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Brownian motion with drift threshold model
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Resumo(s)
In this thesis we implement estimating procedures in order to estimate threshold
parameters for the continuous time threshold models driven by stochastic di®erential
equations. The ¯rst procedure is based on the EM (expectation-maximization) algorithm
applied to the threshold model built from the Brownian motion with drift process. The
second procedure mimics one of the fundamental ideas in the estimation of the thresholds
in time series context, that is, conditional least squares estimation. We implement this
procedure not only for the threshold model built from the Brownian motion with drift
process but also for more generic models as the ones built from the geometric Brownian
motion or the Ornstein-Uhlenbeck process. Both procedures are implemented for simu-
lated data and the least squares estimation procedure is also implemented for real data
of daily prices from a set of international funds. The ¯rst fund is the PF-European Sus-
tainable Equities-R fund from the Pictet Funds company and the second is the Parvest
Europe Dynamic Growth fund from the BNP Paribas company. The data for both funds
are daily prices from the year 2004. The last fund to be considered is the Converging
Europe Bond fund from the Schroder company and the data are daily prices from the
year 2005.