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The estimation of continuous time models with mixed frequency data

混频数据下连续时间模型的估计

This paper derives exact representations for discrete time mixed frequency data generated by an underlying multivariate continuous time model. Allowance is made for different combinations of stock and flow variables as well as deterministic trends, and the variables themselves may be stationary or nonstationary (and possibly cointegrated). The resulting discrete time representations allow for the information contained in high frequency data to be utilised alongside the low…

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Extended Yule–Walker identification of VARMA models with single- or mixed-frequency data

单频或混频数据下 VARMA 模型的扩展 Yule–Walker 识别

Chen and Zadrozny (1998) developed the linear extended Yule–Walker (XYW) method for determining the parameters of a vector autoregressive (VAR) model with available covariances of mixed-frequency observations on the variables of the model. If the parameters are determined uniquely for available population covariances, then, the VAR model is identified. The present paper extends the original XYW method to an extended XYW method for determining all ARMA parameters of a vector…

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EXISTENCE AND CHARACTERIZATION OF CONDITIONAL DENSITY PROJECTIONS

条件密度投影的存在性与刻画

In this paper we propose primitive conditions under which a projection of a conditional density onto a set defined by conditional moment restrictions exists and is unique. Moreover, we provide an analytic expression of the obtained projection. The range of applications where conditional density projections are used is wide. The derived results are potentially useful in a variety of areas including: semiparametric efficient estimation and optimal testing in (conditional)…

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MULTIVARIATE AR SYSTEMS AND MIXED FREQUENCY DATA: G-IDENTIFIABILITY AND ESTIMATION

多元自回归系统与混频数据:一般参数可识别性和估计

This paper is concerned with the problem of identifiability of the parameters of a high frequency multivariate autoregressive model from mixed frequency time series data. We demonstrate identifiability for generic parameter values using the population second moments of the observations. In addition we display a constructive algorithm for the parameter values and establish the continuity of the mapping attaching the high frequency parameters to these population second…

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Rejoinder: In-Sample Inference and Forecasting in Misspecified Factor Models

答复:误设因子模型中的样本内推断与预测

We thank all the discussants for their constructive comments and stimulating discussions of our article. Each of them raised interesting and insightful issues on various themes, which we discuss in...

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In-Sample Inference and Forecasting in Misspecified Factor Models

误设因子模型中的样本内推断与预测

This article considers in-sample prediction and out-of-sample forecasting in regressions with many exogenous predictors. We consider four dimension-reduction devices: principal components, ridge, Landweber Fridman, and partial least squares. We derive rates of convergence for two representative models: an ill-posed model and an approximate factor model. The theory is developed for a large cross-section and a large time-series. As all these methods depend on a tuning…

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Asymmetric Forecast Densities for U.S. Macroeconomic Variables from a Gaussian Copula Model of Cross-Sectional and Serial Dependence

基于横截面与序列依赖高斯Copula模型的美国宏观变量非对称预测密度

Most existing reduced-form macroeconomic multivariate time series models employ elliptical disturbances, so that the forecast densities produced are symmetric. In this article, we use a copula model with asymmetric margins to produce forecast densities with the scope for severe departures from symmetry. Empirical and skew t distributions are employed for the margins, and a high-dimensional Gaussian copula is used to jointly capture cross-sectional and (multivariate) serial…

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Common Drifting Volatility in Large Bayesian VARs

大型贝叶斯 VAR 中的共同时变波动率

The general pattern of estimated volatilities of macroeconomic and financial variables is often broadly similar. We propose two models in which conditional volatilities feature comovement and study them using U.S. macroeconomic data. The first model specifies the conditional volatilities as driven by a single common unobserved factor, plus an idiosyncratic component. We label this model BVAR with general factor stochastic volatility (BVAR-GFSV) and we show that the loss in…

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Of Quantiles and Expectiles: Consistent Scoring Functions, Choquet Representations and Forecast Rankings

分位数与期望分位数:一致评分函数、Choquet 表示与预测排序

Summary In the practice of point prediction, it is desirable that forecasters receive a directive in the form of a statistical functional. For example, forecasters might be asked to report the mean or a quantile of their predictive distributions. When evaluating and comparing competing forecasts, it is then critical that the scoring function used for these purposes be consistent for the functional at hand, in the sense that the expected score is minimized when following the…

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A multi-country approach to forecasting output growth using PMIs

利用采购经理指数预测产出增长的多国方法

This paper derives new theoretical results for forecasting with Global VAR (GVAR) models. It is shown that the presence of strong unobserved common factors can lead to an undetermined GVAR model. To solve this problem, we propose augmenting the GVAR with additional proxy equations for the strong factors and establish conditions under which forecasts from the augmented GVAR model (AugGVAR) uniformly converge in probability (as the panel dimensions N,T→j∞) to the infeasible…

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Large Bayesian VARMAs

大型贝叶斯 VARMA 模型

Vector Autoregressive Moving Average (VARMA) models have many theoretical properties which should make them popular among empirical macroeconomists. However, they are rarely used in practice due to over-parameterization concerns, difficulties in ensuring identification and computational challenges. With the growing interest in multivariate time series models of high dimension, these problems with VARMAs become even more acute, accounting for the dominance of VARs in this…

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The structure of multivariate AR and ARMA systems: Regular and singular systems; the single and the mixed frequency case

多元 AR 与 ARMA 系统结构:常规、奇异及单频与混频情形

This paper is concerned with the structure of multivariate AR and ARMA systems. The emphasis is on two “non-standard” cases: We deal with the structure of singular AR and ARMA systems which generate singular spectral densities and with identifiability of ARMA systems from mixed frequency data. In the mixed frequency case we show that, for the case where the MA order is smaller than or equal to the AR order, identifiability can be achieved generically. Furthermore, we…

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Dynamic prediction pools: An investigation of financial frictions and forecasting performance

动态预测组合:金融摩擦与预测表现

We apply a novel methodology for estimating time-varying weights in linear prediction pools, which we call Dynamic Pools, and use it to investigate the relative forecasting performance of DSGE models with and without financial frictions for output growth and inflation from 1992 to 2011. We find strong evidence of time variation in the pool’s weights, reflecting the fact that the DSGE model with financial frictions produces superior forecasts in periods of financial distress…

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ECB Monetary Policy Surprises: Identification Through Cojumps in Interest Rates

欧洲央行货币政策意外:通过利率共同跳跃识别

This paper proposes a new econometric approach to disentangle two distinct response patterns of the yield curve to monetary policy announcements. Based on cojumps in intraday tick data of short- and long-term interest rate futures, we develop a day-wise test that detects the occurrence of a significant policy surprise and identifies the market perceived source of the surprise. The new test is applied to 133 policy announcements of the European Central Bank (ECB) in the…

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Model averaging in predictive regressions

预测回归中的模型平均

In this paper, we consider forecast combination in a predictive regression. We construct the point forecast by combining predictions from all possible linear regression models, given a set of potentially relevant predictors. We derive the asymptotic risk of least‐squares averaging estimators in a local asymptotic framework. We then develop a frequentist model averaging criterion, an asymptotically unbiased estimator of the asymptotic risk, to select forecast weights. Monte…

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Testing for Granger causality with mixed frequency data

混频数据的格兰杰因果检验

We develop Granger causality tests that apply directly to data sampled at different frequencies. We show that taking advantage of mixed frequency data allows us to better recover causal relationships when compared to the conventional common low frequency approach. We also show that the new causality tests have higher local asymptotic power as well as more power in finite samples compared to conventional tests. In an empirical application involving U.S. macroeconomic…

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Bayesian semiparametric modeling of realized covariance matrices

已实现协方差矩阵的贝叶斯半参数建模

This paper introduces several new Bayesian nonparametric models suitable for capturing the unknown conditional distribution of realized covariance (RCOV) matrices. Existing dynamic Wishart models are extended to countably infinite mixture models of Wishart and inverse-Wishart distributions. In addition to mixture models with constant weights we propose models with time-varying weights to capture time dependence in the unknown distribution. Each of our models can be combined…

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Exploiting the errors: A simple approach for improved volatility forecasting

利用测量误差改进波动率预测的简便方法

We propose a new family of easy-to-implement realized volatility based forecasting models. The models exploit the asymptotic theory for high-frequency realized volatility estimation to improve the accuracy of the forecasts. By allowing the parameters of the models to vary explicitly with the (estimated) degree of measurement error, the models exhibit stronger persistence, and in turn generate more responsive forecasts, when the measurement error is relatively low.…

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Modeling the Dependence of Conditional Correlations on Market Volatility

金融收益条件相关性对市场波动率的依赖建模

Several models have been developed to capture the dynamics of the conditional correlations between time series of financial returns and several studies have shown that the market volatility is a major determinant of the correlations. We extend some models to include explicitly the dependence of the correlations on the market volatility. The models differ by the way—linear or nonlinear, direct or indirect—in which the volatility influences the correlations. Using a wide set…

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Real-time nowcasting of nominal GDP with structural breaks

结构突变下名义 GDP 的实时即时预测

This paper provides early assessments of current U.S. Nominal GDP growth, which has been considered as a potential new monetary policy target. The nowcasts are computed using the exact amount of information that policy makers have available at the time predictions are made. However, real time information arrives at different frequencies and asynchronously, which poses the challenge of mixed frequencies, missing data, and ragged edges. This paper proposes a multivariate state…

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Forecast Rationality Tests in the Presence of Instabilities, with Applications to Federal Reserve and Survey Forecasts

不稳定环境下的预测理性检验:美联储与调查预测的应用

This paper proposes a framework to implement regression-based tests of predictive ability in unstable environments, including, in particular, forecast unbiasedness and efficiency tests, commonly referred to as tests of forecast rationality. Our framework is general: it can be applied to model-based forecasts obtained either with recursive or rolling window estimation schemes, as well as to forecasts that are model free. The proposed tests provide more evidence against…

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