Is there long memory in financial time series?

There has been a large amount of research on long memory in economic and financial time series. However, there is still no consensus on its presence in these series. We argue in this article that spurious short memory may be found because of the use of bandwidth parameters that diverge too quickly when the process exhibits long memory. We propose a new bandwidth parameter that is robust against the presence of long memory and revisit several economic and financial time series using the proposed bandwidth choice. Our results indicate the existence of spurious short memory in real exchange rates when traditional bandwidth parameters are employed, but short memory is rejected when the proposed bandwidth is used. We also find short memory in financial returns and long memory in their volatility.

Testing Unit Root Based on Partially Adaptive Estimation

This paper proposes unit root tests based on partially adaptive estimation. The proposed tests provide an intermediate class of inference procedures that are more efficient than the traditional OLS-based methods and simpler than unit root tests based on fully adaptive estimation using nonparametric methods. Taking into account the well documented characteristic of heavy-tail behavior in economic and financial data, we consider unit root tests coupled with a class of partially adaptive M-estimators based on the student-t distributions, which includes the normal distribution as a limiting case. Monte Carlo experiments indicate that, in the presence of heavy tail distributions, the proposed test is more powerful than the traditional ADF test. We apply the proposed test to several macroeconomic time series that have heavy-tailed distributions. The unit root hypothesis is rejected in U.S. real GNP, supporting the literature of transitory shocks in output. However, evidence against unit root is not found in real exchange rate and nominal interest rate even when heavy-tail is taken into account.

Testing Covariance Stationarity

In this paper, we show that the widely used stationarity tests such as the Kwiatkowski Phillips, Schmidt, and Shin (KPSS) test have power close to size in the presence of time-varying unconditional variance. We propose a new test as a complement of the existing tests. Monte Carlo experiments show that the proposed test possesses the following characteristics: (i) in the presence of unit root or a structural change in the mean, the proposed test is as powerful as the KPSS and other tests; (ii) in the presence of a changing variance, the traditional tests perform badly whereas the proposed test has high power comparing to the existing tests; (iii) the proposed test has the same size as traditional stationarity tests under the null hypothesis of stationarity. An application to daily observations of return on U.S. Dollar/Euro exchange rate reveals the existence of instability in the unconditional variance when the entire sample is considered, but stability is found in subsamples.Asymptotic theory, KPSS, Stationarity testing, Time-varying variance,