353,197 research outputs found
Reaction times of monitoring schemes for ARMA time series
This paper is concerned with deriving the limit distributions of stopping
times devised to sequentially uncover structural breaks in the parameters of an
autoregressive moving average, ARMA, time series. The stopping rules are
defined as the first time lag for which detectors, based on CUSUMs and Page's
CUSUMs for residuals, exceed the value of a prescribed threshold function. It
is shown that the limit distributions crucially depend on a drift term induced
by the underlying ARMA parameters. The precise form of the asymptotic is
determined by an interplay between the location of the break point and the size
of the change implied by the drift. The theoretical results are accompanied by
a simulation study and applications to electroencephalography, EEG, and IBM
data. The empirical results indicate a satisfactory behavior in finite samples.Comment: Published at http://dx.doi.org/10.3150/14-BEJ604 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
An Exact Formula for the Average Run Length to False Alarm of the Generalized Shiryaev-Roberts Procedure for Change-Point Detection under Exponential Observations
We derive analytically an exact closed-form formula for the standard minimax
Average Run Length (ARL) to false alarm delivered by the Generalized
Shiryaev-Roberts (GSR) change-point detection procedure devised to detect a
shift in the baseline mean of a sequence of independent exponentially
distributed observations. Specifically, the formula is found through direct
solution of the respective integral (renewal) equation, and is a general result
in that the GSR procedure's headstart is not restricted to a bounded range, nor
is there a "ceiling" value for the detection threshold. Apart from the
theoretical significance (in change-point detection, exact closed-form
performance formulae are typically either difficult or impossible to get,
especially for the GSR procedure), the obtained formula is also useful to a
practitioner: in cases of practical interest, the formula is a function linear
in both the detection threshold and the headstart, and, therefore, the ARL to
false alarm of the GSR procedure can be easily computed.Comment: 9 pages; Accepted for publication in Proceedings of the 12-th
German-Polish Workshop on Stochastic Models, Statistics and Their
Application
Random walks - a sequential approach
In this paper sequential monitoring schemes to detect nonparametric drifts
are studied for the random walk case. The procedure is based on a kernel
smoother. As a by-product we obtain the asymptotics of the Nadaraya-Watson
estimator and its as- sociated sequential partial sum process under
non-standard sampling. The asymptotic behavior differs substantially from the
stationary situation, if there is a unit root (random walk component). To
obtain meaningful asymptotic results we consider local nonpara- metric
alternatives for the drift component. It turns out that the rate of convergence
at which the drift vanishes determines whether the asymptotic properties of the
monitoring procedure are determined by a deterministic or random function.
Further, we provide a theoretical result about the optimal kernel for a given
alternative
Untenable nonstationarity: An assessment of the fitness for purpose of trend tests in hydrology
The detection and attribution of long-term patterns in hydrological time series have been important research topics for decades. A significant portion of the literature regards such patterns as ‘deterministic components’ or ‘trends’ even though the complexity of hydrological systems does not allow easy deterministic explanations and attributions. Consequently, trend estimation techniques have been developed to make and justify statements about tendencies in the historical data, which are often used to predict future events. Testing trend hypothesis on observed time series is widespread in the hydro-meteorological literature mainly due to the interest in detecting consequences of human activities on the hydrological cycle. This analysis usually relies on the application of some null hypothesis significance tests (NHSTs) for slowly-varying and/or abrupt changes, such as Mann-Kendall, Pettitt, or similar, to summary statistics of hydrological time series (e.g., annual averages, maxima, minima, etc.). However, the reliability of this application has seldom been explored in detail. This paper discusses misuse, misinterpretation, and logical flaws of NHST for trends in the analysis of hydrological data from three different points of view: historic-logical, semantic-epistemological, and practical. Based on a review of NHST rationale, and basic statistical definitions of stationarity, nonstationarity, and ergodicity, we show that even if the empirical estimation of trends in hydrological time series is always feasible from a numerical point of view, it is uninformative and does not allow the inference of nonstationarity without assuming a priori additional information on the underlying stochastic process, according to deductive reasoning. This prevents the use of trend NHST outcomes to support nonstationary frequency analysis and modeling. We also show that the correlation structures characterizing hydrological time series might easily be underestimated, further compromising the attempt to draw conclusions about trends spanning the period of records. Moreover, even though adjusting procedures accounting for correlation have been developed, some of them are insufficient or are applied only to some tests, while some others are theoretically flawed but still widely applied. In particular, using 250 unimpacted stream flow time series across the conterminous United States (CONUS), we show that the test results can dramatically change if the sequences of annual values are reproduced starting from daily stream flow records, whose larger sizes enable a more reliable assessment of the correlation structures
Diagnostics of plasma in the ionospheric D-region: detection and study of different ionospheric disturbance types
Here we discuss our recent investigations of the ionospheric plasma by using
very low and low frequency (VLF/LF) radio waves. We give a review of how to
detect different low ionospheric reactions (sudden ionospheric disturbances) to
various terrestrial and extra-terrestrial events, show their classification
according to intensity and time duration, and present some methods for their
detections in time and frequency domains. Investigations of detection in time
domain are carried out for intensive long-lasting perturbations induced by
solar X-ray flares and for short-lasting perturbations caused by gamma ray
bursts. We also analyze time variations of signals used in the low ionospheric
monitoring after earthquake events. In addition, we describe a procedure for
the detection of acoustic and gravity waves from the VLF/LF signal analysis in
frequency domain. The research of the low ionospheric plasma is based on data
collected by the VLF/LF receivers located in Belgrade, Serbia
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