Persistence and cycles in the US Federal Funds rate

This paper uses long-range dependence techniques to analyse two important features of the US Federal Funds effective rate, namely its persistence and cyclical behaviour. It examines annual, monthly, bi-weekly and weekly data, from 1954 until 2010. Two models are considered. One is based on an I(d) specification with AR(2) disturbances and the other on two fractional differencing structures, one at the zero and the other at a cyclical frequency. Thus, the two approaches differ in the way the cyclical component of the process is modelled. In both cases we obtain evidence of long memory and fractional integration. The in-sample goodness-of-fit analysis supports the second specification in the majority of cases. An out-of-sample forecasting experiment also suggests that the long-memory model with two fractional differencing parameters is the most adequate one, especially over long horizons.This study is partly funded by the Ministerio de Ciencia y Tecnología ECO2011-2014 ECON Y FINANZAS, Spain) and from a Jeronimo de Ayanz project of the Government of Navarra

Modelling Long-Run Trends and Cycles in Financial Time Series Data

This paper proposes a very general time series framework to capture the long-run behaviour of financial series. The suggested model includes linear and non-linear time trends, and stationary and nonstationary processes based on integer and/or fractional degrees of differentiation. Moreover, the spectrum is allowed to contain more than a single pole or singularity, occurring at zero and non-zero (cyclical) frequencies. This model is used to analyse four annual time series with a long span, namely dividends, earnings, interest rates and long-term government bond yields. The results indicate that the four series exhibit fractional integration with one or two poles in the spectrum. A forecasting comparison shows that a model with a non-linear trend along with fractional integration outperforms alternative models over long horizons.fractional integration, financial time series data, trends, cycles

Rocking Subdiffusive Ratchets: Origin, Optimization and Efficiency

We study origin, parameter optimization, and thermodynamic efficiency of isothermal rocking ratchets based on fractional subdiffusion within a generalized non-Markovian Langevin equation approach. A corresponding multi-dimensional Markovian embedding dynamics is realized using a set of auxiliary Brownian particles elastically coupled to the central Brownian particle (see video on the journal web site). We show that anomalous subdiffusive transport emerges due to an interplay of nonlinear response and viscoelastic effects for fractional Brownian motion in periodic potentials with broken space-inversion symmetry and driven by a time-periodic field. The anomalous transport becomes optimal for a subthreshold driving when the driving period matches a characteristic time scale of interwell transitions. It can also be optimized by varying temperature, amplitude of periodic potential and driving strength. The useful work done against a load shows a parabolic dependence on the load strength. It grows sublinearly with time and the corresponding thermodynamic efficiency decays algebraically in time because the energy supplied by the driving field scales with time linearly. However, it compares well with the efficiency of normal diffusion rocking ratchets on an appreciably long time scale

Laws and Limits of Econometrics

We start by discussing some general weaknesses and limitations of the econometric approach. A template from sociology is used to formulate six laws that characterize mainstream activities of econometrics and the scientific limits of those activities, we discuss some proximity theorems that quantify by means of explicit bounds how close we can get to the generating mechanism of the data and the optimal forecasts of next period observations using a finite number of observations. The magnitude of the bound depends on the characteristics of the model and the trajectory of the observed data. The results show that trends are more elusive to model than stationary processes in the sense that the proximity bounds are larger. By contrast, the bounds are of smaller order for models that are unidentified or nearly unidentified, so that lack or near lack of identification may not be as fatal to the use of a model in practice as some recent results on inference suggest, we look at one possible future of econometrics that involves the use of advanced econometric methods interactively by way of a web browser. With these methods users may access a suite of econometric methods and data sets online. They may also upload data to remote servers and by simple web browser selections initiate the implementation of advanced econometric software algorithms, returning the results online and by file and graphics downloads.Activities and limitations of econometrics, automated modeling, nearly unidentified models, nonstationarity, online econometrics, policy analysis, prediction, quantitative bounds, trends, unit roots, weak instruments

Persistence exponents for fluctuating interfaces

Numerical and analytic results for the exponent \theta describing the decay of the first return probability of an interface to its initial height are obtained for a large class of linear Langevin equations. The models are parametrized by the dynamic roughness exponent \beta, with 0 < \beta < 1; for \beta = 1/2 the time evolution is Markovian. Using simulations of solid-on-solid models, of the discretized continuum equations as well as of the associated zero-dimensional stationary Gaussian process, we address two problems: The return of an initially flat interface, and the return to an initial state with fully developed steady state roughness. The two problems are shown to be governed by different exponents. For the steady state case we point out the equivalence to fractional Brownian motion, which has a return exponent \theta_S = 1 - \beta. The exponent \theta_0 for the flat initial condition appears to be nontrivial. We prove that \theta_0 \to \infty for \beta \to 0, \theta_0 \geq \theta_S for \beta 1/2, and calculate \theta_{0,S} perturbatively to first order in an expansion around the Markovian case \beta = 1/2. Using the exact result \theta_S = 1 - \beta, accurate upper and lower bounds on \theta_0 can be derived which show, in particular, that \theta_0 \geq (1 - \beta)^2/\beta for small \beta.Comment: 12 pages, REVTEX, 6 Postscript figures, needs multicol.sty and epsf.st

Multivariate Fractionally Integrated APARCH Modeling of Stock Market Volatility: A multi-country study

Tse (1998) proposes a model which combines the fractionally integrated GARCH formulation of Baillie, Bollerslev and Mikkelsen (1996) with the asymmetric power ARCH speci¯cation of Ding, Granger and Engle (1993). This paper analyzes the applicability of a multivariate constant conditional correlation version of the model to national stock market returns for eight countries. We ¯nd this multivariate speci¯cation to be generally applicable once power, leverage and long-memory e®ects are taken into consideration. In addition, we ¯nd that both the optimal fractional di®erencing parameter and power transformation are remarkably similar across countries. Out-of-sample evidence for the superior forecasting ability of the multivariate FIAPARCH framework is provided in terms of forecast error statistics and tests for equal forecast accuracy of the various models.Asymmetric Power ARCH, Fractional integration, Stock returns, Volatility forecast evaluation