By Philip Hans Franses, Dick van Dijk
This can be the main updated and available consultant to at least one of the quickest turning out to be parts in monetary research by means of of the main finished younger econometricians in Europe. This classroom-tested complicated undergraduate and graduate textbook presents an in-depth therapy of lately built nonlinear types, together with regime-switching and synthetic neural networks, and applies them to describing and forecasting monetary asset returns and volatility. It makes use of a variety of monetary info, drawn from assets together with the markets of Tokyo, London and Frankfurt.
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Extra resources for Non-Linear Time Series Models in Empirical Finance
An example is the bilinear model yt = β2 εt−1 yt−2 + εt . 1 First 50 autocorrelations of (a), (b) daily Frankfurt and (c), (d) Tokyo stock market indexes Figures (a) and (c) show autocorrelations of the log prices; figures (b) and (d) show autocorrelations of returns (solid line with circles), absolute returns (dashed line with squares) and squared returns (dotted line with triangles) not linearly forecastable. Of course, the series is forecastable using a nonlinear model. An alternative strategy is to start off with a linear time series model, based on a rough guess using linear autocorrelation functions, and then, in a next step, to use diagnostic tests which have power against the alternative model of interest.
Given that it can take quite some time before the return series calms down and that scatter observations disappear into the main cloud again, it seems justified to state that a volatile period often starts with a large negative return. 3 contains estimates of the correlation between the squared return at day t and the return at day t − 1 for the various stock indexes. The fact that all these correlations are negative also illustrates that large volatility often follows upon a negative return. For the exchange rate returns this property is much less clear-cut (as it should be, as the return series can be inverted by simply expressing the exchange rate as the number of US dollars per unit of foreign currency).
Diagnostic testing for residual autocorrelation Testing the adequacy of an estimated ARMA model in step (4) of the suggested specification strategy usually involves several elements. 3)). If this turns out not to be the case, there is a need to modify the model by increasing the value of p and/or q. There are three commonly applied methods to test for residual autocorrelation, all of which can also be considered (or modified) for nonlinear time series models. 40) for k = 1, 2, 3, . . Box and Jenkins (1970) show that, given model adequacy, the population equivalents of rk (ˆε) are asymptotically uncorrelated and have 34 Nonlinear time series models in empirical finance −1 variances approximately equal √ to n .
Non-Linear Time Series Models in Empirical Finance by Philip Hans Franses, Dick van Dijk