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Conditional Correlation Models of Autoregressive Conditional Heteroscedasticity With Nonstationary GARCH Equations

含非平稳 GARCH 方程的条件相关模型

In this article, we investigate the effects of careful modeling the long-run dynamics of the volatilities of stock market returns on the conditional correlation structure. To this end, we allow the individual unconditional variances in conditional correlation generalized autoregressive conditional heteroscedasticity (CC-GARCH) models to change smoothly over time by incorporating a nonstationary component in the variance equations such as the spline-GARCH model and the…

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Nowcasting GDP in Real Time: A Density Combination Approach

实时 GDP 即时预测:密度组合方法

In this article, we use U.S. real-time data to produce combined density nowcasts of quarterly Gross Domestic Product (GDP) growth, using a system of three commonly used model classes. We update the density nowcast for every new data release throughout the quarter, and highlight the importance of new information for nowcasting. Our results show that the logarithmic score of the predictive densities for U.S. GDP growth increase almost monotonically, as new information arrives…

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From Amazon to Apple: Modeling Online Retail Sales, Purchase Incidence, and Visit Behavior

从亚马逊到苹果:在线零售销售、购买发生与访问行为建模

In this study, we propose a multivariate stochastic model for Web site visit duration, page views, purchase incidence, and the sale amount for online retailers. The model is constructed by composition from carefully selected distributions and involves copula components. It allows for the strong nonlinear relationships between the sales and visit variables to be explored in detail, and can be used to construct sales predictions. The model is readily estimated using maximum…

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Conditional Transformation Models

条件变换模型

Summary The ultimate goal of regression analysis is to obtain information about the conditional distribution of a response given a set of explanatory variables. This goal is, however, seldom achieved because most established regression models estimate only the conditional mean as a function of the explanatory variables and assume that higher moments are not affected by the regressors. The underlying reason for such a restriction is the assumption of additivity of signal and…

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Is there an optimal forecast combination?

是否存在最优的预测组合?

We consider several geometric approaches for combining forecasts in large samples—a simple eigenvector approach, a mean corrected eigenvector and trimmed eigenvector approach. We give conditions where geometric approach yields identical result as the regression approach. We also consider a mean and scale corrected simple average of all predictive models for finite sample and give conditions where simple average is an optimal combination. Monte Carlos are conducted to compare…

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Forecasting financial and macroeconomic variables using data reduction methods: New empirical evidence

利用数据降维方法预测金融与宏观变量:新的实证证据

In this paper, we empirically assess the predictive accuracy of a large group of models that are specified using principle components and other shrinkage techniques, including Bayesian model averaging and various bagging, boosting, least angle regression and related methods. Our results suggest that model averaging does not dominate other well designed prediction model specification methods, and that using “hybrid” combination factor/shrinkage methods often yields superior…

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Model selection in under-specified equations facing breaks

面对结构突变的设定不足方程中的模型选择

When a model under-specifies the data generation process, model selection can improve over estimating a prior specification, especially if location shifts occur. Impulse-indicator saturation (IIS) can ‘correct’ non-constant intercepts induced by location shifts in omitted variables, which leave slope parameters unaltered even when correlated with included variables. Location shifts in included variables induce changes in estimated slopes when there are correlated omitted…

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Estimating a semiparametric asymmetric stochastic volatility model with a Dirichlet process mixture

用狄利克雷过程混合估计半参数非对称随机波动率模型

We extend the asymmetric, stochastic, volatility model by modeling the return-volatility distribution nonparametrically. The novelty is modeling this distribution with an infinite mixture of Normals, where the mixture unknowns have a Dirichlet process prior. Cumulative Bayes factors show our semiparametric model accurately forecasting market returns. During tranquil markets, expected volatility rises (declines, then rises as the shock increases) when the market shock is…

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Testing predictive regression models with nonstationary regressors

含非平稳解释变量的预测回归模型检验

Due to nonstationary (nearly integrated or integrated) regressors and the embedded endogeneity, a linear predictive regression model produces biased coefficient estimates, which consequentially leads to the conventional t-test to over-reject the misspecification test. In this paper, our aim is to find an appropriate and easily implemented method for estimating and testing coefficients in predictive regression models. We apply a projection method to remove the embedded…

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SMOOTH DYNAMIC FACTOR ANALYSIS WITH APPLICATION TO THE US TERM STRUCTURE OF INTEREST RATES

SUMMARY We consider the dynamic factor model and show how smoothness restrictions can be imposed on factor loadings by using cubic spline functions. We develop statistical procedures based on Wald, Lagrange multiplier and likelihood ratio tests for this purpose. The methodology is illustrated by analyzing a newly updated monthly time series panel of US term structure of interest rates. Dynamic factor models with and without smooth loadings are compared with dynamic models…

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EXCHANGE RATE FUNDAMENTALS, FORECASTING, AND SPECULATION: BAYESIAN MODELS IN BLACK MARKETS

汇率基本面、预测与投机:黑市中的贝叶斯模型

SUMMARY Although speculative activity is central to black markets for currency, the out‐of‐sample performance of structural models in those settings is unknown. We substantially update the literature on empirical determinants of black market rates and evaluate the out‐of‐sample performance of linear models and non‐parametric Bayesian treed Gaussian process (BTGP) models against the random walk benchmark. Fundamentals‐based models outperform the benchmark in out‐of‐sample…

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MAXIMUM LIKELIHOOD ESTIMATION OF FACTOR MODELS ON DATASETS WITH ARBITRARY PATTERN OF MISSING DATA

任意缺失模式数据下因子模型的最大似然估计

SUMMARY In this paper we modify the expectation maximization algorithm in order to estimate the parameters of the dynamic factor model on a dataset with an arbitrary pattern of missing data. We also extend the model to the case with a serially correlated idiosyncratic component. The framework allows us to handle efficiently and in an automatic manner sets of indicators characterized by different publication delays, frequencies and sample lengths. This can be relevant, for…

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INFORMATION IN THE YIELD CURVE: A MACRO‐FINANCE APPROACH

收益率曲线中的信息:宏观金融方法

SUMMARY We use a macro‐finance model, incorporating macroeconomic and financial factors, to study the term premium in the US bond market. Estimating the model using Bayesian techniques, we find that a single factor explains most of the variation in bond risk premiums. Furthermore, the model‐implied risk premiums account for up to 40% of the variability of one‐ and two‐year excess returns. Using the model to decompose yield spreads into an expectations and a term premium…

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Bridging the ensemble Kalman and particle filters

连接集合卡尔曼滤波与粒子滤波

In many applications of Monte Carlo nonlinear filtering, the propagation step is computationally expensive, and hence the sample size is limited. With small sample sizes, the update step becomes crucial. Particle filtering suffers from the well-known problem of sample degeneracy. Ensemble Kalman filtering avoids this, at the expense of treating non-Gaussian features of the forecast distribution incorrectly. Here we introduce a procedure that makes a continuous transition…

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Forecasting by factors, by variables, by both or neither?

用因子、变量、二者还是都不用来预测?

We consider forecasting with factors, variables and both, modeling in-sample using Autometrics so all principal components and variables can be included jointly, while tackling multiple breaks by impulse-indicator saturation. A forecast-error taxonomy for factor models highlights the impacts of location shifts on forecast-error biases. Forecasting US GDP over 1-, 4- and 8-step horizons using the dataset from Stock and Watson (2009) updated to 2011:2 shows factor models are…

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Complete subset regressions

完全子集回归

This paper proposes a new method for combining forecasts based on complete subset regressions. For a given set of potential predictor variables we combine forecasts from all possible linear regression models that keep the number of predictors fixed. We explore how the choice of model complexity, as measured by the number of included predictor variables, can be used to trade off the bias and variance of the forecast errors, generating a setup akin to the efficient frontier…

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Consistent factor estimation in dynamic factor models with structural instability

结构不稳定下动态因子模型的一致因子估计

This paper considers the estimation of approximate dynamic factor models when there is temporal instability in the factor loadings. We characterize the type and magnitude of instabilities under which the principal components estimator of the factors is consistent and find that these instabilities can be larger than earlier theoretical calculations suggest. We also discuss implications of our results for the robustness of regressions based on the estimated factors and of…

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Large time-varying parameter VARs

大型时变参数向量自回归模型

In this paper, we develop methods for estimation and forecasting in large time-varying parameter vector autoregressive models (TVP-VARs). To overcome computational constraints, we draw on ideas from the dynamic model averaging literature which achieve reductions in the computational burden through the use forgetting factors. We then extend the TVP-VAR so that its dimension can change over time. For instance, we can have a large TVP-VAR as the forecasting model at some points…

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Time-varying combinations of predictive densities using nonlinear filtering

利用非线性滤波进行预测密度的时变组合

We propose a Bayesian combination approach for multivariate predictive densities which relies upon a distributional state space representation of the combination weights. Several specifications of multivariate time-varying weights are introduced with a particular focus on weight dynamics driven by the past performance of the predictive densities and the use of learning mechanisms. In the proposed approach the model set can be incomplete, meaning that all models can be…

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Conditional predictive density evaluation in the presence of instabilities

存在不稳定性时的条件预测密度评价

We propose new methods for evaluating predictive densities. The methods include Kolmogorov–Smirnov and Cramér–von Mises-type tests for the correct specification of predictive densities robust to dynamic mis-specification. The novelty is that the tests can detect mis-specification in the predictive densities even if it appears only over a fraction of the sample, due to the presence of instabilities. Our results indicate that our tests are well sized and have good power in…

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Forecasting a long memory process subject to structural breaks

存在结构突变的长记忆过程预测

We develop an easy-to-implement method for forecasting a stationary autoregressive fractionally integrated moving average (ARFIMA) process subject to structural breaks with unknown break dates. We show that an ARFIMA process subject to a mean shift and a change in the long memory parameter can be well approximated by an autoregressive (AR) model and suggest using an information criterion (AIC or Mallows’ Cp) to choose the order of the approximate AR model. Our method avoids…

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Modelling and forecasting government bond spreads in the euro area: A GVAR model

欧元区政府债券利差的建模与预测:GVAR模型

This paper proposes an extension to Global Vector Autoregressive (GVAR) models to capture time-varying interdependence among financial variables. Government bond spreads in the euro area feature a time-varying pattern of co-movement that poses a serious challenge for econometric modelling and forecasting. This pattern of the data is not captured by the standard specification that model spreads as persistent processes reverting to a time-varying mean determined by two…

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Adaptive forecasting in the presence of recent and ongoing structural change

近期及持续结构变化下的自适应预测

We consider time series forecasting in the presence of ongoing structural change where both the time series dependence and the nature of the structural change are unknown. Methods that downweight older data, such as rolling regressions, forecast averaging over different windows and exponentially weighted moving averages, known to be robust to historical structural change, are found also to be useful in the presence of ongoing structural change in the forecast period. A…

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