Structural breaks and switching processes are known to induce apparent long memory in a time series. Here we show that any significant time variation in the mean renders the sample correlogram (and related spectral estimates) inconsistent. In particular, smooth time variation in the mean—i.e., even a weak trend, either stochastic or deterministic—induces apparent long memory. This apparent long memory can be eliminated by either high-pass filtering or by detrending. Here we demonstrate the effectiveness in this regard of nonlinear detrending via penalized-spline nonparametric regression. A time-varying mean can be of economic interest in its own right. This suggests that isolating out and separately examining both a local mean (i.e., a nonlinear trend or the realization of a stochastic trend) and deviations from it is preferable as a modeling strategy to simply estimating a fractionally integrated model. We illustrate the superiority of this strategy using stock return volatility data.

Previous research has found that the dynamic response of hours worked to a technology shock crucially depends on whether the hours variable is assumed to be an I(0) or an I(1) variable ex ante. In this paper we employ a multivariate fractionally integrated model that allows us to simultaneously estimate the order of integration of hours worked and its dynamic response to a technology shock. Our evidence lends support to the hypothesis that hours fall in response to a positive technology shock.

According to AK growth models, permanent changes in investment rates have permanent effects on a country's rate of economic growth. Jones (Quarterly Journal of Economics, 1995, 110, 495-525) finds strong evidence against this prediction studying the time series properties of GDP growth rates and investment output ratios in fifteen OECD countries for the period 1950-1988. In this paper, we test the same hypothesis in four OECD countries using a longer span of data (1870-2002 for Canada, the UK and the US, and 1885-2002 for Japan). Moreover, instead of using classic approaches, which are based on stationary I(0) or unit roots I(1) processes, we use methodologies based on fractional integration. After examining the order of integration of GDP growth rates and non-residential investment ratios for these countries, we do not find much evidence against the “growth effects” prediction of AK models. In fact, we only find clear evidence against this theory for the UK case.

This article examines the real convergence hypothesis in eleven emerging countries by means of fractionally integrated techniques. For this purpose, we examine the order of integration of the real GDP per capita series in Argentina, Brazil, Chile, Colombia, Mexico, Peru, Venezuela, India, Indonesia, Taiwan and South Korea as well as their differences with respect to the US and Japan. We find evidence of smaller degrees of integration in the differenced series only for some of the Latin American countries with respect to the US, and for all the Asian countries with respect to both the US and Japan. However, we only find evidence of real convergence for the cases of Argentina and Chile with respect to the US, and Taiwan with respect to Japan, suggesting thus the possibility of different convergence clubs among both Latin American and Asian countries.

Using the kernel representation of a continuous-time Lévy-driven ARMA (autoregressive moving average) process, we extend the class of nonnegative Lévy-driven Ornstein–Uhlenbeck processes employed by Barndorff-Nielsen and Shephard (2001) to allow for nonmonotone autocovariance functions. We also consider a class of fractionally integrated Lévy-driven continuous-time ARMA processes obtained by a simple modification of the kernel of the continuous-time ARMA process. Asymptotic properties of the kernel and of the autocovariance function are derived.

${{H}^{p}}$ estimate for the multilinear operators which are finite sums of pointwise products of singular integrals and fractional integrals is given. An application to Sobolev space and some examples are also given.