We study the autocorrelation structure and the spectral density function of aggregates from a discrete-time process. The underlying discrete-time process is assumed to be a stationary AutoRegressive Fractionally Integrated Moving-Average (ARFIMA) process, after suitable number of differencing if necessary. We derive closed-form expressions for the limiting autocorrelation function and the norma...

We address the question of unemployment hysteresis within the context of ARFIMA models. Our results suggest that in the post-1973 era, hysteresis is considerably less of a stylized fact for the unemployment rates of key OECD economies. JEL Categories C22, E30 Please address all correspondence to: Philip Rothman, Department of Economics, Brewster * Building, East Carolina University, Greenville,...

We introduce a method for reconstructing macroscopic models of one-dimensional stochastic processes with long-range correlations from sparsely sampled time series by combining fractional calculus and discrete-time Langevin equations. The is illustrated the ARFIMA(1,d,0) process nonlinear autoregressive toy model multiplicative noise. reconstruct daily mean temperature data recorded at Potsdam, ...

In a recent paper in The Journal of Monetary Economics, Michelacci and Zaffaroni (2000) estimate long memory parameters for GDP per capita of 16 OECD countries. In this note we argue that these estimations are questionable for the purposes of clarifying the time series properties of these data (presence of unit roots, mean reversion, long memory) because the authors a) filter out a deterministi...

Quantifying how patterns of behavior relate across multiple levels of measurement typically requires long time series for reliable parameter estimation. We describe a novel analysis that estimates patterns of variability across multiple scales of analysis suitable for time series of short duration. The multiscale coefficient of variation (MSCV) measures the distance between local coefficient of...

Abstract We analyze by simulation the properties of two time domain and two frequency domain estimators for low order autoregressive fractionally integrated moving average Gaussian models, ARFIMA (p; d; q). The estimators considered are the exact maximum likelihood for demeaned data, EML, the associated modi ed pro le likelihood, MPL, and the Whittle estimator with, WLT, and without tapered dat...