Empirical Bayes Forecasts of One Time Series Using Many Predictors

Knox, Thomas; Stock, James H.; Watson, Mark W.

doi:10.3386/t0269

Cited by 9 publications

(16 citation statements)

References 33 publications

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“…Our results are consistent with those of Knox, Stock and Watson (2002) who consider forecasting using a large number of monthly time series using various estimation methods, including empirical Bayesian methods of a di¤erent sort from those used in our paper. These methods include many factors as explanatory variables and a data-based prior to carry out Bayesian inference.…”

Section: Forecasting Exercisesupporting

confidence: 90%

“…These methods include many factors as explanatory variables and a data-based prior to carry out Bayesian inference. Knox, Stock and Watson (2002) …nd very good in-sample performance of their empirical Bayesian methods, but relatively poor forecasting performance in a simulated real-time forecasting exercise similar to that carried out in this paper. Despite the fact that they are using very di¤erent data from us, this pattern of good in-sample performance and bad out-of-sample performance holds in both of our exercises.…”

Section: Forecasting Exercisementioning

confidence: 66%

“…We construct W using principal components, implying a factor structure similar to that used by others in the …eld (e.g. Stock and Watson, 2002). That is, W is simply the matrix of eigenvectors of X 0 X.…”

Section: Bayesian Model Averaging and Selectionmentioning

confidence: 99%

“…Such an empirical Bayesian methodology can be criticized on the grounds that allowing a prior to depend on y violates the rules of conditional probability. Nevertheless, empirical Bayesian methods are popular with many practical econometricians (see, e.g., Knox, Stock and Watson, 2002). There are various approaches which use the label "empirical Bayes".…”

Section: Bayesian Model Averaging and Selectionmentioning

confidence: 99%

“…A theoretical literature has emerged which discusses the statistical properties of various factor-based estimators (see, among many others, Bai and Ng, 2002, Boivin and Ng, 2002, Forni, Hallin, Lippi and Reichlin, 2000, Knox, Stock and Watson, 2002and West, 2002. The purpose of the present paper is to implement alternative approaches to modeling with large macroeconomic panels by drawing on ideas from the Bayesian model averaging (BMA) literature.…”

Section: Introductionmentioning

confidence: 99%

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Forecasting in Large Macroeconomic Panels Using Bayesian Model Averaging

Koop

Potter

2003

SSRN Journal

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This paper considers the problem of forecasting in large macroeconomic panels using Bayesian model averaging. Theoretical justi…cations for averaging across models, as opposed to selecting a single model, are given. Practical methods for implementing Bayesian model averaging with factor models are described. These methods involve algorithms which simulate from the space de…ned by all possible models. We discuss how these simulation algorithms can also be used to select the model with the highest marginal likelihood (or highest value of an information criterion) in an e¢cient manner. We apply these methods to the problem of forecasting GDP and in ‡ation using quarterly U.S. data on 162 time series. For both GDP and in ‡ation, we …nd that the models which contain factors do out-forecast an AR(p), but only by a relatively small amount and only at short horizons. We attribute these …ndings to the presence of structural instability and the fact that lags of dependent variable seem to contain most of the information relevant for forecasting. Relative to the small forecasting gains provided by including factors, the gains provided by using Bayesian model averaging over forecasting methods based on a single model are appreciable.

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Section: Forecasting Exercisesupporting

confidence: 90%

Section: Forecasting Exercisementioning

confidence: 66%

Section: Bayesian Model Averaging and Selectionmentioning

confidence: 99%

Section: Bayesian Model Averaging and Selectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Forecasting in Large Macroeconomic Panels Using Bayesian Model Averaging

Koop

Potter

2003

SSRN Journal

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Can out‐of‐sample forecast comparisons help prevent overfitting?

Clark

2004

Journal of Forecasting

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This paper shows that out-of-sample forecast comparisons can help prevent data mining-induced overfitting. The basic results are drawn from simulations of a simple Monte Carlo design and a real data-based design similar to those used in some previous studies. In each simulation, a general-to-specific procedure is used to arrive at a model. If the selected specification includes any of the candidate explanatory variables, forecasts from the model are compared to forecasts from a benchmark model that is nested within the selected model. In particular, the competing forecasts are tested for equal MSE and encompassing. The simulations indicate most of the post-sample tests are roughly correctly sized. Moreover, the tests have relatively good power, although some are consistently more powerful than others. The paper concludes with an application, modelling quarterly US inflation. Copyright © 2004 John Wiley & Sons, Ltd.

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Regularization for Linear System Identification

Pillonetto

Chen

Chiuso

et al. 2022

Communications and Control Engineering

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Regularization has been intensively used in statistics and numerical analysis to stabilize the solution of ill-posed inverse problems. Its use in System Identification, instead, has been less systematic until very recently. This chapter provides an overview of the main motivations for using regularization in system identification from a “classical” (Mean Square Error) statistical perspective, also discussing how structural properties of dynamical models such as stability can be controlled via regularization. A Bayesian perspective is also provided, and the language of maximum entropy priors is exploited to connect different form of regularization with time-domain and frequency-domain properties of dynamical systems. Some numerical examples illustrate the role of hyper parameters in controlling model complexity, for instance, quantified by the notion of Degrees of Freedom. A brief outlook on more advanced topics such as the connection with (orthogonal) basis expansion, McMillan degree, Hankel norms is also provided. The chapter is concluded with an historical overview on the early developments of the use of regularization in System Identification.

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Empirical Bayes Forecasts of One Time Series Using Many Predictors

Cited by 9 publications

References 33 publications

Forecasting in Large Macroeconomic Panels Using Bayesian Model Averaging

Forecasting in Large Macroeconomic Panels Using Bayesian Model Averaging

Can out‐of‐sample forecast comparisons help prevent overfitting?

Regularization for Linear System Identification

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