Density forecast combinations are becoming increasingly popular as a means of improving forecast 'accuracy', as measured by a scoring rule. In this paper we generalise this literature by letting the combination weights follow more general schemes. Sieve estimation is used to optimise the score of the generalised density combination where the combination weights depend on the variable one is trying to forecast. Specific attention is paid to the use of piecewise linear weight functions that let the weights vary by region of the density. We analyse these schemes theoretically, in Monte Carlo experiments and in an empirical study. Our results show that the generalised combinations outperform their linear counterparts.JEL Codes: C53
a b s t r a c tWhen location shifts occur, cointegration-based equilibrium-correction models (EqCMs) face forecasting problems. We consider alleviating such forecast failure by updating, intercept corrections, differencing, and estimating the future progress of an 'internal' break. Updating leads to a loss of cointegration when an EqCM suffers an equilibrium-mean shift, but helps when collinearities are changed by an 'external' break with the EqCM staying constant. Both mechanistic corrections help compared to retaining a prebreak estimated model, but an estimated model of the break process could outperform. We apply the approaches to EqCMs for UK M1, compared with updating a learning function as the break evolves.
We consider the reasons for nowcasting, the timing of information and sources thereof, especially contemporaneous data, which introduce different aspects compared to forecasting. We allow for the impact of location shifts inducing nowcast failure and nowcasting during breaks, probably with measurement errors. We also apply a variant of the nowcasting strategy proposed in Castle and Hendry (2009) to nowcast Euro Area GDP growth. Models of disaggregate monthly indicators are built by automatic methods, forecasting all variables that are released with a publication lag each period, then testing for shifts in available measures including survey data, switching to robust forecasts of missing series when breaks are detected.
Success in accurately forecasting breaks requires that they are predictable from relevant information available at the forecast origin using an appropriate model form, which can be selected and estimated before the break. To clarify the roles of these six necessary conditions, we distinguish between the information set for 'normal forces' and the one for 'break drivers', then outline sources of potential information. Relevant non-linear, dynamic models facing multiple breaks can have more candidate variables than observations, so we discuss automatic model selection. As a failure to accurately forecast breaks remains likely, we augment our strategy by modelling breaks during their progress, and consider robust forecasting devices.
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