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5 - Monte Carlo techniques

Published online by Cambridge University Press:  02 November 2009

Michael Clements
Affiliation:
University of Warwick
David Hendry
Affiliation:
University of Oxford
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Summary

This chapter provides an introduction to the use of simulation techniques, such as Monte Carlo, in forecasting theory. We begin by presenting a basic theorem that underlies Monte Carlo experimentation. That statistical theorem establishes a link between the Monte Carlo simulation results and the population values of the parameters. An application of the theorem follows in chapter 6, where we consider the relationship between the Monte Carlo estimates of the forecast second-moment measures and their population values (given by asymptotic formulae in section 6.4). The theorem is first illustrated in the context of a simple example, then demonstrated for the example in chapter 6. We next consider ways in which Monte Carlo studies can be made more informative. First, control variates are described, as well as how these can be incorporated into Monte Carlo computations as a method of variance reduction. Secondly, we explain the role of antithetic variates which are also a variance-reduction method intended to make a Monte Carlo more efficient than distribution sampling. Antithetic variates exploit the fact that the random numbers are known to the investigator, and can be re-used so that the uncertainty in the experiment is reduced: the random numbers are selected in sets to offset each other's variability. However, the technique of antithetic variates can also be used as an analytical tool to establish various properties concerning the bias of the forecasts and the impact of deterministic components (such as a constant) in the DGP. […]

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Publisher: Cambridge University Press
Print publication year: 1998

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