Displaying similar documents to “One prediction of autoregressive time series”

Asymptotic distribution of the estimated parameters of an ARMA(p,q) process in the presence of explosive roots

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...

Linear prediction of long-range dependent time series

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...

A versatile scheme for predicting renewal times

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. ...