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Bias in dynamic panel models under time series misspecification

时间序列设定错误下动态面板模型的偏差

We consider within-group estimation of higher-order autoregressive panel models with exogenous regressors and fixed effects, where the lag order is possibly misspecified. Even when disregarding the misspecification bias, the fixed-effect bias formula is quite different from the correctly specified case though its asymptotic order remains the same under the stationarity. We suggest bias reduction methods under the possible time series misspecification.

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Beyond panel unit root tests: Using multiple testing to determine the nonstationarity properties of individual series in a panel

超越面板单位根检验:用多重检验识别各序列的非平稳性

Most panel unit root tests are designed to test the joint null hypothesis of a unit root for each individual series in a panel. After a rejection, it will often be of interest to identify which series can be deemed to be stationary and which series can be deemed nonstationary. Researchers will sometimes carry out this classification on the basis of n individual (univariate) unit root tests based on some ad hoc significance level. In this paper, we suggest and demonstrate how…

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Payout yield, risk, and mispricing: A Bayesian analysis

派付收益率、风险与错误定价:贝叶斯分析

We develop a simple parametric model in which hypotheses about predictability, mispricing, and the risk-return tradeoff can be evaluated simultaneously, while allowing for time variation in both risk and expected return. Most of the return predictability based on aggregate payout yield is unrelated to market risk. We consider a range of Bayesian prior beliefs about the risk-return tradeoff and the extent to which predictability is driven by mispricing. The impact of these…

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Identifying Distributional Characteristics in Random Coefficients Panel Data Models

随机系数面板模型中分布特征的识别

We study the identification of panel models with linear individual-specific coefficients when T is fixed. We show identification of the variance of the effects under conditional uncorrelatedness. Identification requires restricted dependence of errors, reflecting a trade-off between heterogeneity and error dynamics. We show identification of the probability distribution of individual effects when errors follow an Autoregressive Moving Average process under conditional…

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Out-of-Sample Forecast Tests Robust to the Choice of Window Size

对估计窗口大小选择稳健的样本外预测检验

This article proposes new methodologies for evaluating economic models’ out-of-sample forecasting performance that are robust to the choice of the estimation window size. The methodologies involve evaluating the predictive ability of forecasting models over a wide range of window sizes. The study shows that the tests proposed in the literature may lack the power to detect predictive ability and might be subject to data snooping across different window sizes if used…

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Components of Bull and Bear Markets: Bull Corrections and Bear Rallies

牛熊市的内部组成:牛市回调与熊市反弹

Existing methods of partitioning the market index into bull and bear regimes do not identify market corrections or bear market rallies. In contrast, our probabilistic model of the return distribution allows for rich and heterogeneous intraregime dynamics. We focus on the characteristics and dynamics of bear market rallies and bull market corrections, including, for example, the probability of transition from a bear market rally into a bull market versus back to the primary…

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Tests of Short Memory With Thick-Tailed Errors

厚尾误差下的短记忆检验

In this article, we consider the robustness to fat tails of four stationarity tests. We also consider their sensitivity to the number of lags used in long-run variance estimation, and the power of the tests. Lo's modified rescaled range (MR/S) test is not very robust. Choi's Lagrange multiplier (LM) test has excellent robustness properties but is not generally as powerful as the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test. As an analytical framework for fat tails, we…

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Discrete-Time Volatility Forecasting With Persistent Leverage Effect and the Link With Continuous-Time Volatility Modeling

具有持续性杠杆效应的离散时间波动率预测及其与连续时间建模的联系

We first propose a reduced-form model in discrete time for S&P 500 volatility showing that the forecasting performance can be significantly improved by introducing a persistent leverage effect with a long-range dependence similar to that of volatility itself. We also find a strongly significant positive impact of lagged jumps on volatility, which however is absorbed more quickly. We then estimate continuous-time stochastic volatility models that are able to reproduce the…

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Time Varying Dimension Models

时变维度模型

Time varying parameter (TVP) models have enjoyed an increasing popularity in empirical macroeconomics. However, TVP models are parameter-rich and risk over-fitting unless the dimension of the model is small. Motivated by this worry, this article proposes several Time Varying Dimension (TVD) models where the dimension of the model can change over time, allowing for the model to automatically choose a more parsimonious TVP representation, or to switch between different…

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Why Frequency Matters for Unit Root Testing in Financial Time Series

为什么采样频率会影响金融时间序列的单位根检验

It is generally believed that the power of unit root tests is determined only by the time span of observations, not by their sampling frequency. We show that the sampling frequency does matter for stock data displaying fat tails and volatility clustering, such as financial time series. Our claim builds on recent work on unit root testing based on non-Gaussian GARCH-based likelihood functions. Such methods yield power gains in the presence of fat tails and volatility…

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Inference of time-varying regression models

时变回归模型的统计推断

We consider parameter estimation, hypothesis testing and variable selection for partially time-varying coefficient models. Our asymptotic theory has the useful feature that it can allow dependent, nonstationary error and covariate processes. With a two-stage method, the parametric component can be estimated with a $n^{1/2}$-convergence rate. A simulation-assisted hypothesis testing procedure is proposed for testing significance and parameter constancy. We further propose an…

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Misspecification tests based on quantile residuals

基于分位数残差的误设检验

We develop quantile residual‐based misspecification tests and apply them to non‐linear time series models for which conventional residuals are unsuited. We formulate a general framework and use it to obtain computationally simple tests aimed at detecting autocorrelation, conditional heteroscedasticity and non‐normality in quantile residuals. These tests are generalizations of similar previous tests based on conventional residuals and the Lagrange Multiplier principle.…

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Estimating and testing non‐affine option pricing models with a large unbalanced panel of options

利用大型非平衡期权面板估计与检验非仿射期权定价模型

In this paper, we consider joint estimation of objective and risk‐neutral parameters for stochastic volatility option pricing models using both stock and option prices. A common strategy simplifies the task by limiting the analysis to just one option per date. We first discuss its drawbacks on the basis of model interpretation, estimation results and pricing exercises. We then turn the attention to a more flexible approach, that successfully exploits the wealth of…

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Testing for rational bubbles in a coexplosive vector autoregression

共爆炸向量自回归中的理性泡沫检验

We derive the parameter restrictions that a standard equity market model implies for a bivariate vector autoregression for stock prices and dividends, and we show how to test these restrictions using likelihood ratio tests. The restrictions, which imply that stock returns are unpredictable, are derived both for a model without bubbles and for a model with a rational bubble. In both cases we show how the restrictions can be tested through standard chi-squared inference. The…

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A Review of Modelling Nonlinear Economic Time Series

《非线性经济时间序列建模》书评

Nonlinear modelling is becoming part of the ‘standard’ toolkit used by empirical macroeconomics researchers and this book provides a valuable introduction to the methods commonly (and, in some cases, not so commonly) employed in practice. Granger and Teräsvirta provided a slim volume on nonlinear economic modelling in 1993. However, as well as being updated, this new book covers much more territory, so it should not be viewed as simply a second edition of the previous…

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Segmenting mean-nonstationary time series via trending regressions

利用趋势回归分割均值非平稳时间序列

In this paper, we provide a segmentation procedure for mean-nonstationary time series. The segmentation is obtained by casting the problem into the framework of detecting structural breaks in trending regression models in which the regressors are generated by suitably smooth functions. As test statistics we propose to use the maximally selected likelihood ratio statistics and a related statistics based on partial sums of weighted residuals. The main theoretical contribution…

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Dynamic misspecification in nonparametric cointegrating regression

非参数协整回归中的动态误设

Linear cointegration is known to have the important property of invariance under temporal translation. The same property is shown not to apply for nonlinear cointegration. The limit properties of the Nadaraya–Watson (NW) estimator for cointegrating regression under misspecified lag structure are derived, showing the NW estimator to be inconsistent, in general, with a “pseudo-true function” limit that is a local average of the true regression function. In this respect…

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The HESSIAN method: Highly efficient simulation smoothing, in a nutshell

HESSIAN方法:高效模拟平滑的简明框架

I introduce the HESSIAN (highly efficient simulation smoothing in a nutshell) method for numerically efficient simulation smoothing in state space models with univariate states. Given a vector θ of parameters, the vector of states α=(α1,…,αn) is Gaussian and the observed vector y=(y1⊤,…,yn⊤)⊤ need not be. I describe a procedure to construct a close approximation q(α|θ,y) to the target density p(α|θ,y). It requires code to compute five derivatives of logp(yt|θ,αt) with…

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The Variance Profile

方差谱剖面

The variance profile is defined as the power mean of the spectral density function of a stationary stochastic process. It is a continuous and nondecreasing function of the power parameter, p, which returns the minimum of the spectrum (p→−∞), the interpolation error variance (harmonic mean, p=−1), the prediction error variance (geometric mean, p=0), the unconditional variance (arithmetic mean, p=1), and the maximum of the spectrum (p→∞). The variance profile provides a useful…

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Inverse Realized Laplace Transforms for Nonparametric Volatility Density Estimation in Jump-Diffusions

跳跃扩散中以逆已实现拉普拉斯变换估计波动率密度

This article develops a nonparametric estimator of the stochastic volatility density of a discretely observed Itô semimartingale in the setting of an increasing time span and finer mesh of the observation grid. There are two basic steps involved. The first step is aggregating the high-frequency increments into the realized Laplace transform, which is a robust nonparametric estimate of the underlying volatility Laplace transform. The second step is using a regularized kernel…

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Quantile Periodograms

分位数周期图

Two periodogram-like functions, called quantile periodograms, are introduced for spectral analysis of time series. The quantile periodograms are constructed from trigonometric quantile regression and motivated by different interpretations of the ordinary periodogram. Analytical and numerical results demonstrate the capability of the quantile periodograms for detecting hidden periodicity in the quantiles and for providing an additional view of time-series data. A connection…

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Smooth Blockwise Iterative Thresholding: A Smooth Fixed Point Estimator Based on the Likelihood’s Block Gradient

平滑分块迭代阈值法:基于似然分块梯度的固定点估计

The proposed smooth blockwise iterative thresholding estimator (SBITE) is a model selection technique defined as a fixed point reached by iterating a likelihood gradient-based thresholding function. The smooth James–Stein thresholding function has two regularization parameters λ and ν, and a smoothness parameter s. It enjoys smoothness like ridge regression and selects variables like lasso. Focusing on Gaussian regression, we show that SBITE is uniquely defined, and that its…

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New Weighted Portmanteau Statistics for Time Series Goodness of Fit Testing

时间序列拟合优度检验的新加权混成统计量

We exploit ideas from high-dimensional data analysis to derive new portmanteau tests that are based on the trace of the square of the mth order autocorrelation matrix. The resulting statistics are weighted sums of the squares of the sample autocorrelation coefficients that, unlike many other tests appearing in the literature, are numerically stable even when the number of lags considered is relatively close to the sample size. The statistics behave asymptotically as a linear…

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LOCAL INSTRUMENTAL VARIABLE METHOD FOR THE GENERALIZED ADDITIVE-INTERACTIVE NONLINEAR VOLATILITY MODEL ESTIMATION

广义可加交互非线性波动模型的局部工具变量估计

In this article we consider a new separable nonparametric volatility model that includes second-order interaction terms in both mean and conditional variance functions. This is a very flexible nonparametric ARCH model that can potentially explain the behavior of the wide variety of financial assets. The model is estimated using the generalized version of the local instrumental variable estimation method first introduced in Kim and Linton (2004, Econometric Theory 20,…

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