Date(s) : 15/05/2023 iCal
14 h 00 min - 16 h 00 min
Despite their importance in many fields (e.g. dynamic discrete choice models in Econometrics or dynamic graphs in statistics), little has been done to formalize a general probabilistic framework that is flexible enough to analyze complex time series models for categorical data.
In this talk, we will present some general results that can be used to conduct statistical inference with such series when
1) both an endogenous and exogenous (random covariates) part are included in the regressors,
2) mixing conditions are necessary for non-parametric inference,
3) local inference is necessary to deal with nonstationarity.
We will discuss two different formalisms that can be used to solve the three points mentioned above, depending on the exogeneity conditions on the regressors.
The first one, compatible with strictly exogenous covariates, consists in exploiting the properties of finite-state Markov chains in random environments.
The second one, compatible with sequentially exogenous regressors, is based on some coalescence properties of iterated random map systems on finite set.
As a consequence, one can provide theoretical guarantees for statistical inference in almost all the autoregressive time series models found in literature.
FRUMAM, St Charles