Conditional Forecasts in Dynamic Multivariate Models

In the existing literature, conditional forecasts in the vector autoregressive (VAR) framework have not been commonly presented with probability distributions. This paper develops Bayesian methods for computing the exact finite-sample distribution of conditional forecasts. It broadens the class of conditional forecasts to which the methods can be applied. The methods work for both structural and reduced-form VAR models and, in contrast to common practices, account for parameter uncertainty in finite samples. Empirical examples under both a flat prior and a reference prior are provided to show the use of these methods.

[1]  G. Nelson,et al.  Policy analysis with econometric models. , 1996 .

[2]  A. Goldberger,et al.  The Covariance Matrices of Reduced-Form Coefficients and of Forecasts for a Structural Econometric Model , 1961 .

[3]  Peter Christoffersen,et al.  Working Papers Working Papers Working Papers Working Papers Cointegration and Long-horizon Forecasting Cointegration and Long-horizon Forecasting , 2022 .

[4]  John Geweke,et al.  Monte carlo simulation and numerical integration , 1995 .

[5]  Christopher A. Sims,et al.  Using a likelihood perspective to sharpen econometric discourse: Three examples , 2000 .

[6]  Tao Zha,et al.  Error Bands for Impulse Responses , 1999 .

[7]  C. Sims,et al.  Bayesian methods for dynamic multivariate models , 1998 .

[8]  T. Zha Block recursion and structural vector autoregressions , 1999 .

[9]  Robert B. Litterman Forecasting with Bayesian Vector Autoregressions-Five Years of Experience , 1984 .

[10]  Robert B. Litterman,et al.  Forecasting and Conditional Projection Using Realistic Prior Distributions , 1983 .

[11]  C. Sims,et al.  What Does Monetary Policy Do , 1996 .

[12]  Peter Schmidt,et al.  THE ASYMPTOTIC DISTRIBUTION OF FORECASTS IN THE DYNAMIC SIMULATION OF AN ECONOMETRIC MODEL , 1974 .

[13]  Anthony S. Tay,et al.  Evaluating Density Forecasts , 1997 .

[14]  Ellis W. Tallman,et al.  Improving forecasts of the federal funds rate in a policy model , 1999 .

[15]  K. West,et al.  Asymptotic Inference about Predictive Ability , 1996 .

[16]  A. R. Pagan,et al.  Structural Models of the Liquidity Effect , 1998, Review of Economics and Statistics.

[17]  F. Diebold,et al.  The Past, Present, and Future of Macroeconomic Forecasting , 2020, Business Cycles.

[18]  John Geweke,et al.  Federal Reserve Bank of Minneapolis Research Department Staff Report 249 Using Simulation Methods for Bayesian Econometric Models: Inference, Development, and Communication , 2022 .

[19]  C. Whiteman,et al.  Monetary Aggregates as Monetary Targets: A Statistical Investigation , 1992 .

[20]  Normalization, Probability Distribution, and Impulse Responses , 1997 .

[21]  A Dynamic Multivariate Model for Use in Formulating Policy , 1998 .

[22]  L. Kilian Small-sample Confidence Intervals for Impulse Response Functions , 1998, Review of Economics and Statistics.

[23]  Lawrence J. Christiano,et al.  Monetary Policy Shocks: What Have We Learned and to What End? , 1998 .

[24]  Preston J. Miller,et al.  The Quantitative Significance of the Lucas Critique , 1991 .