Dimensions and Lyapunov exponents from exchange rate series

✍ Scribed by Mikael Bask

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 1018 KB
• Volume: 7
• Category: Article
• ISSN: 0960-0779
• DOI: 10.1016/s0960-0779(96)00080-x

✦ Synopsis

Detecting the presence of deterministic chaos in economic time series is an important problem that may be solved by measuring the largest Lyapunov exponent. In this paper we present estimates of the largest Lyapunov exponent in daily data for the Swedish Krona vs Deutsche Mark, ECU, U.S. Dollar and Yen exchange rates. In order to estimate the dimension of the systems producing these exchange rate series, we also present estimates of the correlation dimension. We found indications of deterministic chaos in all exchange rate series. However, the estimates for the largest Lyapunov exponents are not reliable, except in the Swedish Krona-ECU case, because of the limited number of data points. In the Swedish Krona-ECU case, we found indications of a low-order chaotic dynamical system. Copyright @ 1996 Elsevier Science Ltd. 'Taylor [l] reviews the literature on exchange rate theory over the last two decades, with particular reference to recent developments. vwo papers that deal with long-run predictions in chaotic time series are [4, 51. These papers are based on a seminal paper by Farmer and Sidorowich [6]. 'See. for example. the discussion of dimension in Farmer et 01. [ 171, 'In Aleksi'c [19] the reconstruction delay is equal to one.