بازده نرخ ارز غیر خطی و نوسانات

Recent findings of nonlinearities in financial assets can be the product of contamination produced by shifts in the distribution of the data. Using the BDS and Kaplan tests it is shown that, some of the nonlinearities found in foreign exchange rate returns, can be the product of shifts in variance while other do not. Also, the behavior of the volatility is studied, showing that the ARFIMA modeling is able to capture long memory, but, depending on the proxy used for the volatility, is not always able to capture all the nonlinearities of the data

The purpose of this paper is to investigate whether the foreign exchange rates behave nonlinear. At the same time some methodology issues in detecting nonlinear behavior will be discussed. Simulating studies [1], [2], [3], [4], [5] and [6] have shown that the BDS and the Kaplan tests have power against a large class of alternatives, so they will be used in this paper. Also, these tests have been widely applied to investigate the behavior of financial time series as in [1] and [7], most of them yielding to the acceptance of nonlinearity in financial time series. There are two main explanations for the nonlinearity of financial returns. Concretely, one explanation for the nonlinear dependence in exchange rates is that they come from a deterministic process that looks random (e.g. chaotic process). A second explanation is that exchange rates changes are nonlinear stochastic functions of their own past. In this sense, Hinich and Patterson [8] show that stock prices are realizations of nonlinear stationary stochastic processes, also Hsieh [7] finds that rejections of linearity in stock returns are due to neglected conditional heteroskedasticity and cannot be attributed to structural changes. Following the second explanation, some of the models used for asset prices and volatility assume that the unconditional distribution of assets rates is constant over time, which means that returns are stationary. This is the case of the autoregressive conditional heteroskedasticity models or ARCH processes. In this investigation we will use a modification of the test proposed by Lima [9] that attempts to discriminate the findings of nonlinearity caused for intrinsic mechanisms, from those due to nonstationarities in the data. We will show that some of the findings of nonlinearity are due to possible shifts in distribution, that is nonstationarities of exchange rates while others are not. Also, we use this methodology to study the behavior of the volatility using the ARFIMA models that are able to capture the long memory of this variable. 2. Testing nonlinearity Among the tests of nonlinearities, the BDS and the Kaplan tests have been proven as very powerful and it will be used to test nonlinearities in exchange rate series in our paper.

Recent research has put forward the idea that both financial assets returns, and volatilities are nonlinear processes. This paper investigates the impact of nonstationarities on the testing of nonlinearities. For returns time series nonlinearities are found for the exchange rates DM/$ and BP/$, but for the JY/$ a possible shift in conditional variance yields to a rejection of nonlinearity for the hole data set. The behavior of volatility is studied through the behavior of the residuals of the ARFIMA estimated model. Two different behavior are found depending on the proxy of volatility used. For the residuals of the squared returns, similar behavior as the returns time series is found, that means that the ARFIMA model is not able to capture the nonlinearities of the time series under study. However for the log-squared returns the residuals of the ARFIMA model seems to be i.i.d. which means that this kind of model is able to capture, both long-memory and nonlinearities of the series under study.