Speed of adjustment in cointegrated systems

Abstract

This paper considers the speed of adjustment to long-run equilibria, in the context of cointegrated Vector Autoregressive Processes (VAR). We discuss the de…nition of multivariate -lives for any indicator of predictive ability, concentrating on cumulated interim multipliers which converge to impact factor for increasing forecasting horizon. Interim multipliers are related to autoregressive Granger-causality coe¢ cients, structural or generalized cumulative impulse responses. We discuss the relation of the present de…nition of multivariate -lives with existing de…nitions for univariate time series and for nonlinear multivariate stationary processes. For multivariate (possibly cointegrated) VAR systems, -lives are functions of the dynamics of the system only, and do not depend on the history path on which the forecast is based. Hence one can discuss inference on -lives as (discrete) functions of parameters in the VAR model.We discuss a likelihood-based approach, both for point estimation and for con…dence regions. An illustrative application to adjustment to purchasing-power parity (PPP) is presented.

Do emissions and income have a common trend? A country-specific, time-series, global analysis, 1970–2008

“…13 The analysis for longer prediction horizons is more articulate, see Dufour et al (2006), Omtzigt and Paruolo (2005) and Fanelli and Paruolo (2010), and goes beyond the scope of the present paper. are found applying the results in Johansen (1996) and Luetkepohl (2005), and they are simply stated in the following without further references.…”

On the Stability of Euro Area Money Demand and Its Implications for Monetary Policy

“…Finally, we can compute the dynamic adjustment of variables of interest at different horizons (see Fanelli and Paruolo, ). Following Pesaran and Shin (), we estimate the generalized impulse response (GIRF) of real balances to .…”

Government Fiscal Efforts vs. Labour Union Strikes. Strategic Substitutes or Complements?

“…(11) of the paper. The reported measures of speed of long-run adjustment correspond to the long-run λ-lives (obtained with λ = 0.5) introduced in Fanelli & Paruolo (2010). 90% confidence intervals in parentheses are computed by a non-parametric bootstrap procedure based on M=100 replications.…”

“…The estimated model shows that fiscal efforts and strikes are indeed jointly determined and whether they are strategic substitutes or complements, in the long-run. 5 Finally, we analyse the structure of adjustment towards equilibrium, using the concept of 'speed of long-run adjustment' introduced in Fanelli & Paruolo (2010), to discern which player is more effective to reach its goal in the long-run equilibrium.…”