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

The effects of electron and gamma radiation on epoxy-based materials

Specimens of graphite/epoxy composites and epoxy resins were exposed to electron and gamma radiation, followed by mechanical property and fundamental measurements. Measurement techniques included: scanning electron microscopy, X-ray diffraction analysis, and electron spin resonance spectroscopic analysis. Results indicate little or no change in flexural properties of miniature specimens of a graphite/epoxy composite and no change in failure mode at the fiber-resin interface and in the crystallinity of the fiber and the resin. Some doubt in the observation of stable flexural properties is cast by electron paramagnetic resonance spectra of a relatively large number of radiation-generated radicals. These generally lead to a change in cross-linking and in chain-scissioning which should alter mechanical properties

On the validity of resampling methods under long memory

For long-memory time series, inference based on resampling is of crucial importance, since the asymptotic distribution can often be non-Gaussian and is difficult to determine statistically. However due to the strong dependence, establishing the asymptotic validity of resampling methods is nontrivial. In this paper, we derive an efficient bound for the canonical correlation between two finite blocks of a long-memory time series. We show how this bound can be applied to establish the asymptotic consistency of subsampling procedures for general statistics under long memory. It allows the subsample size $b$ to be $o(n)$, where $n$ is the sample size, irrespective of the strength of the memory. We are then able to improve many results found in the literature. We also consider applications of subsampling procedures under long memory to the sample covariance, M-estimation and empirical processes.Comment: 36 pages. To appear in The Annals of Statistic

Aggregation and long memory: recent developments

It is well-known that the aggregated time series might have very different properties from those of the individual series, in particular, long memory. At the present time, aggregation has become one of the main tools for modelling of long memory processes. We review recent work on contemporaneous aggregation of random-coefficient AR(1) and related models, with particular focus on various long memory properties of the aggregated process

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

Long Run Covariance Matrices for Fractionally Integrated Processes

An asymptotic expansion is given for the autocovariance matrix of a vector of stationary long-memory processes with memory parameters d satisfying 0Asymptotic expansion, Autocovariance function, Fourier integral, Long memory, Long run variance, Spectral density