On the minimum error in addition processes of positive floating-point numbers
A. Schurmann (1973)
Applicationes Mathematicae
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A. Schurmann (1973)
Applicationes Mathematicae
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Karel Tříska (1933)
Aktuárské vědy
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Kamel, Nidal, Samraj, Andrews, Mousavi, Arash (2007)
Discrete Dynamics in Nature and Society
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Sugata Sen Roy, Sankha Bhattacharya (2012)
Applicationes Mathematicae
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We consider an autoregressive moving average process of order (p,q)(ARMA(p,q)) with stationary, white noise error variables having uniformly bounded fourth order moments. The characteristic polynomials of both the autoregressive and moving average components involve stable and explosive roots. The autoregressive parameters are estimated by using the instrumental variable technique while the moving average parameters are estimated through a derived autoregressive process using the same...
Fanny Godet (2009)
ESAIM: Probability and Statistics
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We present two approaches for linear prediction of long-memory time series. The first approach consists in truncating the Wiener-Kolmogorov predictor by restricting the observations to the last terms, which are the only available data in practice. We derive the asymptotic behaviour of the mean-squared error as tends to +∞. The second predictor is the finite linear least-squares predictor the projection of the forecast value on the last observations. It is shown that these two predictors...
Li, Ming, Li, Jia-Yue (2010)
Mathematical Problems in Engineering
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Steven C. Wheelwright, Spyros Makridakis (1973)
RAIRO - Operations Research - Recherche Opérationnelle
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O. D. Anderson (1977)
RAIRO - Operations Research - Recherche Opérationnelle
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Olof Widlund (1977)
Publications mathématiques et informatique de Rennes
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Siegmund, David (1998)
Documenta Mathematica
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Shigeru Yamada, Shunji Osaki, Hiroyuki Narihisa (1985)
RAIRO - Operations Research - Recherche Opérationnelle
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Gusztáv Morvai, Benjamin Weiss (2016)
Kybernetika
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There are two kinds of universal schemes for estimating residual waiting times, those where the error tends to zero almost surely and those where the error tends to zero in some integral norm. Usually these schemes are different because different methods are used to prove their consistency. In this note we will give a single scheme where the average error is eventually small for all time instants, while the error itself tends to zero along a sequence of stopping times of density one. ...
Sugata Sen Roy, Sourav Chakraborty (2006)
Applicationes Mathematicae
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Outliers in a time series often cause problems in fitting a suitable model to the data. Hence predictions based on such models are liable to be erroneous. In this paper we consider a stable first-order autoregressive process and suggest two methods of substituting an outlier by imputed values and then predicting on the basis of it. The asymptotic properties of both the process parameter estimators and the predictors are also studied.