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Forecasting Economic Time Series using Locally Stationary Processes

A New Approach with Applications

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Tina Loll

Stationarity has always played an important part in forecasting theory. However, some economic time series show time-varying autocovariances. The question arises whether forecasts can be improved using models that capture such a time-varying second-order structure. One possibility is given by autoregressive models with time-varying parameters. The author focuses on the development of a forecasting procedure for these processes and compares this approach to classical forecasting methods by means of Monte Carlo simulations. An evaluation of the proposed procedure is given by its application to futures prices and the Dow Jones index. The approach turns out to be superior to the classical methods if the sample sizes are large and the forecasting horizons do not range too far into the future.

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6 Conclusion

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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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