270 Claudio Pizzi
Figure 1 shows the time series of the price of the stocks considered, i.e., Ford
Motor (F) and Motorola Inc. (MOT). The speed of adjustment is depicted in Figure
2 (points); its behaviour is very rough and to smooth it we estimate the function of
speed using the local polynomial regression (LOESS procedure) [4] (line).
It is worth mentioning that the velocity increases when strong market shocks
perturb one of the time series disturbing the system from its steady state. As the
adjustment mechanism drives the system towards the new equilibrium, the speed of
adjustment tends to diminish.
4Conclusion
The analysis of the time series of the 15 shares has enabled us to highlight that the
relationships that bind two stocks in the long run do not always follow a linear error
correction structure. To overcome this limit, we have suggested a local error correction
model that enables the investigation of the presence of nonlinear cointegration. By
applying this local model, it has been shown that, out of all those analysed, several
pairs of stocks are bound by a nonlinear cointegration relationship. Furthermore, the
LECM, reformulated in terms of an unrestricted local error correction model, has
also enabled the determination of the correction speed and the long-run relationship
between variables as a function of time, enabling the consideration of a dynamic
cointegration relationship.
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