Conditional Forecasts in Dynamic Multivariate Models

Waggoner, Daniel F.; Zha, Tao

doi:10.2139/ssrn.2511338

Cited by 112 publications

(191 citation statements)

References 33 publications

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“…The Wald metric provides a natural statistic to evaluate the likelihood of observing the conditioning paths. These results can be thought of as the large-sample versions of Waggoner and Zha's (1999) Bayesian derivations and provide asymptotic justification for bootstrap-based, finite-sample inference (Horowitz, 2001). We provide empirical examples to illustrate all of the results introduced in the paper.…”

Section: Introductionmentioning

confidence: 88%

“…It turns out that when the joint predictive density is Gaussian, not only is it simple to obtain what the conditional forecast paths would be, it is straightforward to calculate the associated conditional predictive density. Waggoner and Zha (1999) develop Bayesian methods to compute this distribution in finite samples for VARs whereas Leeper and Zha (2003) further investigate projections based on hypothetical paths of monetary policy.…”

Section: Conditional Path Forecastsmentioning

confidence: 99%

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Path forecast evaluation

Jordà

Marcellino

2010

J of Applied Econometrics

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A forecast path refers to the vector of forecasts over the next 1 to h periods into the future. These forecasts are correlated across horizons so that to properly understand the uncertainty associated with the forecast path, one requires the joint predictive density of the path rather than the collection of marginal predictive densities for each horizon. This paper derives the joint predictive density for forecasts generated by VARs or from direct forecast methods (e.g. Marcellino, Stock and Watson, 2003). Given this density, we introduce the mean square forecast path metric to compare the predictive ability between competing models and appropriately modify Diebold-Mariano-West and GiacominiWhite predictive ability tests. We then use Scheffé's S-method to construct simultaneous confidence regions for the forecast path and show how to construct path forecasts conditional on assumed paths for a subset of the system's variables, along with their conditional predictive density and a test on the assumed path's likelihood.JEL Classification Codes: C32, C52, C53

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Section: Introductionmentioning

confidence: 88%

Section: Conditional Path Forecastsmentioning

confidence: 99%

Path forecast evaluation

Jordà

Marcellino

2010

J of Applied Econometrics

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“…For VAR models, the conditional forecasts are typically computed by using the algorithm developed by Waggoner and Zha (1999). Due to computational burden, the latter approach can easily become impractical or unfeasible for high dimensional data and long forecast horizons.…”

Section: Non-technical Summarymentioning

confidence: 99%

“…For VAR models, the conditional forecasts are typically computed by using the algorithm developed by Waggoner and Zha (1999). Roughly speaking, the methodology involves drawing (the entire) paths of reduced form shocks which are compatible with the conditioning path on the observables.…”

Section: Introductionmentioning

confidence: 99%

“…to conduct scenario analysis. Notable examples of the latter are the stress tests recently conducted in the US and the euro area in order to assess the vulnerability of their banking systems.For VAR models, the conditional forecasts are typically computed by using the algorithm developed by Waggoner and Zha (1999). Due to computational burden, the latter approach can easily become impractical or unfeasible for high dimensional data and long forecast horizons.…”

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Conditional forecasts and scenario analysis with vector autoregressions for large cross-sections

Banbura

Giannone

Lenza

2015

International Journal of Forecasting

122

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In 2014 all ECB publications feature a motif taken from the €20 banknote.NOTE: This Working Paper should not be reported as representing the views of the European Central Bank (ECB). The views expressed are those of the authors and do not necessarily refl ect those of the ECB. AbstractThis paper describes an algorithm to compute the distribution of conditional forecasts, i.e. projections of a set of variables of interest on future paths of some other variables, in dynamic systems. The algorithm is based on Kalman filtering methods and is computationally viable for large models that can be cast in a linear state space representation. We build large vector autoregressions (VARs) and a large dynamic factor model (DFM) for a quarterly data set of 26 euro area macroeconomic and financial indicators. Both approaches deliver similar forecasts and scenario assessments. In addition, conditional forecasts shed light on the stability of the dynamic relationships in the euro area during the recent episodes of financial turmoil and indicate that only a small number of sources drive the bulk of the fluctuations in the euro area economy. JEL Classification: C11, C13, C33, C53Keywords: Vector Autoregression, Bayesian Shrinkage, Dynamic Factor Model, Conditional Forecast, Large Cross-Sections.ECB Working Paper 1733, September 2014 1 Non-technical summaryVector autoregressions (VARs) are very flexible and general models and provide a reliable empirical benchmark for alternative econometric representations such as dynamic stochastic general equilibrium (DSGE) models, which are more grounded in theory but, at the same time, impose more structure on the data.Recent literature has shown that VARs are viable tools also for large sets of data. In this paper we construct a large VAR for the euro area and we apply it to unconditional forecasting as well as for conditional forecasts and scenarios. These, along with structural analysis (assessing the effects of structural shocks), have been the main applications of VARs. Whereas large VARs have been used for unconditional forecasting and structural analysis, limited attention has been devoted as yet to conditional forecasting. This is because popular algorithms for deriving conditional forecasts have been computationally challenging for large data sets. We overcome this problem by computing the conditional forecasts recursively using Kalman filtering techniques.Conditional forecasts and, in particular, scenarios are projections of a set of variables of interest on future paths of some other variables. This is in contrast to unconditional forecasts, where no knowledge of the future path of any variables is assumed. The prior knowledge, albeit imperfect, of the future evolution of some economic variables may carry information for the outlook of other variables. For example, future fiscal packages would affect the future evolution of economic activity and, thus, might provide important off-model information. Moreover, it may be of interest to assess the impact of specific future events on a ...

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A Time‐Simultaneous Prediction Box for a Multivariate Time Series

Kolsrud

2015

Journal of Forecasting

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A sample-based method in Kolsrud (Journal of Forecasting 2007; 26(3): 171-188) for the construction of a time-simultaneous prediction band for a univariate time series is extended to produce a variable-and time-simultaneous prediction box for a multivariate time series. A measure of distance based on the L 1 -norm is applied to a learning sample of multivariate time trajectories, which can be mean-and/or variance-nonstationary. Based on the ranking of distances to the centre of the sample, a subsample of the most central multivariate trajectories is selected. A prediction box is constructed by circumscribing the subsample with a hyperrectangle. The fraction of central trajectories selected into the subsample can be calibrated by bootstrap such that the expected coverage of the box equals a prescribed nominal level. The method is related to the concept of data depth, and thence modified to increase coverage. Applications to simulated and empirical data illustrate the method, which is also compared to several other methods in the literature adapted to the multivariate setting.

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Conditional Forecasts in Dynamic Multivariate Models

Cited by 112 publications

References 33 publications

Path forecast evaluation

Path forecast evaluation

Conditional forecasts and scenario analysis with vector autoregressions for large cross-sections

A Time‐Simultaneous Prediction Box for a Multivariate Time Series

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