The Poisson limit theorem for high extrema of a time series with seasonal component and monotone trend

2012 ◽  
Vol 67 (1) ◽  
pp. 11-15
Author(s):  
I. V. Rodionov
1996 ◽  
Vol 33 (01) ◽  
pp. 146-155 ◽  
Author(s):  
K. Borovkov ◽  
D. Pfeifer

In this paper we consider improvements in the rate of approximation for the distribution of sums of independent Bernoulli random variables via convolutions of Poisson measures with signed measures of specific type. As a special case, the distribution of the number of records in an i.i.d. sequence of length n is investigated. For this particular example, it is shown that the usual rate of Poisson approximation of O(1/log n) can be lowered to O(1/n 2). The general case is discussed in terms of operator semigroups.


2019 ◽  
Vol 2 (1) ◽  
pp. 25-44 ◽  
Author(s):  
S. Mohanasundaram ◽  
G. Suresh Kumar ◽  
Balaji Narasimhan

Abstract Groundwater level prediction and forecasting using univariate time series models are useful for effective groundwater management under data limiting conditions. The seasonal autoregressive integrated moving average (SARIMA) models are widely used for modeling groundwater level data as the groundwater level signals possess the seasonality pattern. Alternatively, deseasonalized autoregressive and moving average models (Ds-ARMA) can be modeled with deseasonalized groundwater level signals in which the seasonal component is estimated and removed from the raw groundwater level signals. The seasonal component is traditionally estimated by calculating long-term averaging values of the corresponding months in the year. This traditional way of estimating seasonal component may not be appropriate for non-stationary groundwater level signals. Thus, in this study, an improved way of estimating the seasonal component by adopting a 13-month moving average trend and corresponding confidence interval approach has been attempted. To test the proposed approach, two representative observation wells from Adyar basin, India were modeled by both traditional and proposed methods. It was observed from this study that the proposed model prediction performance was better than the traditional model's performance with R2 values of 0.82 and 0.93 for the corresponding wells' groundwater level data.


1983 ◽  
Vol 20 (01) ◽  
pp. 47-60 ◽  
Author(s):  
M. Berman ◽  
G. K. Eagleson

Silverman and Brown (1978) have derived Poisson limit theorems for certain sequences of symmetric statistics, based on a sample of independent identically distributed random variables. In this paper an incomplete version of these statistics is considered and a Poisson limit result shown to hold. The powers of some tests based on the incomplete statistic are investigated and the main results of the paper are used to simplify the derivations of the asymptotic distributions of some statistics previously published in the literature.


1973 ◽  
Vol 10 (01) ◽  
pp. 130-145 ◽  
Author(s):  
E. J. Hannan

A linear time-series model is considered to be one for which a stationary time series, which is purely non-deterministic, has the best linear predictor equal to the best predictor. A general inferential theory is constructed for such models and various estimation procedures are shown to be equivalent. The treatment is considerably more general than previous treatments. The case where the series has mean which is a linear function of very general kinds of regressor variables is also discussed and a rather general form of central limit theorem for regression is proved. The central limit results depend upon forms of the central limit theorem for martingales.


1997 ◽  
Vol 34 (1) ◽  
pp. 24-34 ◽  
Author(s):  
Shoou-Ren Hsiau

This paper establishes a compound Poisson limit theorem for the sum of a sequence of multi-state Markov chains. Our theorem generalizes an earlier one by Koopman for the two-state Markov chain. Moreover, a similar approach is used to derive a limit theorem for the sum of the k th-order two-state Markov chain.


1996 ◽  
Vol 117 (1) ◽  
pp. 107-111 ◽  
Author(s):  
J. M. Stuart ◽  
K. Cartwright ◽  
N. J. Andrews

SummaryAlthough viral respiratory tract infections may predispose to meningococcal disease, strong evidence that they do so exists only for influenza. Data on laboratory reported cases of respiratory syncytial virus (RSV) infections and meningococcal disease in England and Wales from mid-1989 to mid-1994 were analysed. Although the rise in RSV cases preceded the rise in meningococcal disease cases each winter, the interval between the rise and fall of the two diseases was inconsistent, no association was found between time series after removal of the seasonal component, and there was no evidence that more cases of meningococcal disease occurred in winters with more RSV disease. RSV may have less effect on the two most likely mechanisms whereby influenza predisposes to meningococcal disease, namely lowered immunity and impaired pharyngeal defences.


2003 ◽  
Vol 24 (3) ◽  
pp. 298-306
Author(s):  
Fang Da-fan ◽  
Wang Han-xing ◽  
Tang Mao-ning

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