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Trend Estimation (trend + estimation)

Distribution by Scientific Domains
Mathematics and Statistics100%

Selected Abstracts

Trend estimation in extremes of synthetic North Sea surges

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 4 2007
Adam Butler
Summary., Mechanistic models for complex atmospheric and hydrological processes are often used to simulate extreme natural events, usually to quantify the risks that are associated with these events. We use novel extreme value methods to analyse the statistical properties of output from a numerical storm surge model for the North Sea. The ,model data' constitute a reconstruction of the storm surge climate for the period 1955,2000 based on a high quality meteorological data set and constitute the only available source of information on surge elevations at offshore and unmonitored coastal locations over this period. Previous studies have used extreme value methods to analyse storm surge characteristics, but we can extend and improve on these analyses by using a local likelihood approach to provide a non-parametric description of temporal and spatial variations in the magnitude and frequency of storm surge events. [source]

Trend estimation of financial time series

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2010
Víctor M. Guerrero
Abstract We propose to decompose a financial time series into trend plus noise by means of the exponential smoothing filter. This filter produces statistically efficient estimates of the trend that can be calculated by a straightforward application of the Kalman filter. It can also be interpreted in the context of penalized least squares as a function of a smoothing constant has to be minimized by trading off fitness against smoothness of the trend. The smoothing constant is crucial to decide the degree of smoothness and the problem is how to choose it objectively. We suggest a procedure that allows the user to decide at the outset the desired percentage of smoothness and derive from it the corresponding value of that constant. A definition of smoothness is first proposed as well as an index of relative precision attributable to the smoothing element of the time series. The procedure is extended to series with different frequencies of observation, so that comparable trends can be obtained for say, daily, weekly or intraday observations of the same variable. The theoretical results are derived from an integrated moving average model of order (1, 1) underlying the statistical interpretation of the filter. Expressions of equivalent smoothing constants are derived for series generated by temporal aggregation or systematic sampling of another series. Hence, comparable trend estimates can be obtained for the same time series with different lengths, for different time series of the same length and for series with different frequencies of observation of the same variable. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Smoothing splines for trend estimation and prediction in time series

ENVIRONMETRICS, Issue 3 2009
Richard Morton
Abstract We consider the use of generalized additive models with correlated errors for analysing trends in time series. The trend is represented as a smoothing spline so that it can be extrapolated. A method is proposed for choosing the smoothing parameter. It is based on the ability to predict a short term into the future. The choice not only addresses the purpose in hand, but also performs very well, and avoids the tendency to under-smooth or to interpolate the data that can occur with other data-driven methods used to choose the smoothing parameter. The method is applied to data from a chemical process and to stream salinity measurements. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Temporal analysis of spatial covariance of SO2 in Europe

ENVIRONMETRICS, Issue 4 2007
Marco Giannitrapani
Abstract In recent years, the number of applications of spatial statistics has enormously increased in environmental and ecological sciences. A typical problem is the sampling of a pollution field, with the common objective of spatial interpolation. In this paper, we present a spatial analysis across time, focusing on sulphur dioxide (SO2) concentrations monitored from 1990 to 2001 at 125 sites across Europe. Four different methods of trend estimation have been used, and comparisons among them are shown. Spherical, Exponential and Gaussian variograms have been fitted to the residuals and compared. Time series analyses of the range, sill and nugget have been undertaken and a suggestion for defining a unique spatial correlation matrix for the overall time period of analysis is proposed. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Optimal designs for parameter estimation of the Ornstein,Uhlenbeck process

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 5 2009
Maroussa Zagoraiou
Abstract This paper deals with optimal designs for Gaussian random fields with constant trend and exponential correlation structure, widely known as the Ornstein,Uhlenbeck process. Assuming the maximum likelihood approach, we study the optimal design problem for the estimation of the trend µ and the correlation parameter , using a criterion based on the Fisher information matrix. For the problem of trend estimation, we give a new proof of the optimality of the equispaced design for any sample size (see Statist. Probab. Lett. 2008; 78:1388,1396). We also show that for the estimation of the correlation parameter, an optimal design does not exist. Furthermore, we show that the optimal strategy for µ conflicts with the one for ,, since the equispaced design is the worst solution for estimating the correlation. Hence, when the inferential purpose concerns both the unknown parameters we propose the geometric progression design, namely a flexible class of procedures that allow the experimenter to choose a suitable compromise regarding the estimation's precision of the two unknown parameters guaranteeing, at the same time, high efficiency for both. Copyright © 2008 John Wiley & Sons, Ltd. [source]