Mixing properties of nonstationary multivariate count processes

We prove absolute regularity ($\beta$-mixing) for nonstationary and multivariate versions of two popular classes of integer-valued processes. We show how this result can be used to prove asymptotic normality of a least squares estimator of an involved model parameter

Autoregressive models for time series of random sums of positive variables: Application to tree growth as a function of climate and insect outbreak

We present a broad class of semi-parametric models for time series of random sums of positive variables. Our methodology allows the number of terms inside the sum to be time-varying and is therefore well suited to many examples encountered in the natural sciences. We study the stability properties of the models and provide a valid statistical inference procedure to estimate the model parameters. It is shown that the proposed quasi-maximum likelihood estimator is consistent and asymptotically Gaussian distributed. This work is complemented by simulation results and applied to time series representing growth rates of white spruce (Picea glauca) trees from a few dozen sites in Quebec (Canada). This time series spans 41 years, including one major spruce budworm (Choristoneura fumiferana) outbreak between 1968 and 1991. We found significant growth reductions related to budworm-induced defoliation up to two years post-outbreak. Our results also revealed the positive effects of maximum summer temperature, precipitation, and the climate moisture index on white spruce growth. We also identified the negative effects of the climate moisture index in the spring and the maximum temperature of the previous summer. However, the model's performance on this data set was not improved when the interactions between climate and defoliation on growth were considered. This study represents a major advance in our understanding of budworm-climate-tree interactions and provides a useful tool to project the combined effects of climate and insect defoliation on tree growth in a context of greater frequency and severity of outbreaks coupled with the anticipated increases in temperature

Adjacent-category models for ordinal time series and their application to climate-dependent spruce budworm defoliation dynamics

This work proposes an adjacent-category autoregressive model for time series of ordinal variables. We apply this model to dendrochronological records to study the effect of climate on the intensity of spruce budworm defoliation during outbreaks in two sites in eastern Canada. The model's parameters are estimated using the maximum likelihood approach. We show that this estimator is consistent and asymptotically Gaussian distributed. We also propose a Portemanteau test for goodness-of-fit. Our study shows that the seasonal ranges of maximum daily temperatures in the spring and summer have a significant quadratic effect on defoliation. The study reveals that for both regions, a greater range of summer daily maximum temperatures is associated with lower levels of defoliation up to a threshold estimated at 22.7C (CI of 0-39.7C at 95%) in T\'emiscamingue and 21.8C (CI of 0-54.2C at 95%) for Matawinie. For Matawinie, a greater range in spring daily maximum temperatures increased defoliation, up to a threshold of 32.5C (CI of 0-80.0C). We also present a statistical test to compare the autoregressive parameter values between different fits of the model, which allows us to detect changes in the defoliation dynamics between the study sites in terms of their respective autoregression structures

Non-linear multivariate time series models with exogenous regressors

Dans cette thèse, on s'intéresse aux propriétés probabilistes et statistiques de modèles de séries temporelles non-linéaires qui prennent en compte des covariables exogènes. Les séries temporelles de comptage ou catégorielles sont en particulier considérées ainsi que la modélisation de données mixtes en multivarié. Des propriétés de stationnarité sont établies pour ces modèles à partir de techniques d'itérations d'application aléatoires dépendantes. Dans le cas multivarié, des approches par pseudo-vraisemblance et/ou utilisation de copules sont utilisées pour l'inférence statistique. Enfin, une application de certains de ces méthodes dans le cadre de l'écologie est présentée.In this dissertation, we are interested in the probabilistic and statistical properties of non-linear time series models with exogenous covariates. In particular, count and categorical time series data are considered as well as the multivariate models for mixed data. Stationarity properties are established for these models using the tehniques of iterations of dependent random maps. In the multivariate case, pseudo-likelihood and/or copula approaches are used for statistical inference. Finally, an application of some of these methods in the context of ecology is presented

Modèles de séries temporelles multivariées non-linéaires avec régresseurs exogènes

In this dissertation, we are interested in the probabilistic and statistical properties of non-linear time series models with exogenous covariates. In particular, count and categorical time series data are considered as well as the multivariate models for mixed data. Stationarity properties are established for these models using the tehniques of iterations of dependent random maps. In the multivariate case, pseudo-likelihood and/or copula approaches are used for statistical inference. Finally, an application of some of these methods in the context of ecology is presented.Dans cette thèse, on s'intéresse aux propriétés probabilistes et statistiques de modèles de séries temporelles non-linéaires qui prennent en compte des covariables exogènes. Les séries temporelles de comptage ou catégorielles sont en particulier considérées ainsi que la modélisation de données mixtes en multivarié. Des propriétés de stationnarité sont établies pour ces modèles à partir de techniques d'itérations d'application aléatoires dépendantes. Dans le cas multivarié, des approches par pseudo-vraisemblance et/ou utilisation de copules sont utilisées pour l'inférence statistique. Enfin, une application de certains de ces méthodes dans le cadre de l'écologie est présentée

Modèles de séries temporelles multivariées non-linéaires avec régresseurs exogènes

In this dissertation, we are interested in the probabilistic and statistical properties of non-linear time series models with exogenous covariates. In particular, count and categorical time series data are considered as well as the multivariate models for mixed data. Stationarity properties are established for these models using the tehniques of iterations of dependent random maps. In the multivariate case, pseudo-likelihood and/or copula approaches are used for statistical inference. Finally, an application of some of these methods in the context of ecology is presented.Dans cette thèse, on s'intéresse aux propriétés probabilistes et statistiques de modèles de séries temporelles non-linéaires qui prennent en compte des covariables exogènes. Les séries temporelles de comptage ou catégorielles sont en particulier considérées ainsi que la modélisation de données mixtes en multivarié. Des propriétés de stationnarité sont établies pour ces modèles à partir de techniques d'itérations d'application aléatoires dépendantes. Dans le cas multivarié, des approches par pseudo-vraisemblance et/ou utilisation de copules sont utilisées pour l'inférence statistique. Enfin, une application de certains de ces méthodes dans le cadre de l'écologie est présentée

Effect of landscape diversity and crop management on the control of the millet head miner, Heliocheilus albipunctella (Lepidoptera: Noctuidae) by natural enemies

The pearl millet head miner, Heliocheilus albipunctella, is a major constraint to increasing crop productivity in sub-Saharan Africa. In the absence of any insecticide application by farmers, its control mostly relies on the action of natural enemies. The objective of the present study is to identify crop management and landscape features affecting biocontrol services by natural enemies. A set of 45 millet fields were selected in a 20 ∗ 20 km area in Senegal, from the analysis of high resolution satellite images (Pleiades), and hypotheses on relative abundance of millet fields and semi-natural habitats (mainly trees) in the agricultural landscape. A biocontrol service index (BSI) was computed for each field over two cropping seasons by experimentally excluding natural enemies from naturally egg-infested millet panicles. Information on crop management was collected through farmer's interviews. An information theoretical approach and model averaging were performed to rank the effect of landscape metrics on BSI at eight spatial scales (from 250 to 2000 m). The BSI was generally high (77%) but highly variable among fields (0–100%), and was greater in compound fields compared to bush fields. The BSI also increased with the abundance of tree patches and the diversity of vegetation in a 1750 m-buffer around millet fields. Results support previous studies stressing the importance of semi-natural areas and vegetation diversity to support pest regulation by natural enemies. Further research is needed to better understand relationships between agroforestry systems and biological control, to promote ecologically-intensive solutions for reducing crop losses