Chaos Analysis of the Exchange Rate Series and Crisis Detection

Abstract

In this study, we consider the time series of Turkish Lira (TRY), Australia Dollar (AUD), Canada Dollar (CAD), Swiss Frank (CHF), Denmark Kron (DKK), United Kingdom Pound (GBP), Japan Yen (JPY), Norway Kron (NOK), Sweden Kron (SEK) and European Union (EUR) exchange rates i.e currencies between 1997-2018. To analyze the exchange rate time series, we compute the mutual information, delay time $ tau$, embedding dimension $m$, false Nearest Neighbour (FNN) and Lyapunov exponent $ lambda$ with help of TISEAN package program cite{TISEAN}. We have shown that these exchange rate series have positive Lyapunov exponents which indicate the presence of chaotic behavior for the long period. Additionally, we search for a meaningful correlation between embedding dimension $m$ and the economical crisis. Therefore, as an example, we analyze embedding dimension $m$ of the TRY exchange rate between 1997-2018. We compare the large embedding dimension $m$ values and the crisis indicators in the economy. We conclude that there may be a significant link between large $m$ values and the existence of an economic crisis.