Title of article :
Parametric estimation of the driving Lévy process of multivariate CARMA processes from discrete observations
Author/Authors :
Brockwell، نويسنده , , Peter J. and Schlemm، نويسنده , , Eckhard، نويسنده ,
Issue Information :
دوفصلنامه با شماره پیاپی سال 2013
Pages :
35
From page :
217
To page :
251
Abstract :
We consider the parametric estimation of the driving Lévy process of a multivariate continuous-time autoregressive moving average (MCARMA) process, which is observed on the discrete time grid ( 0 , h , 2 h , … ) . Beginning with a new state space representation, we develop a method to recover the driving Lévy process exactly from a continuous record of the observed MCARMA process. We use tools from numerical analysis and the theory of infinitely divisible distributions to extend this result to allow for the approximate recovery of unit increments of the driving Lévy process from discrete-time observations of the MCARMA process. We show that, if the sampling interval h = h N is chosen dependent on N , the length of the observation horizon, such that N h N converges to zero as N tends to infinity, then any suitable generalized method of moments estimator based on this reconstructed sample of unit increments has the same asymptotic distribution as the one based on the true increments, and is, in particular, asymptotically normally distributed.
Keywords :
Infinitely divisible distribution , Multivariate CARMA process , Parameter estimation , High-frequency sampling , Generalized Method of Moments
Journal title :
Journal of Multivariate Analysis
Serial Year :
2013
Journal title :
Journal of Multivariate Analysis
Record number :
1566135
Link To Document :
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