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TESTING FOR A SHIFT IN TREND AT AN UNKNOWN DATE: A FIXED- B ANALYSIS OF HETEROSKEDASTICITY AUTOCORRELATION ROBUST OLS-BASED TESTS

未知时点趋势变动检验:OLS 稳健检验的固定 b 分析

This paper analyzes tests for a shift in the trend function of a time series at an unknown date based on ordinary least squares (OLS) estimates of the trend function. Inference about the trend parameters depends on the serial correlation structure of the data through the long-run variance (zero frequency spectral density) of the errors. Asymptotically pivotal tests can be obtained by the use of serial correlation robust standard errors that require an estimate of the…

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SADDLEPOINT AND ESTIMATED SADDLEPOINT APPROXIMATIONS FOR OPTIMAL UNIT ROOT TESTS

最优单位根检验的鞍点与估计鞍点近似

This paper provides a (saddlepoint) tail probability approximation for the distribution of an optimal unit root test. Under restrictive assumptions, Gaussianity, and known covariance structure, the order of error of the approximation is given. More generally, when innovations are a linear process in martingale differences, the estimated saddlepoint is proved to yield valid asymptotic inference. Numerical evidence, considered over a range of models, demonstrates some…

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TESTING FOR UNIT ROOTS IN THE PRESENCE OF A POSSIBLE BREAK IN TREND AND NONSTATIONARY VOLATILITY

可能存在趋势断点与非平稳波动时的单位根检验

We analyze the impact of nonstationary volatility on the break fraction estimator and associated trend break unit root tests of Harris, Harvey, Leybourne, and Taylor (2009) (HHLT). We show that although HHLT’s break fraction estimator retains the same large-sample properties as demonstrated by HHLT for homoskedastic shocks, the limiting null distributions of unit root statistics based around this estimator are not pivotal under nonstationary volatility. A solution to the…

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Functional mixed effects spectral analysis

函数型混合效应谱分析

In many experiments, time series data can be collected from multiple units and multiple time series segments can be collected from the same unit. This article introduces a mixed effects Cramér spectral representation which can be used to model the effects of design covariates on the second-order power spectrum while accounting for potential correlations among the time series segments collected from the same unit. The transfer function is composed of a deterministic component…

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Thick Pen Transformation for Time Series

时间序列的粗笔变换

Summary Traditional visualization of time series data often consists of plotting the time series values against time and ‘connecting the dots’. We propose an alternative, multiscale visualization technique, motivated by the scale–space approach in computer vision. In brief, our method also ‘connects the dots’ but uses a range of pens of varying thicknesses for this. The resulting multiscale map, which is termed the thick pen transform, corresponds to viewing the time series…

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A two-step estimator for large approximate dynamic factor models based on Kalman filtering

基于卡尔曼滤波的大型近似动态因子模型两步估计

This paper shows consistency of a two-step estimation of the factors in a dynamic approximate factor model when the panel of time series is large (n large). In the first step, the parameters of the model are estimated from an OLS on principal components. In the second step, the factors are estimated via the Kalman smoother. The analysis develops the theory for the estimator considered in Giannone et al. (2004) and Giannone et al. (2008) and for the many empirical papers…

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A control function approach for testing the usefulness of trending variables in forecast models and linear regression

检验趋势变量预测价值的控制函数方法

Many predictors employed in forecasting macroeconomic and finance variables display a great deal of persistence. Tests for determining the usefulness of these predictors are typically oversized, overstating their importance. Similarly, hypothesis tests on cointegrating vectors will typically be oversized if there is not an exact unit root. This paper uses a control variable approach where adding stationary covariates with certain properties to the model can result in…

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Understanding models’ forecasting performance

理解模型预测表现的来源

We propose a new methodology to identify the sources of models' forecasting performance. The methodology decomposes the models' forecasting performance into asymptotically uncorrelated components that measure instabilities in the forecasting performance, predictive content, and over-fitting. The empirical application shows the usefulness of the new methodology for understanding the causes of the poor forecasting ability of economic models for exchange rate determination.

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Variable selection, estimation and inference for multi-period forecasting problems

多期预测中的变量选择、估计与推断

This paper conducts a broad-based comparison of iterated and direct multi-period forecasting approaches applied to both univariate and multivariate models in the form of parsimonious factor-augmented vector autoregressions. To account for serial correlation in the residuals of the multi-period direct forecasting models we propose a new SURE-based estimation method and modified Akaike information criteria for model selection. Empirical analysis of the 170 variables studied by…

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Quantile regression for dynamic panel data with fixed effects

带固定效应的动态面板分位数回归

This paper studies a quantile regression dynamic panel model with fixed effects. Panel data fixed effects estimators are typically biased in the presence of lagged dependent variables as regressors. To reduce the dynamic bias, we suggest the use of the instrumental variables quantile regression method of Chernozhukov and Hansen (2006) along with lagged regressors as instruments. In addition, we describe how to employ the estimated models for prediction. Monte Carlo…

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Predictability of stock returns and asset allocation under structural breaks

结构断点下的股票收益可预测性与资产配置

This paper adopts a new approach that accounts for breaks to the parameters of return prediction models both in the historical estimation period and at future points. Empirically, we find evidence of multiple breaks in return prediction models based on the dividend yield or a short interest rate. Our analysis suggests that model instability is a very important source of investment risk for buy-and-hold investors with long horizons and that breaks can lead to a negative slope…

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Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions

含短期与长期约束的 VAR 模型选择、估计与预测

We study the joint determination of the lag length, the dimension of the cointegrating space and the rank of the matrix of short-run parameters of a vector autoregressive (VAR) model using model selection criteria. We suggest a new two-step model selection procedure which is a hybrid of traditional criteria and criteria with data-dependant penalties and we prove its consistency. A Monte Carlo study explores the finite sample performance of this procedure and evaluates the…

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A Measure of Stationarity in Locally Stationary Processes With Applications to Testing

局部平稳过程的平稳性度量及检验应用

In this article we investigate the problem of measuring deviations from stationarity in locally stationary time series. Our approach is based on a direct estimate of the L2-distance between the spectral density of the locally stationary process and its best approximation by a spectral density of a stationary process. An explicit expression of the minimal distance is derived, which depends only on integrals of the spectral density of the locally stationary process and its…

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GLS Estimation of Dynamic Factor Models

动态因子模型的广义最小二乘估计

In this article a simple two-step estimation procedure of the dynamic factor model is proposed. The estimator allows for heteroscedastic and serially correlated errors. It turns out that the feasible two-step estimator has the same limiting distribution as the generalized least squares (GLS) estimator assuming that the covariance parameters are known. In a Monte Carlo study of the small sample properties, we find that the GLS estimators may be substantially more efficient…

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Analysis of Long Period Variable Stars With Nonparametric Tests for Trend Detection

用非参数趋势检验分析长周期变星

In astronomy the study of variable stars—that is, stars characterized by showing significant variation in their brightness over time—has made crucial contributions to our understanding of many phenomena, from stellar birth and evolution to the calibration of the extragalactic distance scale. In this article, we develop a method for analyzing multiple, (pseudo)-periodic time series with the goal of detecting temporal trends in their periods. We allow for nonstationary noise…

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An Asymptotically Pivotal Transform of the Residuals Sample Autocorrelations With Application to Model Checking

用于模型检验的残差样本自相关渐近枢轴变换

We propose an asymptotically distribution-free transform of the sample autocorrelations of residuals in general parametric time series models, possibly nonlinear in variables. The residuals autocorrelation function is the basic model checking tool in time series analysis, but it is not useful when its distribution is incorrectly approximated because the effects of parameter estimation and/or higher-order serial dependence have not been taken into account. The limiting…

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Testing parametric assumptions of trends of a nonstationary time series

非平稳时间序列趋势参数形式的检验

The paper considers testing whether the mean trend of a nonstationary time series is of certain parametric forms. A central limit theorem for the integrated squared error is derived, and a hypothesis-testing procedure is proposed. The method is illustrated in a simulation study, and is applied to assess the mean pattern of lifetime-maximum wind speeds of global tropical cyclones from 1981 to 2006. We also revisit the trend pattern in the central England temperature series.

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Evaluating density forecasts: forecast combinations, model mixtures, calibration and sharpness

密度预测评价:预测组合、模型混合、校准与尖锐度

This paper reviews current density forecast evaluation procedures, and considers a proposal that such procedures be augmented by an assessment of ‘sharpness’. This was motivated by an example in which some standard evaluation procedures using probability integral transforms cannot distinguish the ideal forecast from several competing forecasts. We show that this example has some unrealistic features from a time series forecasting perspective, and so provides insecure…

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Factor analysis of permanent and transitory dynamics of the US economy and the stock market

美国经济与股市永久及暂时动态的因子分析

We analyze dynamics of the permanent and transitory components of the US economic activity and the stock market obtained by multivariate dynamic factor modeling. We capture asymmetries over the phases of economic and stock market trends and cycles using independent Markov-switching processes. We show that both output and stock prices contain significant transitory components, while consumption and dividends are useful to identify their respective permanent components. The…

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Modeling and forecasting short-term interest rates: The benefits of smooth regimes, macroeconomic variables, and bagging

短期利率建模与预测:平滑状态、宏观变量及装袋法的作用

In this paper we propose a smooth transition tree model for both the conditional mean and variance of the short-term interest rate process. The estimation of such models is addressed and the asymptotic properties of the quasi-maximum likelihood estimator are derived. Model specification is also discussed. When the model is applied to the US short-term interest rate we find (1) leading indicators for inflation and real activity are the most relevant predictors in…

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On the range of validity of the autoregressive sieve bootstrap

自回归筛自助法的有效范围

We explore the limits of the autoregressive (AR) sieve bootstrap, and show that its applicability extends well beyond the realm of linear time series as has been previously thought. In particular, for appropriate statistics, the AR-sieve bootstrap is valid for stationary processes possessing a general Wold-type autoregressive representation with respect to a white noise; in essence, this includes all stationary, purely nondeterministic processes, whose spectral density is…

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Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA–GARCH/IGARCH models

ARMA–GARCH/IGARCH 模型的全局自加权与局部准最大指数似然估计

This paper investigates the asymptotic theory of the quasi-maximum exponential likelihood estimators (QMELE) for ARMA–GARCH models. Under only a fractional moment condition, the strong consistency and the asymptotic normality of the global self-weighted QMELE are obtained. Based on this self-weighted QMELE, the local QMELE is showed to be asymptotically normal for the ARMA model with GARCH (finite variance) and IGARCH errors. A formal comparison of two estimators is given…

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Optimal model selection for density estimation of stationary data under various mixing conditions

不同混合条件下平稳数据密度估计的最优模型选择

We propose a block-resampling penalization method for marginal density estimation with nonnecessary independent observations. When the data are β or τ-mixing, the selected estimator satisfies oracle inequalities with leading constant asymptotically equal to 1. We also prove in this setting the slope heuristic, which is a data-driven method to optimize the leading constant in the penalty.

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Inference and prediction in a multiple-structural-break model

多重结构断点模型中的推断与预测

This paper develops a new Bayesian approach to structural break modeling. The focuses of the approach are the modeling of in-sample structural breaks and forecasting time series allowing out-of-sample breaks. The model has several desirable features. First, the number of regimes is not fixed but is treated as a random variable. Second, the model adopts a hierarchical prior for regime coefficients, which allows for the coefficients of one regime to contain information about…

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