new approach for sequential monitoring of a general class of parameters of a d-dimensional time series, which can be estimated by approximately linear functionals of the empirical distribution function. We consider a closed-end method, which is motivated by the likelihood ratio test principle and compare the new method with two alternative procedures. We also incorporate self-normalization such that estimation of the long-run variance is not…

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Bayesian Model Search for Nonstationary Periodic Time Series

非平稳周期时间序列的贝叶斯模型搜索

We propose a novel Bayesian methodology for analyzing nonstationary time series that exhibit oscillatory behavior. We approximate the time series using a piecewise oscillatory model with unknown periodicities, where our goal is to estimate the change-points while simultaneously identifying the potentially changing periodicities in the data. Our proposed methodology is based on a trans-dimensional Markov chain Monte Carlo algorithm that simultaneously updates the…

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Dynamic Vector Mode Regression

动态向量众数回归

We study the semiparametric estimation of the conditional mode of a random vector that has a continuous conditional joint density with a well-defined global mode. A novel full-system estimator is proposed and its asymptotic properties are studied. We specifically consider the estimation of vector autoregressive conditional mode models and of systems of linear simultaneous equations defined by mode restrictions. The proposed estimator is easy to implement and simulations…

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A New Class of Change Point Test Statistics of Rényi Type

一类新的 Rényi 型变点检验统计量

A new class of change point test statistics is proposed that utilizes a weighting and trimming scheme for the cumulative sum (CUSUM) process inspired by Rényi. A thorough asymptotic analysis and simulations both demonstrate that this new class of statistics possess superior power compared to traditional change point statistics based on the CUSUM process when the change point is near the beginning or end of the sample. Generalizations of these “Rényi” statistics are also…

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Term Structures of Inflation Expectations and Real Interest Rates

通胀预期与实际利率的期限结构

I use a statistical model to combine various surveys to produce a term structure of inflation expectations—inflation expectations at any horizon—and an associated term structure of real interest rates. Inflation expectations extracted from this model track realized inflation quite well, and in terms of forecast accuracy, they are at par with or superior to some popular alternatives. The real interest rates obtained from the model follow Treasury Inflation-Protected…

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Heterogeneity and Unemployment Dynamics

异质性与失业动态

Many previous articles have studied the contribution of inflows and outflows to the cyclical variation in unemployment, but ignored the critical role of unobserved heterogeneity across workers. This article develops new estimates of unemployment inflows and outflows that allow for unobserved heterogeneity as well as direct effects of unemployment duration on unemployment-exit probabilities. With this approach, we can measure the contribution of different shocks to the…

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Time Series Seasonal Adjustment Using Regularized Singular Value Decomposition

基于正则化奇异值分解的时间序列季节调整

We propose a new seasonal adjustment method based on the Regularized Singular Value Decomposition (RSVD) of the matrix obtained by reshaping the seasonal time series data. The method is flexible enough to capture two kinds of seasonality: the fixed seasonality that does not change over time and the time-varying seasonality that varies from one season to another. RSVD represents the time-varying seasonality by a linear combination of several seasonal patterns. The right…

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Identification and Estimation in Non-Fundamental Structural VARMA Models

非基本结构VARMA模型的识别与估计

Abstract The basic assumption of a structural vector autoregressive moving average (SVARMA) model is that it is driven by a white noise whose components are uncorrelated or independent and can be interpreted as economic shocks, called “structural” shocks. When the errors are Gaussian, independence is equivalent to non-correlation and these models face two identification issues. The first identification problem is “static” and is due to the fact that there is an infinite…

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Testing Relevant Hypotheses in Functional Time Series via Self-Normalization

通过自标准化检验函数型时间序列的实质性差异

Summary We develop methodology for testing relevant hypotheses about functional time series in a tuning-free way. Instead of testing for exact equality, e.g. for the equality of two mean functions from two independent time series, we propose to test the null hypothesis of no relevant deviation. In the two-sample problem this means that an L2-distance between the two mean functions is smaller than a prespecified threshold. For such hypotheses self-normalization, which was…

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Frequency domain estimation of cointegrating vectors with mixed frequency and mixed sample data

混合频率与混合样本数据的协整向量频域估计

This paper proposes a simple method for exploiting the information contained in mixed frequency and mixed sample data in the estimation of cointegrating vectors. The asymptotic properties of easy-to-compute spectral regression estimators of the cointegrating vectors are derived and these estimators are shown to belong to the class of optimal cointegration estimators. Furthermore, Wald statistics based on these estimators have asymptotic chi-square distributions which enable…

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Relevant parameter changes in structural break models

结构突变模型中的相关参数变化

Structural break time series models, which are commonly used in macroeconomics and finance, capture unknown structural changes by allowing for abrupt changes to model parameters. However, many specifications suffer from an over-parametrization issue, since typically all parameters have to change when a break occurs. We introduce a sparse change-point model to detect which parameters change over time. We propose a shrinkage prior distribution, which controls model parsimony…

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Segmentation and estimation of change-point models: False positive control and confidence regions

变点模型的分割与估计:假阳性控制和置信区域

To segment a sequence of independent random variables at an unknown number of change-points, we introduce new procedures that are based on thresholding the likelihood ratio statistic, and give approximations for the probability of a false positive error when there are no change-points. We also study confidence regions based on the likelihood ratio statistic for the change-points and joint confidence regions for the change-points and the parameter values. Applications to…

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The dynamic factor network model with an application to international trade

动态因子网络模型及其国际贸易应用

We introduce a dynamic network model with probabilistic link functions that depend on stochastically time-varying parameters. We adopt a blockmodel framework and allow the high-dimensional vector of link probabilities to be a function of a low-dimensional set of dynamic factors. The resulting dynamic factor network model has a basic and transparent structure. However, parameter estimation, signal extraction of stochastic loadings and dynamic factors, and the econometric…

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