3,695 research outputs found
Daily minimum and maximum temperature simulation over complex terrain
Spatiotemporal simulation of minimum and maximum temperature is a fundamental
requirement for climate impact studies and hydrological or agricultural models.
Particularly over regions with variable orography, these simulations are
difficult to produce due to terrain driven nonstationarity. We develop a
bivariate stochastic model for the spatiotemporal field of minimum and maximum
temperature. The proposed framework splits the bivariate field into two
components of "local climate" and "weather." The local climate component is a
linear model with spatially varying process coefficients capturing the annual
cycle and yielding local climate estimates at all locations, not only those
within the observation network. The weather component spatially correlates the
bivariate simulations, whose matrix-valued covariance function we estimate
using a nonparametric kernel smoother that retains nonnegative definiteness and
allows for substantial nonstationarity across the simulation domain. The
statistical model is augmented with a spatially varying nugget effect to allow
for locally varying small scale variability. Our model is applied to a daily
temperature data set covering the complex terrain of Colorado, USA, and
successfully accommodates substantial temporally varying nonstationarity in
both the direct-covariance and cross-covariance functions.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS602 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Compression and Conditional Emulation of Climate Model Output
Numerical climate model simulations run at high spatial and temporal
resolutions generate massive quantities of data. As our computing capabilities
continue to increase, storing all of the data is not sustainable, and thus it
is important to develop methods for representing the full datasets by smaller
compressed versions. We propose a statistical compression and decompression
algorithm based on storing a set of summary statistics as well as a statistical
model describing the conditional distribution of the full dataset given the
summary statistics. The statistical model can be used to generate realizations
representing the full dataset, along with characterizations of the
uncertainties in the generated data. Thus, the methods are capable of both
compression and conditional emulation of the climate models. Considerable
attention is paid to accurately modeling the original dataset--one year of
daily mean temperature data--particularly with regard to the inherent spatial
nonstationarity in global fields, and to determining the statistics to be
stored, so that the variation in the original data can be closely captured,
while allowing for fast decompression and conditional emulation on modest
computers
A Bayesian Nonparametric Markovian Model for Nonstationary Time Series
Stationary time series models built from parametric distributions are, in
general, limited in scope due to the assumptions imposed on the residual
distribution and autoregression relationship. We present a modeling approach
for univariate time series data, which makes no assumptions of stationarity,
and can accommodate complex dynamics and capture nonstandard distributions. The
model for the transition density arises from the conditional distribution
implied by a Bayesian nonparametric mixture of bivariate normals. This implies
a flexible autoregressive form for the conditional transition density, defining
a time-homogeneous, nonstationary, Markovian model for real-valued data indexed
in discrete-time. To obtain a more computationally tractable algorithm for
posterior inference, we utilize a square-root-free Cholesky decomposition of
the mixture kernel covariance matrix. Results from simulated data suggest the
model is able to recover challenging transition and predictive densities. We
also illustrate the model on time intervals between eruptions of the Old
Faithful geyser. Extensions to accommodate higher order structure and to
develop a state-space model are also discussed
Inference of time-varying regression models
We consider parameter estimation, hypothesis testing and variable selection
for partially time-varying coefficient models. Our asymptotic theory has the
useful feature that it can allow dependent, nonstationary error and covariate
processes. With a two-stage method, the parametric component can be estimated
with a -convergence rate. A simulation-assisted hypothesis testing
procedure is proposed for testing significance and parameter constancy. We
further propose an information criterion that can consistently select the true
set of significant predictors. Our method is applied to autoregressive models
with time-varying coefficients. Simulation results and a real data application
are provided.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1010 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Dynamic modeling of mean-reverting spreads for statistical arbitrage
Statistical arbitrage strategies, such as pairs trading and its
generalizations, rely on the construction of mean-reverting spreads enjoying a
certain degree of predictability. Gaussian linear state-space processes have
recently been proposed as a model for such spreads under the assumption that
the observed process is a noisy realization of some hidden states. Real-time
estimation of the unobserved spread process can reveal temporary market
inefficiencies which can then be exploited to generate excess returns. Building
on previous work, we embrace the state-space framework for modeling spread
processes and extend this methodology along three different directions. First,
we introduce time-dependency in the model parameters, which allows for quick
adaptation to changes in the data generating process. Second, we provide an
on-line estimation algorithm that can be constantly run in real-time. Being
computationally fast, the algorithm is particularly suitable for building
aggressive trading strategies based on high-frequency data and may be used as a
monitoring device for mean-reversion. Finally, our framework naturally provides
informative uncertainty measures of all the estimated parameters. Experimental
results based on Monte Carlo simulations and historical equity data are
discussed, including a co-integration relationship involving two
exchange-traded funds.Comment: 34 pages, 6 figures. Submitte
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