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 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

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 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

The Role of the Log Transformation in Forecasting Economic Variables

For forecasting and economic analysis many variables are used in logarithms (logs). In time series analysis this transformation is often considered to stabilize the variance of a series. We investigate under which conditions taking logs is beneficial for forecasting. Forecasts based on the original series are compared to forecasts based on logs. It is found that it depends on the data generation process whether the former or the latter are preferable. For a range of economic variables substantial forecasting improvements from taking logs are found if the log transformation actually stabilizes the variance of the underlying series. Using logs can be damaging for the forecast precision if a stable variance is not achieved.autoregressive moving average process, forecast mean squared error, instantaneous transformation, integrated process, heteroskedasticity

Stock Prices and Economic Fluctuations: A Markov Switching Structural Vector Autoregressive Analysis

The role of expectations for economic fluctuations has received considerable attention in recent business cycle analysis. We exploit Markov regime switching models to identify shocks in cointegrated structural vector autoregressions and investigate different identification schemes for bivariate systems comprising U.S. stock prices and total factor productivity. The former variable is viewed as re°ecting expectations of economic agents about future productivity. It is found that some previously used identification schemes can be rejected in our model setup. The results crucially depend on the measure used for total factor productivity.Cointegration, Markov regime switching model, vector error correction model, structural vector autoregression, mixed normal distribution