arXiv subjects

Anne Philippe

Publications and source records attributed to Anne Philippe.

At least 19 recordsLinked to original sources

arXiv2026

A Frequency-Domain approach to detect nonstationarity in dependent data

Distinguishing long memory behaviour from nonstationarity can be very difficult as in both cases the sample autocovariance function decays very slowly. Available stationarity tests either do not include long memory or fare poorly in terms of empirical size, especially near the boundary between long memory and nonstationarity. We propose a testing procedure based on evaluating periodograms at different epochs. Limiting distributions established here are easily tractable as sum of weighted independent $\chi^2$ random variables. Moreover, numerical studies are provided to show that the proposed approach seems to outperform existing methods.

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arXiv2026

Irregularly observed long-memory Levy-driven moving average processes

We study long-memory continuous-time moving-average processes driven by a Levy process and observed at random renewal times. The sampling scheme introduces an additional source of randomness through irregular observation times. We establish the asymptotic behaviour of normalized partial sums under both finite- and infinite-mean renewal sampling.

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arXiv2026

From nonstationarity to stationarity via $1/f$ noise: discrete Fourier transforms and sample mean asymptotics for testing

We study the asymptotic behaviour of different statistics for time series exhibiting long memory and nonstationarity. For processes with memory parameter $d\in(-1/2,3/2)$, we derive the joint limiting distribution of discrete Fourier transforms at a fixed number of Fourier frequencies, with a unified normalization. The resulting limits are Gaussian with an explicit covariance structure. Particular attention is given to the boundary case $d=1/2$, also known as $1/f$ noise. We show that logarithmic corrections yield nondegenerate limits for sample mean and sample variance leading to explicit asymptotic distributions of $\chi^2$ type. We construct a statistic that combines the sample mean, the sample variance, and low-frequency periodogram ordinates, designed so that, at the boundary case $(d=1/2)$, it admits a tractable limit distribution. These results are applied to construct a consistent parameter-free test of nonstationarity against long memory stationarity.

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arXiv2025

A Frequency-Domain NonStationarity Test for dependent data

Distinguishing long-memory behaviour from nonstationarity is challenging, as both produce slowly decaying sample autocovariances. Existing stationarity tests either fail to account for long-memory processes or exhibit poor empirical size, particularly near the boundary between stationarity and nonstationarity. We propose a new, parameter-free testing procedure based on the evaluation of periodograms across multiple epochs. The limiting distributions derived here are obtained under stationarity and nonstationarity assumptions and analytically tractable, expressed as finite sums of weighted independent $\chi^2$ random variables. Simulation studies indicate that the proposed method performs favorably compared to existing approaches.

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arXiv2024

Asymptotics for irregularly observed long memory processes

We study the effect of observing a stationary process at irregular time points via a renewal process. We establish a sharp difference in the asymptotic behaviour of the self-normalized sample mean of the observed process depending on the renewal process. In particular, we show that if the renewal process has a moderate heavy tail distribution then the limit is a so-called Normal Variance Mixture (NVM) and we characterize the randomized variance part of the limiting NVM as an integral function of a L\'evy stable motion. Otherwise, the normalized sample mean will be asymptotically normal.

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arXiv2020

Bayesian hierarchical models for the prediction of the driver flow and passenger waiting times in a stochastic carpooling service

Carpooling is an integral component in smart carbon-neutral cities, in particular to facilitate homework commuting. We study an innovative carpooling service developed by the start-up Ecov which specialises in homework commutes in peri-urban and rural regions. When a passenger makes a carpooling request, a designated driver is not assigned as in a traditional carpooling service; rather the passenger waits for the first driver, from a population of non-professional drivers who are already en route, to arrive. We propose a two-stage Bayesian hierarchical model to overcome the considerable difficulties, due to the sparsely observed driver and passenger data from an embryonic stochastic carpooling service, to deliver high-quality predictions of driver flow and passenger waiting times. The first stage focuses on the driver flow, whose predictions are aggregated at the daily level to compensate the data sparsity. The second stage processes this single daily driver flow into sub-daily (e.g. hourly) predictions of the passenger waiting times. We demonstrate that our model mostly outperforms frequentist and non-hierarchical Bayesian methods for observed data from operational carpooling service in Lyon, France and we also validated our model on simulated data.

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arXiv2019

Inference for continuous-time long memory randomly sampled processes

From a continuous-time long memory stochastic process, a discrete-time randomly sampled one is drawn. We investigate the second-order properties of this process and establish some time-and frequency-domain asymptotic results. We mainly focus on the case when the initial process is Gaussian. The challenge being that, although marginally remains Gaussian, the randomly sampled process will no longer be jointly Gaussian.

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arXiv2019

Shadow Simulated Annealing algorithm: a new tool for global optimisation and statistical inference

This paper develops a new global optimisation method that applies to a family of criteria that are not entirely known. This family includes the criteria obtained from the class of posteriors that have nor-malising constants that are analytically not tractable. The procedure applies to posterior probability densities that are continuously differen-tiable with respect to their parameters. The proposed approach avoids the re-sampling needed for the classical Monte Carlo maximum likelihood inference, while providing the missing convergence properties of the ABC based methods. Results on simulated data and real data are presented. The real data application fits an inhomogeneous area interaction point process to cosmological data. The obtained results validate two important aspects of the galaxies distribution in our Universe : proximity of the galaxies from the cosmic filament network together with territorial clustering at given range of interactions. Finally, conclusions and perspectives are depicted.

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arXiv2018

Sample covariances of random-coefficient AR(1) panel model

The present paper obtains a complete description of the limit distributions of sample covariances in N x n panel data when N and n jointly increase, possibly at different rate. The panel is formed by N independent samples of length n from random-coefficient AR(1) process with the tail distribution function of the random coefficient regularly varying at the unit root with exponent $\beta$ > 0. We show that for $\beta$ $\in$ (0, 2) the sample covariances may display a variety of stable and non-stable limit behaviors with stability parameter depending on $\beta$ and the mutual increase rate of N and n.

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arXiv2017

Estimating long memory in panel random-coefficient AR(1) data

It is well-known that random-coefficient AR(1) process can have long memory depending on the index $\beta$ of the tail distribution function of the random coefficient, if it is a regularly varying function at unity. We discuss estimation of $\beta$ from panel data comprising N random-coefficient AR(1) series, each of length T. The estimator of $\beta$ is constructed as a version of the tail index estimator of Goldie and Smith (1987) applied to sample lag 1 autocorrelations of individual time series. Its asymptotic normality is derived under certain conditions on N, T and some parameters of our statistical model. Based on this result, we construct a statistical procedure to test if the panel random-coefficient AR(1) data exhibit long memory. A simulation study illustrates finite-sample performance of the introduced estimator and testing procedure.

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arXiv2015

Nonparametric estimation of the distribution of the autoregressive coefficient from panel random-coefficient AR(1) data

We discuss nonparametric estimation of the distribution function $G(x)$ of the autoregressive coefficient $a \in (-1,1)$ from a panel of $N$ random-coefficient AR(1) data, each of length $n$, by the empirical distribution function of lag 1 sample autocorrelations of individual AR(1) processes. Consistency and asymptotic normality of the empirical distribution function and a class of kernel density estimators is established under some regularity conditions on $G(x)$ as $N$ and $n$ increase to infinity. The Kolmogorov-Smirnov goodness-of-fit test for simple and composite hypotheses of Beta distributed $a$ is discussed. A simulation study for goodness-of-fit testing compares the finite-sample performance of our nonparametric estimator to the performance of its parametric analogue discussed in Beran et al. (2010).

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arXiv2015

Hypothesis testing for markovian models with random time observations

The aim of this paper is to propose a methodology for testing general hypothesis in a Markovian setting with random sampling. A discrete Markov chain X is observed at random time intervals $\tau$ k, assumed to be iid with unknown distribution $\mu$. Two test procedures are investigated. The first one is devoted to testing if the transition matrix P of the Markov chain X satisfies specific affine constraints, covering a wide range of situations such as symmetry or sparsity. The second procedure is a goodness-of-fit test on the distribution $\mu$, which reveals to be consistent under mild assumptions even though the time gaps are not observed. The theoretical results are supported by a Monte Carlo simulation study to show the performance and robustness of the proposed methodologies on specific numerical examples.

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arXiv2014

Construction of an informative hierarchical prior for a small sample with the help of historical data and application to electricity load forecasting

We are interested in the estimation and prediction of a parametric model on a short dataset upon which it is expected to overfit and perform badly. To overcome the lack of data (relatively to the dimension of the model) we propose the construction of an informative hierarchical Bayesian prior based upon another longer dataset which is assumed to share some similarities with the original, short dataset. We illustrate the performance of our prior on simulated dataset from three standard models. Then we apply the methodology to a working model for the electricity load forecasting on real datasets, where it leads to a substantial improvement of the quality of the predictions.

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arXiv2013

Contemporaneous aggregation of triangular array of random-coefficient AR(1) processes

We discuss contemporaneous aggregation of independent copies of a triangular array of random-coefficient AR(1) processes with i.i.d. innovations belonging to the domain of attraction of an infinitely divisible law W. The limiting aggregated process is shown to exist, under general assumptions on W and the mixing distribution, and is represented as a mixed infinitely divisible moving-average. Partial sums process of $ is discussed under the assumption E(W^2) is finite and a mixing density regularly varying at the "unit root" x=1 with exponent β>0. We show that the above partial sums process may exhibit four different limit behaviors depending on βand the Lévy triplet of W. Finally, we study the disaggregation problem in spirit of Leipus et al. (2006) and obtain the weak consistency of the corresponding estimator of the mixing distribution in a suitable L_2-space.

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arXiv2013

Aggregation and long memory: recent developments

It is well-known that the aggregated time series might have very different properties from those of the individual series, in particular, long memory. At the present time, aggregation has become one of the main tools for modelling of long memory processes. We review recent work on contemporaneous aggregation of random-coefficient AR(1) and related models, with particular focus on various long memory properties of the aggregated process.

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arXiv2013

On particle filters applied to electricity load forecasting

We are interested in the online prediction of the electricity load, within the Bayesian framework of dynamic models. We offer a review of sequential Monte Carlo methods, and provide the calculations needed for the derivation of so-called particles filters. We also discuss the practical issues arising from their use, and some of the variants proposed in the literature to deal with them, giving detailed algorithms whenever possible for an easy implementation. We propose an additional step to help make basic particle filters more robust with regard to outlying observations. Finally we use such a particle filter to estimate a state-space model that includes exogenous variables in order to forecast the electricity load for the customers of the French electricity company Électricité de France and discuss the various results obtained.

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arXiv2012

Detection of non-constant long memory parameter

This article deals with detection of nonconstant long memory parameter in time series. The null hypothesis presumes stationary or nonstationary time series with constant long memory parameter, typically an I(d) series with d>-.5. The alternative corresponds to an increase in persistence and includes in particular an abrupt or gradual change from I(d_1) to I(d_2).

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arXiv2012

Estimation of Scale and Hurst Parameters of Semi-Selfsimilar Processes

The characteristic feature of semi-selfsimilar process is the invariance of its finite dimensional distributions by certain dilation for specific scaling factor. Estimating the scale parameter $λ$ and the Hurst index of such processes is one of the fundamental problem in the literature. We present some iterative method for estimation of the scale and Hurst parameters which is addressed for semi-selfsimilar processes with stationary increments. This method is based on some flexible sampling scheme and evaluating sample variance of increments in each scale intervals $[λ^{n-1}, λ^n)$, $n\in \mathbb{N}$. For such iterative method we find the initial estimation for the scale parameter by evaluating cumulative sum of moving sample variances and also by evaluating sample variance of preceding and succeeding moving sample variance of increments. We also present a new efficient method for estimation of Hurst parameter of selfsimilar processes. As an example we introduce simple fractional Brownian motion (sfBm) which is semi-selfsimilar with stationary increments. We present some simulations and numerical evaluation to illustrate the results and to estimate the scale for sfBm as a semi-selfsimilar process. We also present another simulation and show the efficiency of our method in estimation of Hurst parameter by comparing its performance with some previous methods.

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