direct multi-step estimation and forecasting - OFCE - Sciences Po

Direct multi-step estimation and forecasting
and k :
lim (MSFE IMS − MSFE DMS ) > 0.
T →∞
Non parametric direct multi-step estimation was also the focus of Clements and Hendry (1996) and
Chevillon and Hendry (2005). But these authors analyse estimation for forecasting rather than
the design of the DMS FGP. They shed light on the dynamic properties leading direct estimation
to improve accuracy and hence we present their contributions in section 8 where we review the
features advocating the use of DMS.
Discussion
There is an extended literature on non-parametric DMS where the authors focus particularly on
designing information criteria and on estimating long-memory time series. Results concur to show
that these methods need reasonably large samples and strong time dependence, hence a recent
focus of researchers on forecasting fractionally integrated time series.
Ing (2003) provides an
analytical justification for these asymptotic results. The multivariate framework in Liu (1996) has
the disadvantage that it partitions the set of observations in non-overlapping subsets and thus
loses a lot of information. It therefore cannot be used when only one forecast horizon matters, and
it is not sure that estimating all horizons at once yield any better results than forecasting each
separately, thus taking full advantage of the DMS framework. The definition of non-parametric
DMS by Bhansali is constrained to model design or choice. He thus omits work on the estimation
approach to DMS where the focus is not, as in the parametric approach, on the 1S parameters,
but on the multi-step parameters that matter for forecasting.
7 Robustness of multi-step forecasts from ARMA models.
Tiao and Xu (1993) develop an extensive analysis of the properties of the DMS forecasts generated
by an exponential smoothing formula—the FGP—which is estimated when the (true) DGP follows
an ARIMA(p, d = 0 or 1, q). They, thus, extend the results by Cox (1961) and show that multi-step
estimation may be preferable. They motivate their study by comparing IMS and DMS forecasting
properties for series A, from Box and Jenkins (1976): they fit an ARIMA(0, 1, 1) model where
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