Essays on spurious long memory time series

Abstract

This thesis contains three essays on spurious long memory with an introduction to the literature in the first Chapter. Chapter 2 presents a multivariate score-type test against spurious long memory. We prove the consistency of the test against the alternatives of random level shifts and smooth trends. The test statistic is based on the weighted sum of the partial derivatives of the multivariate local Whittle likelihood function. To apply the test to fractionally cointegrated series, the test statistic is calculated for the linearly transformed system after estimating the cointegrating matrix. We derive the limiting distribution and show consistency of this procedure. The test is applied to log-absolute returns and log-realized volatilities of the S&P 500, DAX, FTSE, and NIKKEI. Chapter 3 analyzes inflation rates with newly available econometric methods which allow for a consistent estimation of the persistence parameter under low frequency contaminations and con- sistent break point estimation under long memory without a priori assumptions on the presence of breaks. The persistence of inflation rates is of major importance to central banks due to the fact that it determines the costs of monetary policy according to the Phillips curve. In contrast to previous studies, smooth trends are allowed in addition to breaks as a source of spurious long memory. We support the finding of reduced memory parameters in monthly inflation rates of the G7 countries as well as spurious long memory, except for the US. Nevertheless, only a few breaks can be located. Instead, all countries exhibit significant trends at the 5% level with the exception of the US. Finally, Chapter 4 provides an overview and compares the performance of nine semiparametric estimation methods. Among them are two standard methods, four modified approaches to account for low frequency contaminations and three procedures developed for perturbed fractional processes. Several modified estimation methods of the memory parameter have been introduced in the past years. They aim to decrease the upward bias of the memory parameter in cases of low frequency contaminations or an additive noise component, especially in situations with a short-memory process being contaminated. We conduct an extensive Monte Carlo study for a variety of parameter constellations and several DGPs. Furthermore, an empirical application of the log-absolute return series of the S&P 500 shows that the estimation results combined with a long-memory test indicate a spurious long-memory process.