
on Econometric Time Series 
By:  Norman Morin 
Abstract:  Cointegration theory provides a flexible class of statistical models that combine longrun relationships and shortrun dynamics. This paper presents three likelihood ratio (LR) tests for simultaneously testing restrictions on cointegrating relationships and on how quickly the system reacts to the deviation from equilibrium implied by the cointegrating relationships. Both the orthogonal complements of the cointegrating vectors and of the vectors of adjustment speeds have been used to define the common stochastic trends of a nonstationary system. The restrictions implicitly placed on the orthogonal complements of the cointegrating vectors and of the adjustment speeds are identified for a class of LR tests, including those developed in this paper. It is shown how these tests can be interpreted as tests for restrictions on the orthogonal complements of the cointegrating relationships and adjustment vectors, which allow one to combine and test for economically meaningful restrictions on cointegrating relationships and on common stochastic trends. 
Date:  2006 
URL:  http://d.repec.org/n?u=RePEc:fip:fedgfe:200621&r=ets 
By:  Todd E. Clark; Michael W. McCracken 
Abstract:  Smallscale VARs have come to be widely used in macroeconomics, for purposes ranging from forecasting output, prices, and interest rates to modeling expectations formation in theoretical models. However, a body of recent work suggests such VAR models may be prone to instabilities. In the face of such instabilities, a variety of estimation or forecasting methods might be used to improve the accuracy of forecasts from a VAR. These methods include using different approaches to lag selection, observation windows for estimation, (over) differencing, intercept correction, stochastically timevarying parameters, break dating, discounted least squares, Bayesian shrinkage, detrending of inflation and interest rates, and model averaging. Focusing on simple models of U.S. output, prices, and interest rates, this paper compares the effectiveness of such methods. Our goal is to identify those approaches that, in real time, yield the most accurate forecasts of these variables. We use forecasts from simple univariate time series models, the Survey of Professional Forecasters and the Federal Reserve Board's Greenbook as benchmarks. 
Keywords:  Economic forecasting ; Timeseries analysis 
Date:  2006 
URL:  http://d.repec.org/n?u=RePEc:fip:fedkrw:rwp0609&r=ets 
By:  James H. Stock; Mark W. Watson 
Abstract:  Forecasts of the rate of price inflation play a central role in the formulation of monetary policy, and forecasting inflation is a key job for economists at the Federal Reserve Board. This paper examines whether this job has become harder and, to the extent that it has, what changes in the inflation process have made it so. The main finding is that the univariate inflation process is well described by an unobserved component trendcycle model with stochastic volatility or, equivalently, an integrated moving average process with timevarying parameters; this model explains a variety of recent univariate inflation forecasting puzzles. It appears currently to be difficult for multivariate forecasts to improve on forecasts made using this timevarying univariate model. 
JEL:  C53 E37 
Date:  2006–06 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:12324&r=ets 
By:  Anders B. Trolle; Eduardo S. Schwartz 
Abstract:  We develop a tractable and flexible stochastic volatility multifactor model of the term structure of interest rates. It features correlations between innovations to forward rates and volatilities, quasianalytical prices of zerocoupon bond options and dynamics of the forward rate curve, under both the actual and riskneutral measure, in terms of a finitedimensional affine state vector. The model has a very good fit to an extensive panel data set of interest rates, swaptions and caps. In particular, the model matches the implied cap skews and the dynamics of implied volatilities. The model also performs well in forecasting interest rates and derivatives. 
JEL:  E43 G13 
Date:  2006–06 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:12337&r=ets 
By:  Lawrence J. Christiano; Martin Eichenbaum; Robert Vigfusson 
Abstract:  This paper analyzes the quality of VARbased procedures for estimating the response of the economy to a shock. We focus on two key issues. First, do VARbased confidence intervals accurately reflect the actual degree of sampling uncertainty associated with impulse response functions? Second, what is the size of bias relative to confidence intervals, and how do coverage rates of confidence intervals compare with their nominal size? We address these questions using data generated from a series of estimated dynamic, stochastic general equilibrium models. We organize most of our analysis around a particular question that has attracted a great deal of attention in the literature: How do hours worked respond to an identified shock? In all of our examples, as long as the variance in hours worked due to a given shock is above the remarkably low number of 1 percent, structural VARs perform well. This finding is true regardless of whether identification is based on shortrun or longrun restrictions. Confidence intervals are wider in the case of longrun restrictions. Even so, longrun identified VARs can be useful for discriminating among competing economic models. 
JEL:  C1 
Date:  2006–07 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:12353&r=ets 