This paper proves consistency and asymptotic normality for the conditional-sum-of-squares estimator, which is equivalent to the conditional maximum likelihood estimator, in multivariate fractional time series models. The model is parametric and quite general, and, in particular, encompasses the...

Semiparametric estimation of the memory parameter is studied in models of fractional integration in the nonstationary case, and some new representation theory for the discrete Fourier transform of a fractional process is used to assist in the analysis. A limit theory is developed for an...

Over the last years there has been considerable interest in the application of long memory time series models in economics using ARFIMA models. Nowadays, the most popular estimator of the difference parameter in economic applications is that proposed by Geweke and Porter-Hudak (GPH) although has...

In many fields of economic analysis the order of integration of some economic magnitudes is of particular interest. Among other aspects, the order of integration determines the degree of persistence of that magnitude. The rate of inflation is a very interesting example because many contradictory...

In short-term evolution analysis, the economic time series are contamined by different types of noises which need to be erased in order to extract a trend signal. In the last years there has been increasingly developed some methods to estimate unobserved components based on the assumption that...

In this article we show that multiple cycles can occur in financial and economic time series. We model these cycles by means of Gegenbauer processes, using a procedure that permits us to test multiple roots at fixed frequencies over time and thus, it permits us to approximate the length of each...

In this paper we specify a multi-factor long-memory process that enables us to estimate the fractional differencing parameters at each frequency separately, and adopt this framework to model quarterly prices in three European countries (France, Italy and the UK). The empirical results suggest...

This paper considers the application of long memory processes to describe inflation with seasonal behaviour. We use three different long memory models taking into account the seasonal pattern in the data. Namely, the ARFIMA model with deterministic seasonality, the ARFISMA model, and the...

Time series data affect many aspects of our lives. This paper highlights ten things we should all know about time series, namely: a good working knowledge of econometrics and statistics, an awareness of measurement errors, testing for zero frequency, seasonal and periodic unit roots, analysing...