منابع مشابه
Prediction for discrete time series
Let {Xn} be a stationary and ergodic time series taking values from a finite or countably infinite set X . Assume that the distribution of the process is otherwise unknown. We propose a sequence of stopping times λn along which we will be able to estimate the conditional probability P (Xλn+1 = x|X0, . . . , Xλn) from data segment (X0, . . . , Xλn) in a pointwise consistent way for a restricted ...
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Extended Abstract. Forecasting is one of the most important purposes of time series analysis. For many years, classical methods were used for this aim. But these methods do not give good performance results for real time series due to non-linearity and non-stationarity of these data sets. On one hand, most of real world time series data display a time-varying second order structure. On th...
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Let {Xn} be a stationary and ergodic time series taking values from a finite or countably infinite set X and that f(X) is a function of the process with finite second moment. Assume that the distribution of the process is otherwise unknown. We construct a sequence of stopping times λn along which we will be able to estimate the conditional expectation E(f(Xλn+1)|X0, . . . , Xλn) from the observ...
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The problem of extracting as much information as possible from a sequence of observations of a stationary stochastic process X0,X1, ...Xn has been considered by many authors from different points of view. It has long been known through the work of D. Bailey that no universal estimator for P(Xn+1|X0,X1, ...Xn) can be found which converges to the true estimator almost surely. Despite this result,...
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One of the main goals of studying the time series is estimation of prediction interval based on an observed sample path of the process. In recent years, different semiparametric bootstrap methods have been proposed to find the prediction intervals without any assumption of error distribution. In semiparametric bootstrap methods, a linear process is approximated by an autoregressive process. The...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2004
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-004-0386-3