A New Approach with Applications
Carlo simulations. Thereby, the eﬀects of varying sample sizes, diverse coeﬃcient functions, and diﬀerent approaches to predict the (future) co- eﬃcients are examined. If sample sizes are large and forecasting horizons do not range too far into the future, our approach turns out to be supe- rior to classical methods. This is due to the good approximation of the coeﬃcient functions. Application Finally, in Chapter 5 a practical evaluation of the proposed procedure is given by applying it to the Dow Jones Utility index and to futures prices. 6.2 Possible directions for future research Some problems remain for future research. Modelling This work focuses on TVAR processes. A natural next step would be to investigate the more general class of TVARMA processes. Besides only models with stationary innovation processes are examined. A more real- istic ansatz is to assume that the innovation processes are non-stationary. One interesting possibility would be to use GARCH processes (see Boller- slev 1982). A recursive algorithm for estimating time-varying ARCH pro- cesses (see Engle 1982) has already been given by Dahlhaus and Subba Rao (2007). Model selection The choice of a convenient smoothing method and the bandwidth selec- tion should be a topic of further research as it quite has a great impact on the model size selection. Also a formal proof showing the asymptot- ical distribution of the local partial autocorrelation estimator should be derived. Estimation The selection of the factor ζ has to be investigated in more details. 6.2...
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