Forecasting Nonlinear Aggregates and Aggregates with Time-varying Weights

Despite the fact that many aggregates are nonlinear functions and the aggregation weights of many macroeconomic aggregates are time-varying, much of the literature on forecasting aggregates considers the case of linear aggregates with fixed, time-invariant aggregation weights. In this study a framework for nonlinear contemporaneous aggregation with possibly stochastic or time-varying weights is developed and different predictors for an aggregate are compared theoretically as well as with simulations. Two examples based on European unemployment and inflation series are used to illustrate the virtue of the theoretical setup and the forecasting results.forecasting, stochastic aggregation, autoregression, moving average, vector autoregressive process

Problems Related to Over-identifying Restrictions for Structural Vector Error Correction Models

Structural vector autoregressive (VAR) models are in frequent use for impulse response analysis. If cointegrated variables are involved, the corresponding vector error correction models offer a convenient framework for imposing structural long-run and short-run restrictions. Occasionally it is desirable to impose over-identifying restrictions in this context. Some related problems are pointed out. They result from the fact that the over-identifying restrictions have to be in the admissible parameter space which is not always obvious. Conditions are given that can help in avoiding the problems.Cointegration, vector autoregressive process, vector error correction model, impulse responses

Forecasting Nonlinear Aggregates and Aggregates with Time-varying Weights

Despite the fact that many aggregates are nonlinear functions and the aggregation weights of many macroeconomic aggregates are timevarying, much of the literature on forecasting aggregates considers the case of linear aggregates with fixed, time-invariant aggregation weights. In this study a framework for nonlinear contemporaneous aggregation with possibly stochastic or time-varying weights is developed and different predictors for an aggregate are compared theoretically as well as with simulations. Two examples based on European unemployment and inflation series are used to illustrate the virtue of the theoretical setup and the forecasting results.Forecasting, stochastic aggregation, autoregression, moving average,vector autoregressive process

Forecasting Aggregated Time Series Variables: A Survey

Aggregated times series variables can be forecasted in different ways. For example, they may be forecasted on the basis of the aggregate series or forecasts of disaggregated variables may be obtained first and then these forecasts may be aggregated. A number of forecasts are presented and compared. Classical theoretical results on the relative efficiencies of different forecasts are reviewed and some complications are discussed which invalidate the theoretical results. Contemporaneous as well as temporal aggregation are considered.Autoregressive moving-average process, temporal aggregation, contemporaneous aggregation, vector autoregressive moving-average process

Structural Vector Autoregressions with Markov Switching: Combining Conventional with Statistical Identification of Shocks

In structural vector autoregressive (SVAR) analysis a Markov regime switching (MS) property can be exploited to identify shocks if the reduced form error covariance matrix varies across regimes. Unfortunately, these shocks may not have a meaningful structural economic interpretation. It is discussed how statistical and conventional identifying information can be combined. The discussion is based on a VAR model for the US containing oil prices, output, consumer prices and a short-term interest rate. The system has been used for studying the causes of the early millennium economic slowdown based on traditional identi¯cation with zero and long-run restrictions and using sign restrictions. We find that previously drawn conclusions are questionable in our framework.Vector autoregressive model, Markov process, EM algorithm, impulse responses

Forecasting Contemporaneous Aggregates with Stochastic Aggregation Weights

Many contemporaneously aggregated variables have stochasticaggregation weights. We compare different forecasts for such variables including univariate forecasts of the aggregate, a multivariate forecast of the aggregate that uses information from the disaggregate components, a forecast which aggregates a multivariate forecast of the disaggregate components and the aggregation weights, and a forecast which aggregates univariate forecasts for individual disaggregate components and the aggregation weights. In empirical illustrations based on aggregate GDP and money growth rates, we find forecast efficiency gains from using the information in the stochastic aggregation weights. A Monte Carlo study confirms that using the information on stochastic aggregation weights explicitly may result in forecast mean squared error reductions.Aggregation, autoregressive process, mean squared error

Structural Vector Autoregressions with Nonnormal Residuals

In structural vector autoregressive (SVAR) models identifying restrictions for shocks and impulse responses are usually derived from economic theory or institutional constraints. Sometimes the restrictions are insufficient for identifying all shocks and impulse responses. In this paper it is pointed out that specific distributional assumptions can also help in identifying the structural shocks. In particular, a mixture of normal distributions is considered as a plausible model that can be used in this context. Our model setup makes it possible to test restrictions which are just-identifying in a standard SVAR framework. In particular, we can test for the number of transitory and permanent shocks in a cointegrated SVAR model. The results are illustrated using a data set from King, Plosser, Stock and Watson (1991) and a system of US and European interest rates.mixture normal distribution, cointegration, vector autoregressive process, vector error correction model, impulse responses

A Statistical Comparison of Alternative Identification Schemes for Monetary Policy Shocks

Different identification schemes for monetary policy shocks have been proposed in the literature. They typically specify just-identifying restrictions in a standard structural vector autoregressive (SVAR) framework. Thus, in this framework the different schemes cannot be checked against the data with statistical tests. We consider different approaches how to use the data properties to augment the standard SVAR setup for identifying the shocks. Thereby it becomes possible to test models which are just identified in a standard setting. For monthly US data it is found that a model where monetary shocks are induced via the federal funds rate is the only one which cannot be rejected when the data properties are used for identification.Mixed normal distribution, structural vector autoregressive model, vector autoregressive process