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Computational intensive methods for prediction and imputation in time series analysis

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Neves M., Cordeiro C.
Discussiones Mathematicae Probability and Statistics
|
2011
|
tom 31
|
nr 1-2
121-139
EN
One of the main goals in times series analysis is to forecast future values. Many forecasting methods have been developed and the most successful are based on the concept of exponential smoothing, based on the principle of obtaining forecasts as weighted combinations of past observations. Classical procedures to obtain forecast intervals assume a known distribution for the error process, what is not true in many situations. A bootstrap methodology can be used to compute distribution free forecast intervals. First an adequately chosen model is fitted to the data series. Afterwards, and inspired on sieve bootstrap, an AR(p) is used to filter the series of the random component, under the stationarity hypothesis. The centered residuals are then resampled and the initial series is reconstructed. This methodology will be used to obtain forecasting intervals and for treating missing data, which often appear in a real time series. An automatic procedure was developed in R language and will be applied in simulation studies as well as in real examples.
2
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Extremal behaviour of stationary processes: the calibration technique in the extremal index estimation

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Gomes D., Neves M.
Discussiones Mathematicae Probability and Statistics
|
2010
|
tom 30
|
nr 1
21-33
EN
Classical extreme value methods were derived when the underlying process is assumed to be a sequence of independent random variables. However when observations are taken along the time and/or the space the independence is an unrealistic assumption. A parameter that arises in this situation, characterizing the degree of local dependence in the extremes of a stationary series, is the extremal index, θ. In several areas such as hydrology, telecommunications, finance and environment, for example, the dependence between successive observations is observed so large values tend to occur in clusters. The extremal index is a quantity which, in an intuitive way, allows one to characterise the relationship between the dependence structure of the data and their extremal behaviour. Several estimators have been studied in the literature, but they endure a problem that usually appears in semiparametric estimators - a strong dependence on the high level uₙ, with an increasing bias and a decreasing variance as the threshold decreases. The calibration technique (Scheffé, 1973) is here considered as a procedure of controlling the bias of an estimator. It also leads to the construction of confidence intervals for the extremal index. A simulation study was performed for a stationary sequence and two sets of stationary data are under study for applying this technique.
3
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Exponential smoothing and resampling techniques in time series prediction

100%
Neves M., Cordeiro C.
Discussiones Mathematicae Probability and Statistics
|
2010
|
tom 30
|
nr 1
87-101
EN
Time series analysis deals with records that are collected over time. The objectives of time series analysis depend on the applications, but one of the main goals is to predict future values of the series. These values depend, usually in a stochastic manner, on the observations available at present. Such dependence has to be considered when predicting the future from its past, taking into account trend, seasonality and other features of the data. Some of the most successful forecasting methods are based on the concept of exponential smoothing. There are a variety of methods that fall into the exponential smoothing family, each having the property that forecasts are weighted combinations of past observations. But time series analysis needs proper statistical modeling. The model that better describes the behavior of the series in study can be crucial in obtaining 'good' forecasts. Departures from the true underlying distribution can adversely affect those forecasts. Resampling techniques have been considered in many situations to overcome that difficulty. For time series, several authors have proposed bootstrap methodologies. Here we will present an automatic procedure built in R language that first selects the best exponential smoothing model (among a set of possibilities) for fitting the data, followed by a bootstrap approach for obtaining forecasts. A real data set has been used to illustrate the performance of the proposed procedure.
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