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Optimal forecasts in the presence of structural breaks

存在结构突变时的最优预测

This paper considers the problem of forecasting under continuous and discrete structural breaks and proposes weighting observations to obtain optimal forecasts in the MSFE sense. We derive optimal weights for one step ahead forecasts. Under continuous breaks, our approach largely recovers exponential smoothing weights. Under discrete breaks, we provide analytical expressions for optimal weights in models with a single regressor, and asymptotically valid weights for models…

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Moving average stochastic volatility models with application to inflation forecast

含移动平均误差的随机波动率模型及其通胀预测应用

We introduce a new class of models that has both stochastic volatility and moving average errors, where the conditional mean has a state space representation. Having a moving average component, however, means that the errors in the measurement equation are no longer serially independent, and estimation becomes more difficult. We develop a posterior simulator that builds upon recent advances in precision-based algorithms for estimating these new models. In an empirical…

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Factor-Augmented VARMA Models With Macroeconomic Applications

因子增强 VARMA 模型及其宏观经济应用

We study the relationship between vector autoregressive moving-average (VARMA) and factor representations of a vector stochastic process. We observe that, in general, vector time series and factors cannot both follow finite-order VAR models. Instead, a VAR factor dynamics induces a VARMA process, while a VAR process entails VARMA factors. We propose to combine factor and VARMA modeling by using factor-augmented VARMA (FAVARMA) models. This approach is applied to forecasting…

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Constrained Regression for Interval-Valued Data

区间值数据的约束回归

Current regression models for interval-valued data do not guarantee that the predicted lower bound of the interval is always smaller than its upper bound. We propose a constrained regression model that preserves the natural order of the interval in all instances, either for in-sample fitted intervals or for interval forecasts. Within the framework of interval time series, we specify a general dynamic bivariate system for the upper and lower bounds of the intervals. By…

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Adaptively combined forecasting for discrete response time series

离散响应时间序列的自适应组合预测

Adaptive combining is generally a desirable approach for forecasting, which, however, has rarely been explored for discrete response time series. In this paper, we propose an adaptively combined forecasting method for such discrete response data. We demonstrate in theory that the proposed forecast is of the desired adaptation with respect to the widely used squared risk and other significant risk functions under mild conditions. Furthermore, we study the issue of adaptation…

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Bayesian semiparametric multivariate GARCH modeling

贝叶斯半参数多元GARCH建模

This paper proposes a Bayesian nonparametric modeling approach for the return distribution in multivariate GARCH models. In contrast to the parametric literature the return distribution can display general forms of asymmetry and thick tails. An infinite mixture of multivariate normals is given a flexible Dirichlet process prior. The GARCH functional form enters into each of the components of this mixture. We discuss conjugate methods that allow for scale mixtures and…

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FACTOR ANALYSIS OF A LARGE DSGE MODEL

大型 DSGE 模型的因子分析

SUMMARY We study the workings of the factor analysis of high‐dimensional data using artificial series generated from a large, multi‐sector dynamic stochastic general equilibrium (DSGE) model. The objective is to use the DSGE model as a laboratory that allows us to shed some light on the practical benefits and limitations of using factor analysis techniques on economic data. We explain in what sense the artificial data can be thought of having a factor structure, study the…

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Determining the MSE-optimal cross section to forecast

确定预测所需的均方误差最优序列子集

In this paper, we address the question of which subset of time series should be selected among a given set in order to forecast another series. We evaluate the quality of the forecasts in terms of Mean Squared Error. We propose a family of criteria to estimate the optimal subset. Consistency results are proved, both in the weak (in probability) and strong (almost sure) sense. We present the results of a Monte Carlo experiment and a real data example in which the criteria are…

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MULTISTEP PREDICTION OF PANEL VECTOR AUTOREGRESSIVE PROCESSES

面板向量自回归过程的多步预测

This paper considers the conventional recursive (otherwise known as plug-in) and direct multistep forecasts in a panel vector autoregressive framework. We derive asymptotic expressions for the mean square prediction error (MSPE) of both forecasts as N (cross sections) and T (time periods) grow large. Both the bias and variance of the least squares fitting are manifest in the MSPE. Using these expressions, we consider the effect of model specification on predictor accuracy.…

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MULTIVARIATE VOLATILITY MODELING OF ELECTRICITY FUTURES

电力期货的多元波动率建模

SUMMARY We model the dynamic volatility and correlation structure of electricity futures of the European Energy Exchange index. We use a new multiplicative dynamic conditional correlation (mDCC) model to separate long‐run from short‐run components. We allow for smooth changes in the unconditional volatilities and correlations through a multiplicative component that we estimate nonparametrically. For the short‐run dynamics, we use a GJR‐GARCH model for the conditional…

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EVALUATING REAL‐TIME VAR FORECASTS WITH AN INFORMATIVE DEMOCRATIC PRIOR

利用信息性民主先验评估实时VAR预测

SUMMARY This paper proposes Bayesian forecasting in a vector autoregression using a democratic prior. This prior is chosen to match the predictions of survey respondents. In particular, the unconditional mean for each series in the vector autoregression is centered around long‐horizon survey forecasts. Heavy shrinkage toward the democratic prior is found to give good real‐time predictions of a range of macroeconomic variables, as these survey projections are good at quickly…

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Realized Volatility Forecasting in the Presence of Time-Varying Noise

时变噪声下的已实现波动率预测

Observed high-frequency financial prices can be considered as having two components, a true price and a market microstructure noise perturbation. It is an empirical regularity, coherent with classical market microstructure theories of price determination, that the second moment of market microstructure noise is time-varying. We study the optimal, from a finite-sample forecast mean squared error (MSE) standpoint, frequency selection for realized variance in linear variance…

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Moment bounds and mean squared prediction errors of long-memory time series

长记忆时间序列的矩界与均方预测误差

A moment bound for the normalized conditional-sum-of-squares (CSS) estimate of a general autoregressive fractionally integrated moving average (ARFIMA) model with an arbitrary unknown memory parameter is derived in this paper. To achieve this goal, a uniform moment bound for the inverse of the normalized objective function is established. An important application of these results is to establish asymptotic expressions for the one-step and multi-step mean squared prediction…

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ON THE RECOVERABILITY OF FORECASTERS’ PREFERENCES

预测者偏好的可恢复性

We study the problem of identifying a forecaster’s loss function from observations on forecasts, realizations, and the forecaster’s information set. Essentially different loss functions can lead to the same forecasts in all situations, though within the class of all continuous loss functions, this is strongly nongeneric. With the small set of exceptional cases ruled out, generic nonparametric preference recovery is theoretically possible, but identification depends…

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NONCAUSAL VECTOR AUTOREGRESSION

非因果向量自回归模型

In this paper, we propose a new noncausal vector autoregressive (VAR) model for non-Gaussian time series. The assumption of non-Gaussianity is needed for reasons of identifiability. Assuming that the error distribution belongs to a fairly general class of elliptical distributions, we develop an asymptotic theory of maximum likelihood estimation and statistical inference. We argue that allowing for noncausality is of particular importance in economic applications that…

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Predicting binary outcomes

二元结果预测

We address the issue of using a set of covariates to categorize or predict a binary outcome. This is a common problem in many disciplines including economics. In the context of a prespecified utility (or cost) function we examine the construction of forecasts suggesting an extension of the Manski (1975, 1985) maximum score approach. We provide analytical properties of the method and compare it to more common approaches such as forecasts or classifications based on…

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Should Macroeconomic Forecasters Use Daily Financial Data and How?

宏观预测者是否应使用日度金融数据,以及如何使用?

We introduce easy-to-implement, regression-based methods for predicting quarterly real economic activity that use daily financial data and rely on forecast combinations of mixed data sampling (MIDAS) regressions. We also extract a novel small set of daily financial factors from a large panel of about 1000 daily financial assets. Our analysis is designed to elucidate the value of daily financial information and provide real-time forecast updates of the current (nowcasting)…

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Structural Dynamic Factor Analysis Using Prior Information From Macroeconomic Theory

利用宏观经济理论先验信息的结构动态因子分析

Dynamic factor models are becoming increasingly popular in empirical macroeconomics due to their ability to cope with large datasets. Dynamic stochastic general equilibrium (DSGE) models, on the other hand, are suitable for the analysis of policy interventions from a methodical point of view. In this article, we provide a Bayesian method to combine the statistically rich specification of the former with the conceptual advantages of the latter by using information from a DSGE…

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Bayesian Analysis of Latent Threshold Dynamic Models

潜在阈值动态模型的贝叶斯分析

We discuss a general approach to dynamic sparsity modeling in multivariate time series analysis. Time-varying parameters are linked to latent processes that are thresholded to induce zero values adaptively, providing natural mechanisms for dynamic variable inclusion/selection. We discuss Bayesian model specification, analysis and prediction in dynamic regressions, time-varying vector autoregressions, and multivariate volatility models using latent thresholding. Application…

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REAL‐TIME FORECASTING OF INFLATION AND OUTPUT GROWTH WITH AUTOREGRESSIVE MODELS IN THE PRESENCE OF DATA REVISIONS

数据修订下利用自回归模型实时预测通胀与产出增长

SUMMARY We examine how the accuracy of real‐time forecasts from models that include autoregressive terms can be improved by estimating the models on ‘lightly revised’ data instead of using data from the latest‐available vintage. The benefits of estimating autoregressive models on lightly revised data are related to the nature of the data revision process and the underlying process for the true values. Empirically, we find improvements in root mean square forecasting error of…

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POOLING VERSUS MODEL SELECTION FOR NOWCASTING GDP WITH MANY PREDICTORS: EMPIRICAL EVIDENCE FOR SIX INDUSTRIALIZED COUNTRIES

多预测变量下 GDP 即时预测的模型合并与选择:六个工业化国家的证据

SUMMARY This paper discusses pooling versus model selection for nowcasting with large datasets in the presence of model uncertainty. In practice, nowcasting a low‐frequency variable with a large number of high‐frequency indicators should account for at least two data irregularities: (i) unbalanced data with missing observations at the end of the sample due to publication delays; and (ii) different sampling frequencies of the data. Two model classes suited in this context are…

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REVERSE REGRESSIONS AND LONG‐HORIZON FORECASTING

反向回归与长期限预测

SUMMARY Long‐horizon predictive regressions in finance pose formidable econometric problems when estimated using available sample sizes. Hodrick in 1992 proposed a remedy that is based on running a reverse regression of short‐horizon returns on the long‐run mean of the predictor. Unfortunately, this only allows the null of no predictability to be tested, and assumes stationary regressors. In this paper, we revisit long‐horizon forecasting from reverse regressions, and argue…

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On loss functions and ranking forecasting performances of multivariate volatility models

损失函数与多元波动模型预测表现的排序

The ranking of multivariate volatility models is inherently problematic because when the unobservable volatility is substituted by a proxy, the ordering implied by a loss function may be biased with respect to the intended one. We point out that the size of the distortion is strictly tied to the level of the accuracy of the volatility proxy. We propose a generalized necessary and sufficient functional form for a class of non-metric distance measures of the Bregman type which…

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Extending the State-Space Model to Accommodate Missing Values in Responses and Covariates

允许响应与协变量缺失的扩展状态空间模型

This article proposes an extended state-space model for accommodating multivariate panel data. The novel aspect of this contribution is an adjustment to the classical model for multiple subjects that allows missingness in the covariates in addition to the responses. Missing covariate data are handled by a second state-space model nested inside the first to represent unobserved exogenous information. Relevant Kalman filter equations are derived, and explicit expressions are…

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