733 research outputs found
Modeling electricity spot prices using mean-reverting multifractal processes
We discuss stochastic modeling of volatility persistence and
anti-correlations in electricity spot prices, and for this purpose we present
two mean-reverting versions of the multifractal random walk (MRW). In the first
model the anti-correlations are modeled in the same way as in an
Ornstein-Uhlenbeck process, i.e. via a drift (damping) term, and in the second
model the anti-correlations are included by letting the innovations in the MRW
model be fractional Gaussian noise with H < 1/2. For both models we present
approximate maximum likelihood methods, and we apply these methods to estimate
the parameters for the spot prices in the Nordic electricity market. The
maximum likelihood estimates show that electricity spot prices are
characterized by scaling exponents that are significantly different from the
corresponding exponents in stock markets, confirming the exceptional nature of
the electricity market. In order to compare the damped MRW model with the
fractional MRW model we use ensemble simulations and wavelet-based variograms,
and we observe that certain features of the spot prices are better described by
the damped MRW model. The characteristic correlation time is estimated to
approximately half a year.Comment: 13 pages, 4 figures, 2 table
Measuring the Direction and Angular Velocity of a Black Hole Accretion Disk via Lagged Interferometric Covariance
We show that interferometry can be applied to study irregular, rapidly
rotating structures, as are expected in the turbulent accretion flow near a
black hole. Specifically, we analyze the lagged covariance between
interferometric baselines of similar lengths but slightly different
orientations. For a flow viewed close to face-on, we demonstrate that the peak
in the lagged covariance indicates the direction and angular velocity of the
emission pattern from the flow. Even for moderately inclined flows, the
covariance robustly estimates the flow direction, although the estimated
angular velocity can be significantly biased. Importantly, measuring the
direction of the flow as clockwise or counterclockwise on the sky breaks a
degeneracy in accretion disk inclinations when analyzing time-averaged images
alone. We explore the potential efficacy of our technique using
three-dimensional, general relativistic magnetohydrodynamic (GRMHD)
simulations, and we highlight several baseline pairs for the Event Horizon
Telescope (EHT) that are well-suited to this application. These results
indicate that the EHT may be capable of estimating the direction and angular
velocity of the emitting material near Sagittarius A*, and they suggest that a
rotating flow may even be utilized to improve imaging capabilities.Comment: 8 Pages, 4 Figures, accepted for publication in Ap
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
Long-term X-ray variability of Swift J1644+57
We studied the X-ray timing and spectral variability of the X-ray source Sw
J1644+57, a candidate for a tidal disruption event. We have separated the
long-term trend (an initial decline followed by a plateau) from the short-term
dips in the Swift light-curve. Power spectra and Lomb-Scargle periodograms hint
at possible periodic modulation. By using structure function analysis, we have
shown that the dips were not random but occurred preferentially at time
intervals ~ [2.3, 4.5, 9] x 10^5 s and their higher-order multiples. After the
plateau epoch, dipping resumed at ~ [0.7, 1.4] x 10^6 s and their multiples. We
have also found that the X-ray spectrum became much softer during each of the
early dip, while the spectrum outside the dips became mildly harder in its
long-term evolution. We propose that the jet in the system undergoes precession
and nutation, which causes the collimated core of the jet briefly to go out of
our line of sight. The combined effects of precession and nutation provide a
natural explanation for the peculiar patterns of the dips. We interpret the
slow hardening of the baseline flux as a transition from an extended, optically
thin emission region to a compact, more opaque emission core at the base of the
jet.Comment: 16 pages, 12 figures. Accepted by MNRAS on 2012 Feb 11; minor
improvements in the introduction and discussion from the previous arXiv
versio
Arnold maps with noise: Differentiability and non-monotonicity of the rotation number
Arnold's standard circle maps are widely used to study the quasi-periodic
route to chaos and other phenomena associated with nonlinear dynamics in the
presence of two rationally unrelated periodicities. In particular, the El
Nino-Southern Oscillation (ENSO) phenomenon is a crucial component of climate
variability on interannual time scales and it is dominated by the seasonal
cycle, on the one hand, and an intrinsic oscillatory instability with a period
of a few years, on the other. The role of meteorological phenomena on much
shorter time scales, such as westerly wind bursts, has also been recognized and
modeled as additive noise. We consider herein Arnold maps with additive,
uniformly distributed noise. When the map's nonlinear term, scaled by the
parameter , is sufficiently small, i.e. , the map is
known to be a diffeomorphism and the rotation number is a
differentiable function of the driving frequency . We concentrate on
the rotation number's behavior as the nonlinearity becomes large, and show
rigorously that is a differentiable function of ,
even for , at every point at which the noise-perturbed map is
mixing. We also provide a formula for the derivative of the rotation number.
The reasoning relies on linear-response theory and a computer-aided proof. In
the diffeomorphism case of , the rotation number
behaves monotonically with respect to . We show, using again a
computer-aided proof, that this is not the case when and the
map is not a diffeomorphism.Comment: Electronic copy of final peer-reviewed manuscript accepted for
publication in the Journal of Statistical Physic
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