Palgrave Handbook of Econometrics: Applied Econometrics

212 Recent Developments in Density Forecasting forecasts, again under quadratic loss (see Clements, 1997, for an extension), the ...

Stephen G. Hall and James Mitchell 213 5.4.1 Interval forecasts A “good” interval forecast should, at a minimum, have correct co ...

214 Recent Developments in Density Forecasting impliesλ=1,α=0 andβ=0 in the following variant of (5.21): It=λpt|t− 1 +α+βt− 1 + ...

Stephen G. Hall and James Mitchell 215 5.4.2.1 Goodness-of-fit tests: in theory Diebold, Gunther and Tay (1998) popularized the ...

216 Recent Developments in Density Forecasting zt|t−h. For empirical examples and references, see Clements and Smith (2000), Cle ...

Stephen G. Hall and James Mitchell 217 density forecasts are optimal with dynamic misspecification under both the null and alter ...

218 Recent Developments in Density Forecasting z∗t|t− 1 following an AR(1) process:z∗t|t− 1 =μ+ρz∗t− 1 |t− 2 +εt, whereεt∼N(0,σ^ ...

Stephen G. Hall and James Mitchell 219 for density forecast evaluation, as well as comparison and combination, to which we turn ...

220 Recent Developments in Density Forecasting consider the two degrees-of-freedom LR test referred to above, whereq(z∗it|t−h)= ...

Stephen G. Hall and James Mitchell 221 then constructed based on { dt|t−h }T t= 1 , where: dt|t−h= [ lnf(yt|!t−h)−lng(yt| 1 t−h ...

222 Recent Developments in Density Forecasting the mean square error between the c.d.f. of the density forecast and the true c.d ...

Stephen G. Hall and James Mitchell 223 has begun to explore further why point forecast combination works through analytical and ...

224 Recent Developments in Density Forecasting The “linear opinion pool” takes a weighted linear combination of the forecasters’ ...

Stephen G. Hall and James Mitchell 225 is essentially nonparametric and can accommodate any possible distribution. For finiteNth ...

226 Recent Developments in Density Forecasting the so-called regression approach, is to tune the weights to reflect the historic ...

Stephen G. Hall and James Mitchell 227 the KLIC, such as the Berkowitz (2001) LR test, the KLIC can also be minimized by searchi ...

228 Recent Developments in Density Forecasting weights are given as: wiBMA=Pr(Si|t−h)= Pr(t−h|Si)Pr(Si) ∑N i= 1 Pr(t−h|Si)Pr( ...

Stephen G. Hall and James Mitchell 229 to the truth given the data (posterior probabilities) when attaching equal (prior) weight ...

230 Recent Developments in Density Forecasting likelihood as an out-of-sample measure of fit relies on the prior being informati ...

Stephen G. Hall and James Mitchell 231 gains in forecast accuracy when some variant of KLIC minimizing or BMA, rather than equal ...