Financial markets occasionally exhibit extreme price fluctuations that are difficult to explain, notably October 1987. A mathematical system in which a small initial change (the butterfly wing beat) can produce a sudden major disturbance, is provided by a non-linear deterministic model, or chaos theory. This latter title has a seductive ring, especially as a proposed explanation of financial developments.
It is, therefore, not surprising that a number of economists have examined whether economic time series show evidence of 'chaotic' behaviour, and some have even reported to find such evidence. The tests for the presence, or otherwise, of 'chaos', however, involve modern mathematical techniques, and require a very large number of data points, with 5000, perhaps, representing a lower bound.
The authors, Tata and Vassilicos, take two series, continuous tick-by-tick Dollar/Dm foreign exchange spot rate (for one week), and daily returns series from the New York Stock Exchange (for over a century), both of which have over 20,000 data points. They apply a battery of three alternative mathematical tests for chaos, but fail to find any signs of chaotic behaviour. They suggest that earlier announced findings of chaos in economic time series may have been due to using time series with too few data points.
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