0000000000627238
AUTHOR
Zaka Ratsimalahelo
Théorie de système et séries temporelles
The aim of this paper is to present a different representation of state space models, (innovation state space representation) which is relatively new and apparently unknown in the economics and econometrics literature and to describe some of its properties. state space representation is a very flexible form for time series and the approach taken in this paper therefore allows a broad class of models it does not impose a priori the decomposition of data series into trend and cycle
Recursive estimators 2
In this paper the techniques for recursive estimation of linear model are extended to non-spherical disturbances. First we present the recursive formulae of generalized least squares. The recurrence relation for the residual sum of squares are derived. We show in the second part of the paper a recursive formulae of generalized instrumental variables.
La décomposition canonique et la cointégration
This paper has introduced state space models for cointegrated time series. In doing so, the notion of cointegration is slightly generalized. We develop the notion of dynamic aggregation link with error correction model and common trends.
On approximate system dynamic
In this paper concepts and techniques from system theory are used to obtain state-space (Markovian ) models of dynamic economic processes instead of the usual VARMA models. In this respect the concept of state is reviewed as are Hankel norm approximations,and balanced realizations for stochastic models. We clarify some aspects of the balancing method for state space modelling of observed time series. This method may fail to satisfy the so-called positive real condition for stochastic processes. We us a state variance factorization algorithm which does not require us to solve the algebraic Riccati equation. We relate the Aoki-Havenner method to the Arun - Kung method.
Canonical correlation in multivariate time series analysis
We analyze a class o f state space identification algorithms for time series, based on canonical correlation analysis in the ligth of recent results on stochastic systems theory calle d « subspace methods » .These can be describe as covariance estimation followed b y stochastic realization .The methods offer the major advantage o f converting the nonlinear parameter estimation phase in traditional V A R M A models identification in to the solution o f Riccati equation but introduce at the same time some no n trivial mathematical problem s related to positivity. The states o f the forward -backward innovations representation have an interpretation : Instrumental Variables estimators .
Recursive estimators 1
In this paper, we present first the recursive estimation of parameters of linear regression models and we show the link between a matrix of projection and a matrix of gain. Two cases are examined : constant parameters and parameters changing over time. In the second part the recursion formulae for the two stage least squares are given.