Forecasting Accuracy and Estimation Uncertainty using VAR Models with Short- and Long-Term Economic Restrictions: A Monte-Carlo Study

Using vector autoregressive (VAR) models and Monte-Carlo simulation methods we investigate the potential gains for forecasting accuracy and estimation uncertainty of two commonly used restrictions arising from economic relationships. The first reduces parameter space by imposing long-term restrictions on the behavior of economic variables as discussed by the literature on cointegration, and the second reduces parameter space by imposing short-term restrictions as discussed by the literature on serial-correlation common features (SCCF). Our simulations cover three important issues on model building, estimation, and forecasting. First, we examine the performance of standard and modified information criteria in choosing lag length for cointegrated VARs with SCCF restrictions. Second, we provide a comparison of forecasting accuracy of fitted VARs when only cointegration restrictions are imposed and when cointegration and SCCF restrictions are jointly imposed. Third, we propose a new estimation algorithm where short- and long-term restrictions interact to estimate the cointegrating and the cofeature spaces respectively. We have three basic results. First, ignoring SCCF restrictions has a high cost in terms of model selection, because standard information criteria chooses too frequently inconsistent models, with too small a lag length. Criteria selecting lag and rank simultaneously have a superior performance in this case. Second, this translates into a superior forecasting performance of the restricted VECM over the VECM, with important improvements in forecasting accuracy - reaching more than 100% in extreme cases. Third, the new algorithm proposed here fares very well in terms of parameter estimation, even when we consider the estimation of long-term parameters, opening up the discussion of joint estimation of short- and long-term parameters in VAR models.reduced rank models, model selection criteria, forecasting accuracy

Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions

We study the joint determination of the lag length, the dimension of the cointegrating space andthe rank of the matrix of short-run parameters of a vector autoregressive (VAR) model using modelselection criteria. We consider model selection criteria which have data-dependent penalties aswell as the traditional ones. We suggest a new two-step model selection procedure which is ahybrid of traditional criteria and criteria with data-dependant penalties and we prove its consistency.Our Monte Carlo simulations measure the improvements in forecasting accuracy that can arisefrom the joint determination of lag-length and rank using our proposed procedure, relative to anunrestricted VAR or a cointegrated VAR estimated by the commonly used procedure of selecting thelag-length only and then testing for cointegration. Two empirical applications forecasting Brazilianinflation and U.S. macroeconomic aggregates growth rates respectively show the usefulness of themodel-selection strategy proposed here. The gains in different measures of forecasting accuracy aresubstantial, especially for short horizons.

Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions

We study the joint determination of the lag length, the dimension of the cointegrating space andthe rank of the matrix of short-run parameters of a vector autoregressive (VAR) model using modelselection criteria. We consider model selection criteria which have data-dependent penalties for alack of parsimony, as well as the traditional ones. We suggest a new procedure which is a hybridof traditional criteria and criteria with data-dependant penalties. In order to compute the fit ofeach model, we propose an iterative procedure to compute the maximum likelihood estimates ofparameters of a VAR model with short-run and long-run restrictions. Our Monte Carlo simulationsmeasure the improvements in forecasting accuracy that can arise from the joint determination oflag-length and rank, relative to the commonly used procedure of selecting the lag-length only andthen testing for cointegration.

Selection of Optimal Lag Length in Cointegrated VAR Models with Weak Form of Common Cyclical Features

An important aspect of empirical research based on the vector autoregressive (VAR) model is the choice of the lag order, since all inference in the VAR model depends on the correct model specification. Literature has shown important studies of how to select the lag order of a nonstationary VAR model subject to cointegration restrictions. In this work, we consider an additional weak form (WF) restriction of common cyclical features in the model in order to analyze the appropriate way to select the correct lag order. Two methodologies have been used: the traditional information criteria (AIC, HQ and SC) and an alternative criterion (IC(p,s)) which select simultaneously the lag order p and the rank structure s due to the WF restriction. A Monte-Carlo simulation is used in the analysis. The results indicate that the cost of ignoring additional WF restrictions in vector autoregressive modeling can be high, especially when SC criterion is used.

Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions

We study the joint determination of the lag length, the dimension of the cointegrating space andthe rank of the matrix of short-run parameters of a vector autoregressive (VAR) model using modelselection criteria. We suggest a new two-step model selection procedure which is a hybrid of traditionalcriteria and criteria with data-dependant penalties and we prove its consistency. A MonteCarlo study explores the finite sample performance of this procedure and evaluates the forecastingaccuracy of models selected by this procedure. Two empirical applications confirm the usefulnessof the model selection procedure proposed here for forecasting.

Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions

We study the joint determination of the lag length, the dimension of the cointegrating spaceand the rank of the matrix of short-run parameters of a vector autoregressive (VAR) model usingmodel selection criteria. We consider model selection criteria which have data-dependent penaltiesas well as the traditional ones. We suggest a new two-step model selection procedure which is ahybrid of traditional criteria and criteria with data-dependant penalties and we prove its consistency.Our Monte Carlo simulations measure the improvements in forecasting accuracy that can arisefrom the joint determination of lag-length and rank using our proposed procedure, relative to anunrestricted VAR or a cointegrated VAR estimated by the commonly used procedure of selecting thelag-length only and then testing for cointegration. Two empirical applications forecasting Brazilianin ation and U.S. macroeconomic aggregates growth rates respectively show the usefulness of themodel-selection strategy proposed here. The gains in di¤erent measures of forecasting accuracy aresubstantial, especially for short horizons.

Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions

We study the joint determination of the lag length, the dimension of the cointegrating space and the rank of the matrix of short-run parameters of a vector autoregressive (VAR) model using model selection criteria. We consider model selection criteria which have data-dependent penalties as well as the traditional ones. We suggest a new two-step model selection procedure which is a hybrid of traditional criteria and criteria with data-dependant penalties and we prove its consistency. Our Monte Carlo simulations measure the improvements in forecasting accuracy that can arise from the joint determination of lag-length and rank using our proposed procedure, relative to an unrestricted VAR or a cointegrated VAR estimated by the commonly used procedure of selecting the lag-length only and then testing for cointegration. Two empirical applications forecasting Brazilian inflation and U.S. macroeconomic aggregates growth rates respectively show the usefulness of the model-selection strategy proposed here. The gains in different measures of forecasting accuracy are substantial, especially for short horizons.