80,314 research outputs found
Lag space estimation in time series modelling
The purpose of this contribution is to investigate some techniques for finding the relevant lag-space, i.e. input information, for time series modelling. This is an important aspect of time series modelling, as it conditions the design of the model through the regressor vector a.k.a. input layer in a neural network. We give a rough description of the problem, insist on the concept of generalisation, and propose a generalisation-based method. We compare it to a non-parametric test, and carry out experiments, both on the well-known H'enon map, and on a real data set. 1. INTRODUCTION Let us assume that a time series is obtained from a mapping X t = f (X t\Gammau 1 ; X t\Gammau 2 ; : : : ; X t\Gammau m ). The m delays can include long term dependencies, in order to take into account e.g. some seasonality. The (u i ) are the primary dependencies, the smallest set of sufficient, not necessarily consecutive delays. All other dependencies are obtained through a combination of mappings and a..
Advancement of Fractionally Differenced Gegenbauer Processes with Long Memory
The class of long memory time series models involving Gegenbauer processes is investigated in detail in terms of formulation, parameter estimation, prediction and testing. Corresponding truncated AR (autoregressive) and MA (moving average) approximations driven by Gaussian white noise are analysed through state space modelling and Kalman filtering to assess the viability of estimating techniques . The optimal approximation option is employed to proceed with the estimation of model parameters. The resulting mean square errors are validated by the predictive accuracy to establish an optimal lag order through a large scale simulation study. It is shown that the use of this newly established lag order for a real data application provides benchmarks which are comparable and mostly better than a number of existing results in the literature. It is followed by an execution of this technique to extract and assess seasonal models through a Monte Carlo experiment. Thereafter empirical applications were provided. The above approach has been extended to model fractionally differenced Gegenbauer processes with conditional heteroskedastic errors and models with seasonality. Potential applications are provided. In addition, quasi-likelihood type ratio tests have been developed for testing unit roots, stationarity versus non-stationarity and Gegenbauer long memory versus standard long memory
A SARIMAX coupled modelling applied to individual load curves intraday forecasting
A dynamic coupled modelling is investigated to take temperature into account
in the individual energy consumption forecasting. The objective is both to
avoid the inherent complexity of exhaustive SARIMAX models and to take
advantage of the usual linear relation between energy consumption and
temperature for thermosensitive customers. We first recall some issues related
to individual load curves forecasting. Then, we propose and study the
properties of a dynamic coupled modelling taking temperature into account as an
exogenous contribution and its application to the intraday prediction of energy
consumption. Finally, these theoretical results are illustrated on a real
individual load curve. The authors discuss the relevance of such an approach
and anticipate that it could form a substantial alternative to the commonly
used methods for energy consumption forecasting of individual customers.Comment: 17 pages, 18 figures, 2 table
General relativistic modelling of the negative reverberation X-ray time delays in AGN
We present the first systematic physical modelling of the time-lag spectra
between the soft (0.3-1 keV) and the hard (1.5-4 keV) X-ray energy bands, as a
function of Fourier frequency, in a sample of 12 active galactic nuclei which
have been observed by XMM-Newton. We concentrate particularly on the negative
X-ray time-lags (typically seen above Hz) i.e. soft band variations
lag the hard band variations, and we assume that they are produced by
reprocessing and reflection by the accretion disc within a lamp-post X-ray
source geometry. We also assume that the response of the accretion disc, in the
soft X-ray bands, is adequately described by the response in the neutral iron
line (Fe k) at 6.4 keV for which we use fully general relativistic
ray-tracing simulations to determine its time evolution. These response
functions, and thus the corresponding time-lag spectra, yield much more
realistic results than the commonly-used, but erroneous, top-hat models.
Additionally we parametrize the positive part of the time-lag spectra
(typically seen below Hz) by a power-law. We find that the
best-fitting BH masses, M, agree quite well with those derived by other
methods, thus providing us with a new tool for BH mass determination. We find
no evidence for any correlation between M and the BH spin parameter, ,
the viewing angle, , or the height of the X-ray source above the disc,
. Also on average, the X-ray source lies only around 3.7 gravitational radii
above the accretion disc and the viewing angles are distributed uniformly
between 20 and 60 degrees. Finally, there is a tentative indication that the
distribution of spin parameters may be bimodal above and below 0.62.Comment: Accepted for publication in MNRAS. The paper is 22 pages long and
contains 19 figures and 2 table
Reducing and meta-analysing estimates from distributed lag non-linear models.
BACKGROUND: The two-stage time series design represents a powerful analytical tool in environmental epidemiology. Recently, models for both stages have been extended with the development of distributed lag non-linear models (DLNMs), a methodology for investigating simultaneously non-linear and lagged relationships, and multivariate meta-analysis, a methodology to pool estimates of multi-parameter associations. However, the application of both methods in two-stage analyses is prevented by the high-dimensional definition of DLNMs. METHODS: In this contribution we propose a method to synthesize DLNMs to simpler summaries, expressed by a reduced set of parameters of one-dimensional functions, which are compatible with current multivariate meta-analytical techniques. The methodology and modelling framework are implemented in R through the packages dlnm and mvmeta. RESULTS: As an illustrative application, the method is adopted for the two-stage time series analysis of temperature-mortality associations using data from 10 regions in England and Wales. R code and data are available as supplementary online material. DISCUSSION AND CONCLUSIONS: The methodology proposed here extends the use of DLNMs in two-stage analyses, obtaining meta-analytical estimates of easily interpretable summaries from complex non-linear and delayed associations. The approach relaxes the assumptions and avoids simplifications required by simpler modelling approaches
Two Approaches to Imputation and Adjustment of Air Quality Data from a Composite Monitoring Network
An analysis of air quality data is provided for the municipal area of Taranto characterized by high environmental risks, due to the massive presence of industrial sites with elevated environmental impact activities. The present study is focused on particulate matter as measured by PM10 concentrations. Preliminary analysis involved addressing several data problems, mainly: (i) an imputation techniques were considered to cope with the large number of missing data, due to both different working periods for groups of monitoring stations and occasional malfunction of PM10 sensors; (ii) due to the use of different validation techniques for each of the three monitoring networks, a calibration procedure was devised to allow for data comparability. Missing data imputation and calibration were addressed by three alternative procedures sharing a leave-one-out type mechanism and based on {\it ad hoc} exploratory tools and on the recursive Bayesian estimation and prediction of spatial linear mixed effects models. The three procedures are introduced by motivating issues and compared in terms of performance
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