arXiv subjects

William Kengne

Publications and source records attributed to William Kengne.

26 records · Page 2Linked to original sources

arXiv2020

Strong consistent model selection for general causal time series

We consider the strongly consistent question for model selection in a large class of causal time series models, including AR($\infty$), ARCH($\infty$), TARCH($\infty$), ARMA-GARCH and many classical others processes. We propose a penalized criterion based on the quasi likelihood of the model. We provide sufficient conditions that ensure the strong consistency of the proposed procedure. Also, the estimator of the parameter of the selected model obeys the law of iterated logarithm. It appears that, unlike the result of the weak consistency obtained by Bardet {\it et al.} \cite{Bardet2020}, a dependence between the regularization parameter and the model structure is not needed.

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arXiv2020

Poisson QMLE for change-point detection in general integer-valued time series models

We consider together the retrospective and the sequential change-point detection in a general class of integer-valued time series. The conditional mean of the process depends on a parameter $θ^*$ which may change over time. We propose procedures which are based on the Poisson quasi-maximum likelihood estimator of the parameter, and where the updated estimator is computed without the historical observations in the sequential framework. For both the retrospective and the sequential detection, the test statistics converge to some distributions obtained from the standard Brownian motion under the null hypothesis of no change and diverge to infinity under the alternative; that is, these procedures are consistent. Some results of simulations as well as real data application are provided.

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arXiv2020

Inference for nonstationary time series of counts with application to change-point problems

We consider an integer-valued time series $Y=(Y_t)_{t\in\Z}$ where the models after a time $k^*$ is Poisson autoregressive with the conditional mean that depends on a parameter $θ^*\inΘ\subset\R^d$. The structure of the process before $k^*$ is unknown;? it could be any other integer-valued time series, that is, the process $Y$ could be nonstationary.? It is established that the maximum likelihood estimator of $θ^*$ computed on the nonstationary observations is consistent and asymptotically normal. Next, we carry out the sequential change-point detection in a large class of Poisson autoregressive models. We propose a monitoring scheme for detecting change in the model. The procedure is based on an updated estimator which is computed without the historical observations. The asymptotic behavior of the detector is studied, in particular, the above result on the inference in a nonstationary setting are applied to prove that the proposed procedure is consistent. A simulation study as well as a real data application are provided.

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arXiv2020

Consistent model selection procedure for general integer-valued time series

This paper deals with the problem of model selection for a general class of integer-valued time series. We propose a penalized criterion based on the Poisson quasi-likelihood of the model. Under certain regularity conditions, the consistency of the procedure as well as the consistency and the asymptotic normality of the Poisson quasi-likelihood estimator of the selected model are established. Simulation experiments are conducted for some classical models such as Poisson, binary INGARCH and negative binomial model with nonlinear dynamic. Also, an application to a real dataset is provided.

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arXiv2019

Piecewise autoregression for general integer-valued time series

This paper proposes a piecewise autoregression for general integer-valued time series. The conditional mean of the process depends on a parameter which is piecewise constant over time. We derive an inference procedure based on a penalized contrast that is constructed from the Poisson quasi-maximum likelihood of the model. The consistency of the proposed estimator is established. From practical applications, we derive a data-driven procedure based on the slope heuristic to calibrate the penalty term of the contrast; and the implementation is carried out through the dynamic programming algorithm, which leads to a procedure of $\mathcal{O}(n^2)$ time complexity. Some simulation results are provided, as well as the applications to the US recession data and the number of trades in the stock of Technofirst.

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arXiv2019

Consistent model selection criteria and goodness-of-fit test for affine causal processes

This paper studies the model selection problem in a large class of causal time series models, which includes both the ARMA or AR($\infty$) processes, as well as the GARCH or ARCH($\infty$), APARCH, ARMA-GARCH and many others processes. To tackle this issue, we consider a penalized contrast based on the quasi-likelihood of the model. We provide sufficient conditions for the penalty term to ensure the consistency of the proposed procedure as well as the consistency and the asymptotic normality of the quasi-maximum likelihood estimator of the chosen model. It appears from these conditions that the Bayesian Information Criterion (BIC) does not always guarantee the consistency. We also propose a tool for diagnosing the goodness-of-fit of the chosen model based on the portmanteau Test. Numerical simulations and an illustrative example on the FTSE index are performed to highlight the obtained asymptotic results, including a numerical evidence of the non consistency of the usual BIC penalty for order selection of an AR(p) models with ARCH($\infty$) errors.

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arXiv2016

Testing for parameter change in general integer-valued time series

We consider the structural change in a class of discrete valued time series that the conditional distribution follows a one-parameter exponential family. We propose a change-point test based on the maximum likelihood estimator of the parameter of the model. Under the null hypothesis (of no change), the test statistics converges to a well known distribution, allowing for the calculation of the critical values of the test. The test statistic diverges to infinity under the alternative, that is, the test asymptotically has power one. Some simulation results and real data applications are reported to show the applicability of the test procedure.

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arXiv2013

Inference and testing for structural change in time series of counts model

We consider here together the inference questions and the change-point problem in Poisson autoregressions (see Tjøstheim, 2012). The conditional mean (or intensity) of the process is involved as a non-linear function of it past values and the past observations. Under Lipschitz-type conditions, it is shown that the conditional mean can be written as a function of lagged observations. In the latter model, assume that the link function depends on an unknown parameter $θ_0$. The consistency and the asymptotic normality of the maximum likelihood estimator of the parameter are proved. These results are used to study change-point problem in the parameter $θ_0$. We propose two tests based on the likelihood of the observations. Under the null hypothesis (i.e. no change), it is proved that both those test statistics converge to an explicit distribution. Consistencies under alternatives are proved for both tests. Simulation results show how those procedure work practically, and an application to real data is also processed.

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