Palgrave Handbook of Econometrics: Applied Econometrics

232 Recent Developments in Density Forecasting VAR model forecast densities, as measured by the logarithmic score, over the hold ...

Stephen G. Hall and James Mitchell 233 Notes However, Granger and Machina (2006) show that, under conditions on the second deri ...

234 Recent Developments in Density Forecasting Bianchi, C. and G. Calzolari (1980) The one period forecast error in non-linear e ...

Stephen G. Hall and James Mitchell 235 Clements, M.P. and J. Smith (2002) Evaluating multivariate forecast densities: a comparis ...

236 Recent Developments in Density Forecasting Fair, R.C. (1980) Estimating the predictive accuracy of econometric models.Intern ...

Stephen G. Hall and James Mitchell 237 Hamilton, J.D. (1994).Time Series Analysis. Princeton: Princeton University Press. Harvey ...

238 Recent Developments in Density Forecasting Mitchell, J. (2007b) Density estimates for real-time eurozone output gap estimate ...

Stephen G. Hall and James Mitchell 239 Stock, J.H. and M. Watson (2004) Combination forecasts of output growth in a seven-countr ...

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Part III Time Series Applications ...

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6 Investigating Economic Trends and Cycles D.S.G. Pollock Abstract Methods are described for extracting the trend from an econom ...

244 Investigating Economic Trends and Cycles 6.9 Band-limited processes 289 6.9.1 The Shannon–Whittaker sampling theorem 290 6.1 ...

D.S.G. Pollock 245 wherey(t)=lnY(t),τ(t)=lnT(t),c(t)=lnC(t),s(t)=lnS(t)andε(t)=lnE(t). An additional assumption, which might be ...

246 Investigating Economic Trends and Cycles 0 2.5ε + 4 5.0ε + 4 7.5ε + 4 1.0ε + 5 0 30 90 90 120 Figure 6.1 The functionY(t)=βe ...

D.S.G. Pollock 247 On the one hand, the linear trendξ(t)=μ+rtcan be subtracted fromy(t)to create the pure business cycleγcos(ωt) ...

248 Investigating Economic Trends and Cycles We define[T/ 2 ]to be the integer part toT/2, which will ben=T/2, ifTis even, or(T− ...

D.S.G. Pollock 249 Since the trigonometrical functions are mutually orthogonal, the Fourier co- efficients can be obtained via a ...

250 Investigating Economic Trends and Cycles 6.3.1 Approximations, resampling and Fourier interpolation By lettingt=0,...,T−1 in ...

D.S.G. Pollock 251 10.0 10.5 11.0 11.5 12.0 1960 1970 1980 1990 2000 Figure 6.4 The quarterly sequence of the logarithms of hous ...