1,977 research outputs found
Nonparametric inference of quantile curves for nonstationary time series
The paper considers nonparametric specification tests of quantile curves for
a general class of nonstationary processes. Using Bahadur representation and
Gaussian approximation results for nonstationary time series, simultaneous
confidence bands and integrated squared difference tests are proposed to test
various parametric forms of the quantile curves with asymptotically correct
type I error rates. A wild bootstrap procedure is implemented to alleviate the
problem of slow convergence of the asymptotic results. In particular, our
results can be used to test the trends of extremes of climate variables, an
important problem in understanding climate change. Our methodology is applied
to the analysis of the maximum speed of tropical cyclone winds. It was found
that an inhomogeneous upward trend for cyclone wind speeds is pronounced at
high quantile values. However, there is no trend in the mean lifetime-maximum
wind speed. This example shows the effectiveness of the quantile regression
technique.Comment: Published in at http://dx.doi.org/10.1214/09-AOS769 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Bayesian spectral modeling for multiple time series
We develop a novel Bayesian modeling approach to spectral density estimation for multiple time series. The log-periodogram distribution for each series is modeled as a mixture of Gaussian distributions with frequency-dependent weights and mean functions. The implied model for the log-spectral density is a mixture of linear mean functions with frequency-dependent weights. The mixture weights are built through successive differences of a logit-normal distribution function with frequency-dependent parameters. Building from the construction for a single spectral density, we develop a hierarchical extension for multiple time series. Specifically, we set the mean functions to be common to all spectral densities and make the weights specific to the time series through the parameters of the logit-normal distribution. In addition to accommodating flexible spectral density shapes, a practically important feature of the proposed formulation is that it allows for ready posterior simulation through a Gibbs sampler with closed form full conditional distributions for all model parameters. The modeling approach is illustrated with simulated datasets, and used for spectral analysis of multichannel electroencephalographic recordings (EEGs), which provides a key motivating application for the proposed methodology
Local likelihood estimation for covariance functions with spatially-varying parameters: the convoSPAT package for R
In spite of the interest in and appeal of convolution-based approaches for
nonstationary spatial modeling, off-the-shelf software for model fitting does
not as of yet exist. Convolution-based models are highly flexible yet
notoriously difficult to fit, even with relatively small data sets. The general
lack of pre-packaged options for model fitting makes it difficult to compare
new methodology in nonstationary modeling with other existing methods, and as a
result most new models are simply compared to stationary models. Using a
convolution-based approach, we present a new nonstationary covariance function
for spatial Gaussian process models that allows for efficient computing in two
ways: first, by representing the spatially-varying parameters via a discrete
mixture or "mixture component" model, and second, by estimating the mixture
component parameters through a local likelihood approach. In order to make
computation for a convolution-based nonstationary spatial model readily
available, this paper also presents and describes the convoSPAT package for R.
The nonstationary model is fit to both a synthetic data set and a real data
application involving annual precipitation to demonstrate the capabilities of
the package
The Periodogram of fractional processes.
We analyse asymptotic properties of the discrete Fourier transform and the periodogram of time series obtained through (truncated) linear filtering of stationary processes. The class of filters contains the fractional differencing operator and its coefficients decay at an algebraic rate, implying long-range-dependent properties for the filtered processes when the degree of integration α is positive. These include fractional time series which are nonstationary for any value of the memory parameter (α ≠ 0) and possibly nonstationary trending (α ≥ 0.5). We consider both fractional differencing or integration of weakly dependent and long-memory stationary time series. The results obtained for the moments of the Fourier transform and the periodogram at Fourier frequencies in a degenerating band around the origin are weaker compared with the stationary nontruncated case for α > 0, but sufficient for the analysis of parametric and semiparametric memory estimates. They are applied to the study of the properties of the log-periodogram regression estimate of the memory parameter α for Gaussian processes, for which asymptotic normality could not be showed using previous results. However, only consistency can be showed for the trending cases, 0.5 ≤ αDiscrete Fourier transform; Long-range dependence; Long memory; Nonstationary series; Log-periodogram regression; Asymptotic normality; Primary: 62M15; Secondary: 62M10, 60G18;
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