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Parameter estimation in nonlinear multivariate stochastic differential equations based on splitting schemes

基于分裂格式的非线性多元随机微分方程参数估计

The likelihood functions for discretely observed nonlinear continuous time models based on stochastic differential equations are not available except for a few cases. Various parameter estimation techniques have been proposed, each with advantages, disadvantages and limitations depending on the application. Most applications still use the Euler–Maruyama discretization, despite many proofs of its bias. More sophisticated methods, such as Kessler’s Gaussian approximation,…

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ℓ2 inference for change points in high-dimensional time series via a Two-Way MOSUM

通过双向MOSUM对高维时间序列变点进行ℓ2推断

We propose an inference method for detecting multiple change points in high-dimensional time series, targeting dense or spatially clustered signals. Our method aggregates moving sum (MOSUM) statistics cross-sectionally by an ℓ2-norm and maximizes them over time. We further introduce a novel Two-Way MOSUM, which utilizes spatial-temporal moving regions to search for breaks, with the added advantage of enhancing testing power when breaks occur in only a few groups. The…

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A general framework to quantify deviations from structural assumptions in the analysis of nonstationary function-valued processes

量化非平稳函数值过程结构假设偏离的一般框架

We present a general theory to quantify the uncertainty from imposing structural assumptions on the second-order structure of nonstationary Hilbert space-valued processes, which can be measured via functionals of time-dependent spectral density operators. The second-order dynamics are well known to be elements of the space of trace class operators, the latter is a Banach space of type 1 and of cotype 2, which makes the development of statistical inference tools more…

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Identifiability and estimation of possibly non-invertible SVARMA Models: The normalised canonical WHF parametrisation

可能不可逆 SVARMA 模型的识别与估计:规范化典范 WHF 参数化

This article focuses on the parametrisation, identifiability, and (quasi-) maximum likelihood (QML) estimation of possibly non-invertible structural vector autoregressive moving average (SVARMA) models. SVAR models are routinely adopted due to their well-known implementation strategy. However, for various economic and statistical reasons, multivariate SVARMA settings are often more suitable. These settings introduce complexity in the analysis, primarily due to the presence…

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The local to unity dynamic Tobit model

局部趋于单位根的动态 Tobit 模型

This paper considers highly persistent time series that are subject to nonlinearities in the form of censoring or an occasionally binding constraint, such as are regularly encountered in macroeconomics. A tractable candidate model for such series is the dynamic Tobit with a root local to unity. We show that this model generates a process that converges weakly to a non-standard limiting process, that is constrained (regulated) to be positive. Surprisingly, despite the…

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Estimation and inference for high dimensional factor model with regime switching

载荷机制切换高维因子模型的估计与推断

This paper proposes maximum (quasi)likelihood estimation for high dimensional factor models with regime switching in the loadings. The model parameters are estimated jointly by the EM (expectation maximization) algorithm, which in the current context only requires iteratively calculating regime probabilities and principal components of the weighted sample covariance matrix . When regime dynamics are taken into account, smoothed regime probabilities are calculated using a…

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Robust inference of panel data models with interactive fixed effects under long memory: A frequency domain approach

长记忆下交互固定效应面板模型的稳健推断:频域方法

This paper studies a linear panel data model with interactive fixed effects wherein regressors, factors and idiosyncratic error terms are all stationary but with potential long memory. The setup involves a new formulation of panel data models, where weakly dependent regressors, factors and idiosyncratic errors are embedded as a special case. Standard methods based on principal component decomposition and least squares estimation, as in Bai (2009), are found to be biased and…

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Predictive ability tests with possibly overlapping models

允许模型重叠的预测能力检验

This paper provides novel tests for comparing out-of-sample predictive ability of two or more competing models that are possibly overlapping. The tests do not require pre-testing, they allow for dynamic misspecification and are valid under different estimation schemes and loss functions. In pairwise model comparisons, the test is constructed by adding a random perturbation to both the numerator and denominator of a standard Diebold–Mariano test statistic. This prevents…

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Bayesian estimation of cluster covariance matrices of unknown form

未知聚类结构协方差矩阵的贝叶斯估计

We develop a flexible Bayesian model for cluster covariance matrices in large dimensions where the number of clusters and the assignment of cross-sectional units to a cluster are a-priori unknown and estimated from the data. In a cluster covariance matrix, the variances and covariances are equal within each diagonal block, while the covariances are equal in each off-diagonal block. This reduces the number of parameters by pooling those parameters together that are in the…

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Advance layoff notices and aggregate job loss

提前裁员通知与总体就业损失

Summary We collect data from Worker Adjustment and Retraining Notification (WARN) Act notices and establish their usefulness as an indicator of aggregate job loss. The number of workers affected by WARN notices (“WARN layoffs”) leads state‐level initial unemployment insurance claims and unemployment rate (UR) and private employment changes. WARN layoffs comove with aggregate layoffs from Mass Layoff Statistics and the Job Openings and Labor Turnover Survey but are timelier…

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Statistically identified structural VAR model with potentially skewed and fat‐tailed errors

允许偏斜厚尾误差的统计识别结构 VAR

Abstract We introduce a structural vector autoregressive model in which the mutually independent errors follow skewed generalized t ‐distributions, whose flexibility compared with commonly considered Student's t ‐distributions diminishes the risk of misspecification and strengthens identification. Because of statistical identification due to non‐Gaussianity, the plausibility of economic identifying restrictions can be formally assessed. In an empirical application, the data…

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The macroeconomy as a random forest

将宏观经济建模为随机森林

Summary I develop the macroeconomic random forest (MRF), an algorithm adapting the canonical machine learning (ML) tool, to flexibly model evolving parameters in a linear macro equation. Its main output, generalized time‐varying parameters (GTVPs), is a versatile device nesting many popular nonlinearities (threshold/switching, smooth transition, and structural breaks/change) and allowing for sophisticated new ones. The approach delivers clear forecasting gains over numerous…

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Is Newey–West optimal among first-order kernels?

Newey–West在一阶核中是否最优?

Newey–West (1987) standard errors are the dominant standard errors used for heteroskedasticity and autocorrelation robust (HAR) inference in time series regression. The Newey–West estimator uses the Bartlett kernel, which is a first-order kernel, meaning that its characteristic exponent, q, is equal to 1, where q is defined as the largest value of r for which the quantity k[r](0)=limt→0|t|−r(k(0)−k(t)) is defined and finite. This raises the apparently uninvestigated question…

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Maximum likelihood estimation of latent Markov models using closed-form approximations

利用闭式近似估计隐状态 Markov 模型的极大似然

This paper proposes and implements an efficient and flexible method to compute maximum likelihood estimators of continuous-time models when part of the state vector is latent. Stochastic volatility and term structure models are typical examples. Existing methods integrate out the latent variables using either simulations as in MCMC, or replace the latent variables by observable proxies. By contrast, our approach relies on closed-form approximations to estimate parameters and…

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Robust inference on correlation under general heterogeneity

一般异质性下相关性的稳健推断

Considerable evidence in past research shows size distortion in standard tests for zero autocorrelation or zero cross-correlation when time series are not independent identically distributed random variables, pointing to the need for more robust procedures. Recent tests for serial correlation and cross-correlation in Dalla, Giraitis, and Phillips (2022) provide a more robust approach, allowing for heteroskedasticity and dependence in uncorrelated data under restrictions that…

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Bias in local projections

局部投影的偏差

Local projections (LPs) are a popular tool in macroeconomic research. We show that LPs are often used with very small samples in the time dimension and, consequently, that LP point estimates can be severely biased. Under regularity conditions, we derive simple expressions to approximate this bias and propose a way to correct for bias in LPs. Using a medium-scale macroeconomic time-series model, we demonstrate that the bias in point estimates can be economically meaningful.…

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Time-varying forecast combination for factor-augmented regressions with smooth structural changes

平滑结构变化下因子增强回归的时变预测组合

This study proposes a time-varying forecast combination for factor-augmented (TVFCFA) regressions with smooth structural changes. First, we establish the limiting distribution of the estimators of the time-varying factor-augmented regressions. To estimate the optimal time-varying combination weights, we propose a local leave-l-out cross-validation (LLOCV) criterion that is asymptotically unbiased for the local mean squared forecast error (LMSFE). The TVFCFA method was shown…

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Panel data models with time-varying latent group structures

具有时变潜在分组结构的面板数据模型

This paper considers a linear panel model with interactive fixed effects and unobserved individual and time heterogeneities that are captured by some latent group structures and an unknown structural break, respectively. To enhance realism, the model may have different numbers of groups and/or different group memberships before and after the break. With preliminary nuclear norm regularized estimation followed by row- and column-wise linear regressions, we estimate the break…

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Cross-section bootstrap for CCE regressions

共同相关效应回归的横截面 Bootstrap

The Common Correlated Effects (CCE) methodology is now well established for the analysis of factor-augmented panel data models. Yet, it is often neglected that the pooled variant is biased unless the cross-section dimension (N) of the dataset dominates the time series length (T). This is problematic for inference with typical macroeconomic datasets, where T is often equal or larger than N. In response, we establish in this paper the theoretical foundation of the…

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Likelihood approach to dynamic panel models with interactive effects

具有交互效应的动态面板模型似然方法

This paper studies dynamic panel models with a factor error structure that is correlated with the regressors. Both short panels (small T) and long panels (large T) are considered. A dynamic panel forms a simultaneous-equation system, and under the factor error structure, there exist constraints between the mean and the covariance matrix. We explore the constraints through a quasi-FIML (full information maximum likelihood) approach. The quasi-FIML approach does not estimate…

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Forecasting GDP in Europe with textual data

利用文本数据预测欧洲 GDP

Summary We evaluate the informational content of news‐based sentiment indicators for forecasting gross domestic product (GDP) and other macroeconomic variables of the five major European economies. Our dataset includes over 27 million articles for 26 major newspapers in five different languages. The evidence indicates that these sentiment indicators are significant predictors to forecast macroeconomic variables and their predictive content is robust to controlling for other…

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Nonlinearities in macroeconomic tail risk through the lens of big data quantile regressions

通过大数据分位数回归研究宏观尾部风险的非线性

Summary Modeling and predicting extreme movements in GDP is notoriously difficult, and the selection of appropriate covariates and/or possible forms of nonlinearities are key in obtaining precise forecasts. In this paper, our focus is on using large datasets in quantile regression models to forecast the conditional distribution of US GDP growth. To capture possible nonlinearities, we include several nonlinear specifications. The resulting models will be huge dimensional, and…

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The vector error correction index model: representation, estimation and identification

向量误差修正指数模型:表示、估计与识别

Summary This paper extends the multivariate index autoregressive model to the case of cointegrated time series of order (1,1). In this new modelling, namely the vector error-correction index model (VECIM), the first differences of series are driven by some linear combinations of the variables, namely the indexes. When the indexes are significantly fewer than the variables, the VECIM achieves a substantial dimension reduction with reference to the vector error correction…

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Revealing priors from posteriors with an application to inflation forecasting in the UK

由后验揭示先验:英国通胀预测的应用

Summary A Bayesian typically uses data and a prior to produce a posterior. We shall follow the opposite route, using data and the posterior information to reveal the prior. We then apply this theory to inflation forecasts by the Bank of England and the National Institute of Economic and Social Research in an attempt to get some insight into the prior beliefs of the policy makers in these two institutions, especially under the uncertainties about the Brexit referendum, the…

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