A brief history of long memory: Hurst, Mandelbrot and the road to ARFIMA

Long memory plays an important role in many fields by determining the behaviour and predictability of systems; for instance, climate, hydrology, finance, networks and DNA sequencing. In particular, it is important to test if a process is exhibiting long memory since that impacts the accuracy and confidence with which one may predict future events on the basis of a small amount of historical data. A major force in the development and study of long memory was the late Benoit B. Mandelbrot. Here we discuss the original motivation of the development of long memory and Mandelbrot's influence on this fascinating field. We will also elucidate the sometimes contrasting approaches to long memory in different scientific communitiesComment: 40 page

Accelerating sequential programs using FastFlow and self-offloading

FastFlow is a programming environment specifically targeting cache-coherent shared-memory multi-cores. FastFlow is implemented as a stack of C++ template libraries built on top of lock-free (fence-free) synchronization mechanisms. In this paper we present a further evolution of FastFlow enabling programmers to offload part of their workload on a dynamically created software accelerator running on unused CPUs. The offloaded function can be easily derived from pre-existing sequential code. We emphasize in particular the effective trade-off between human productivity and execution efficiency of the approach.Comment: 17 pages + cove

Long-Range Dependence in Daily Interest Rate

We employ a number of parametric and non-parametric techniques to establish the existence of long-range dependence in daily interbank o er rates for four countries. We test for long memory using classical R=S analysis, variance-time plots and Lo's (1991) modi ed R=S statistic. In addition we estimate the fractional di erencing parameter using Whittle's (1951) maximum likelihood estimator and we shu e the data to destroy long and short memory in turn, and we repeat our non-parametric tests. From our non-parametric tests we And strong evidence of the presence of long memory in all four series independently of the chosen statistic. We nd evidence that supports the assertion of Willinger et al (1999) that Lo's statistic is biased towards non-rejection of the null hypothesis of no long-range dependence. The parametric estimation concurs with these results. Our results suggest that conventional tests for capital market integration and other similar hypotheses involving nominal interest rates should be treated with cautio

Mainstream parallel array programming on cell

We present the E] compiler and runtime library for the ‘F’ subset of the Fortran 95 programming language. ‘F’ provides first-class support for arrays, allowing E] to implicitly evaluate array expressions in parallel using the SPU coprocessors of the Cell Broadband Engine. We present performance results from four benchmarks that all demonstrate absolute speedups over equivalent ‘C’ or Fortran versions running on the PPU host processor. A significant benefit of this straightforward approach is that a serial implementation of any code is always available, providing code longevity, and a familiar development paradigm

RANDOM WALKS AND FRACTAL STRUCTURES IN AGRICULTURAL COMMODITY FUTURES PRICES

This paper investigates whether the assumption of Brownian motion often used to describe commodity price movements is satisfied. Using historical data from 17 commodity futures contracts specific tests of fractional and ordinary Brownian motion are conducted. The analyses are conducted under the null hypothesis of ordinary Brownian motion against the alternative of persistent or ergodic fractional Brownian motion. Tests for fractional Brownian motion are based on a variance ratio test and compared with conventional R-S analyses. However, standard errors based on Monte Carlo simulations are quite high, meaning that the acceptance region for the null hypothesis is large. The results indicate that for the most part, the null hypothesis of ordinary Brownian motion cannot be rejected for 14 of 17 series. The three series that did not satisfy the tests were rejected because they violated the stationarity property of the random walk hypothesis.Demand and Price Analysis, Marketing,

Does New Zealand visitors follow the Joseph Effect? Some empirical evidence

The report departs from conventional time series analysis and investigates the existence of long memory (LRD) in the stream of daily visitors, arriving from various sources to New Zealand from 1997 to 2010, using selected estimators of the Hurst-exponent. The daily arrivals of visitors are treated as a stream of "digital signals" with the inherent noise. After minimizing the noise (i.e. the presence of short-term trends, periodicities, and cycles) we found the existence of significant long memory embedded in our data of daily visitors from all sources and in the aggregate. Strong evidence of embedded “long memory” implies that Joseph Effect – that good times beget good times and bad times beget bad – whose existence in the underlying process may have interesting implications for tourism policy makers. Our findings suggest evidence of such long term memory in tourist arrival data. Further, unless this long memory effect is taken into consideration, any traditional statistical analysis based on Gaussian and Poisson assumptions may be overly biased

Markov Processes, Hurst Exponents, and Nonlinear Diffusion Equations with application to finance

We show by explicit closed form calculations that a Hurst exponent H that is not 1/2 does not necessarily imply long time correlations like those found in fractional Brownian motion. We construct a large set of scaling solutions of Fokker-Planck partial differential equations where H is not 1/2. Thus Markov processes, which by construction have no long time correlations, can have H not equal to 1/2. If a Markov process scales with Hurst exponent H then it simply means that the process has nonstationary increments. For the scaling solutions, we show how to reduce the calculation of the probability density to a single integration once the diffusion coefficient D(x,t) is specified. As an example, we generate a class of student-t-like densities from the class of quadratic diffusion coefficients. Notably, the Tsallis density is one member of that large class. The Tsallis density is usually thought to result from a nonlinear diffusion equation, but instead we explicitly show that it follows from a Markov process generated by a linear Fokker-Planck equation, and therefore from a corresponding Langevin equation. Having a Tsallis density with H not equal to 1/2 therefore does not imply dynamics with correlated signals, e.g., like those of fractional Brownian motion. A short review of the requirements for fractional Brownian motion is given for clarity, and we explain why the usual simple argument that H unequal to 1/2 implies correlations fails for Markov processes with scaling solutions. Finally, we discuss the question of scaling of the full Green function g(x,t;x',t') of the Fokker-Planck pde.Comment: to appear in Physica

The sources and nature of long-term memory in the business cycle

This paper examines the stochastic properties of aggregate macroeconomic time series from the standpoint of fractionally integrated models, focusing on the persistence of economic shocks. We develop a simple macroeconomic model that exhibits long-range dependence, a consequence of aggregation in the presence of real business cycles. We then derive the relation between properties of fractionally integrated macroeconomic time series and those of microeconomic data and discuss how fiscal policy may alter the stochastic behavior of the former. To implement these results empirically, we employ a test for fractionally integrated time series based on the Hurst-Mandelbrot rescaled range. This test, which is robust to short-term dependence, is applied to quarterly and annual real GNP to determine the sources and nature of long-term dependence in the business cycle..Business cycles ; Time-series analysis