Log periodogram (LP) regression is shown to be consistent and to have a mixed normal limit distribution when the memory parameter d 1⁄4 1. Gaussian errors are not required. The proof relies on a new result showing that asymptotically infinite collections of discrete Fourier transforms (dft’s) of a short memory process at the fundamental frequencies in the vicinity of the origin can be treated a...

In this paper we provide empirical findings on the significance of positive feedback trading for the return behavior in the German stock market. Relying on the ShillerSentana-Wadhwani model, we use the link between index return auto-correlation and volatility to obtain a better understanding into the return characteristics generated by traders adhering to positive feedback trading strategies. O...

We show how temporal aggregation affects the size and power of the DOLS residualbased KPSS test of the null of cointegration. Size is effectively controlled by setting the minimum number of leads equal to one – as opposed to zero – when selecting the lag/lead order of the DOLS regression, but at a cost to power in finite samples. If highfrequency data for one or more series are available, we sh...

This paper develops an asymptotic theory for a non-linear parametric co-integrating regression model. We establish a general framework for weak consistency that is easy to apply for various non-stationary time series, including partial sum of linear process and Harris recurrent Markov chain. We provide a limit distribution for the nonlinear least square estimator which significantly extends the...

Existing estimates of the Federal Reserve’s implicit inflation target typically rely on the assumption that it is constant for the duration of the period of analysis. This paper relaxes this assumption and estimates the implicit inflation target using a time-varying parameter model and the Kalman filter. In applying this method to the Volcker–Greenspan period, it finds significant time variatio...

We model elasticity of volatility as a stochastic process with an eye to merge popular constant elasticity of variance (CEV) and stochastic volatility (SV) models in order to understand when it is appropriate to use absolute or relative changes or some intermediate transformation as well as to compare with more traditional autoregressive exponential stochastic volatility formulations. We descri...

This work presents a new technique for temporally benchmarking a time series according to the growth rates preservation principle (GRP) by Causey and Trager (1981). A procedure is developed which (i) transforms the original constrained problem into an unconstrained one, and (ii) applies a Newton’s method exploiting the analytic Hessian of the GRP objective function. We show that the proposed te...

We propose a new methodology for designing flexible proposal densities for the joint posterior density of parameters and states in a nonlinear, non-Gaussian state space model. We show that a highly efficient Bayesian procedure emerges when these proposal densities are used in an independent Metropolis-Hastings algorithm or in importance sampling. Our method provides a computationally more effic...

This paper considers the estimation of average autoregressive roots-near-unity in panels where the time-series have heterogenous local-to-unity parameters. The pooled estimator is shown to have a potentially severe bias and a robust median based procedure is proposed instead. This median estimator has a small asymptotic bias that can be eliminated almost completely by a bias correction procedur...

Much time series data are recorded on economic and financial variables. Statistical modelling of such data is now very well developed, and has applications in forecasting. We review a variety of statistical models from the viewpoint of ’memory’, or strength of dependence across time, which is a helpful discriminator between different phenomena of interest. Both linear and nonlinear models are d...