In recent years, methods to estimate the memory parameter using wavelet analysis have gained popularity in many areas of science. Despite its widespread use, a rigorous semi-parametric asymptotic theory, comparable with the one developed for Fourier methods, is still lacking. In this article, we...

This article investigates a general class of stochastic cycles, presenting the main properties in the time and frequency domains. Harvey and Trimbur [Review of Economics and statistics (2003) Vol. 85, pp. 244-55] showed how generalized cyclical processes may be used in unobserved components...

This paper is concerned with the problem of joint determination of the state dimension and autoregressive order of models with Markov-switching parameters. A model selection procedure is proposed which is based on optimization of complexity-penalized likelihood criteria. The efficacy of the...

In this paper, an approximate innovation method is introduced for the estimation of diffusion processes, given a set of discrete and noisy observations of some of their components. The method is based on a recent extension of local linearization filters to the general case of continuous-discrete...

This paper considers a minimum alpha-divergence estimation for a class of ARCH(p) models. For these models with unknown volatility parameters, the exact form of the innovation density is supposed to be unknown in detail but is thought to be close to members of some parametric family. To...

This paper proposes a method for testing seasonal unit roots that combines monthly and quarterly Hylleberg, Engle, Granger and Yoo (HEGY) tests. The new approach is more powerful than the method that does not use quarterly information, i.e. the monthly HEGY test. An empirical illustration of the...

It is now well known that how the initial observation is generated can have a significant effect on the power of a unit-root test. In this article, we show that by taking a simple data-dependent weighted average of the initial condition-robust test of Elliott and Müller [Journal of Econometrics...

For linear processes, semiparametric estimation of the memory parameter, based on the log-periodogram and local Whittle estimators, has been exhaustively examined and their properties well established. However, except for some specific cases, little is known about the estimation of the memory...

One method of describing the properties of a fitted autoregressive model of order p is to show the p roots that are implied by the lag operator. Considering autoregressive models fitted to 215 US macro series, with lags chosen by either the Bayesian or Schwarz information criteria or Akaike...