Testing and estimating change-points in time series

1985 ◽  
Vol 17 (4) ◽  
pp. 841-867 ◽  
Author(s):  
Dominique Picard
Keyword(s):  
Time Series ◽  
Asymptotic Distribution ◽  
Likelihood Ratio ◽  
Asymptotic Properties ◽  
Likelihood Ratio Tests ◽  
Parametric Models ◽  
The Other ◽  
Change Points ◽  
Analysis Of Time Series

The aim of this paper is to present a few techniques which may be useful in the analysis of time series when a failure is suspected. We present two categories of tests and investigate their asymptotic properties: one, of nonparametric type, is intended to detect a general failure in spectrum; the other investigates the properties of likelihood ratio tests in parametric models which have a non-standard behaviour in this situation. Finally, we obtain the asymptotic distribution of the likelihood estimators of the change parameters.

Testing and estimating change-points in time series

1985 ◽  
Vol 17 (04) ◽  
pp. 841-867 ◽  
Author(s):  
Dominique Picard
Keyword(s):  
Time Series ◽  
Asymptotic Distribution ◽  
Likelihood Ratio ◽  
Asymptotic Properties ◽  
Likelihood Ratio Tests ◽  
Parametric Models ◽  
The Other ◽  
Change Points ◽  
Analysis Of Time Series

The aim of this paper is to present a few techniques which may be useful in the analysis of time series when a failure is suspected. We present two categories of tests and investigate their asymptotic properties: one, of nonparametric type, is intended to detect a general failure in spectrum; the other investigates the properties of likelihood ratio tests in parametric models which have a non-standard behaviour in this situation. Finally, we obtain the asymptotic distribution of the likelihood estimators of the change parameters.

Asymptotic properties of certain functionals of the periodogram

1974 ◽  
Vol 11 (3) ◽  
pp. 578-581
Author(s):  
Herbert T. Davis
Keyword(s):  
Time Series ◽  
Asymptotic Distribution ◽  
Gaussian Processes ◽  
Asymptotic Properties ◽  
Innovation Process ◽  
Triangular Array ◽  
Stationary Time Series ◽  
Riemann Sums ◽  
Stationary Time ◽  
Fundamental Frequencies

The asymptotic properties of the periodogram of a weakly stationary time series for the triangular array of fundamental frequencies is studied. For linear Gaussian processes, results are obtained relating the asymptotic distribution of certain Riemann sums of the periodogram of the process to those of the periodogram of the innovation process.

scholarly journals Specification of deformation congruence models using combinatorial iterative DIA testing procedure

2020 ◽  
Vol 94 (12) ◽  
Author(s):  
Krzysztof Nowel
Keyword(s):  
Likelihood Ratio ◽  
Computer Simulations ◽  
Testing Procedure ◽  
Likelihood Ratio Tests ◽  
The Other ◽  
Deformation Analysis ◽  
Characteristic Points ◽  
The One ◽  
Congruence Test ◽  
Combinatorial Methods

AbstractDeformation congruence models form the basis for conventional deformation analysis (CDA). In geometrical sense, these models connect an epochal object states—represented by its characteristic points—at stable/congruent points to disclose possible deformations. To this day, the deformation congruence models are usually specified using the global congruence test (GCT) procedure which, however, has a weakness in the case of multiple displacements. More precisely, the GCT procedure is based on consecutive point-by-point specification which may suffer from so-called displacement smearing. To overcome the above weakness, a revolutionary—in the context of GCT—concept (two methods) involving combinatorial possibilities was suggested in recent years. Admittedly, this concept avoids the problem of consecutive point-by-point specification. Nevertheless, it generates another weakness, namely the problem of the comparison of different-dimensional models. This paper makes a step forward in this new combinatorial field and discusses a more sophisticated combinatorial procedure, denoted as CIDIA. It was shown that, thanks to an appropriately used the possibilities of combinatorics and generalized likelihood ratio tests performed in the detection–identification–adaptation (DIA) iterative steps, the above weaknesses can be overcome. In the context of GCT, the suggested procedure has rather evolutionary—than revolutionary—character and the general concepts of both procedures have similar heuristic substantiation. To demonstrate the efficacy of CIDIA against GCT and the two existing combinatorial methods, various deformation scenarios were being randomized independently many times with the use of comprehensive computer simulations and then processed. Generally, the obtained results confirmed the statement that the suggested CIDIA procedure—unlike the existing combinatorial methods—can be substantially more resistant to displacement smearing than the GCT procedure, at no significant costs. The efficacy of CIDIA—unlike the ones of the two existing combinatorial methods—turned out always higher (on average by several percentages) than the one of GCT for all considered deformation scenarios. At the same time, the CIDIA procedure turned out substantially less time-consuming than the other combinatorial methods.

A Note on Asymptotic Power Calculations in Nearly Nonstationary Time Series

1993 ◽  
Vol 9 (4) ◽  
pp. 659-667 ◽  
Author(s):  
Anders Rygh Swensen
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Asymptotic Distribution ◽  
Likelihood Ratio ◽  
Power Function ◽  
Nonstationary Time Series ◽  
Double Root ◽  
Asymptotic Power ◽  
Ito Process ◽  
Nikodym Derivative

In the AR(2) model, with a double root at unity, we consider the asymptotic distribution of the likelihood ratio with respect to a nearly nonstationary alternative. It is shown how the distribution can be represented as a Radon-Nikodym derivative of an Ito process with respect to Brownian motion. Using this result, we point out how standard contiguity arguments can be applied to obtain a representation of the asymptotic power function in nearly nonstationary alternatives.

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