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ASYMPTOTIC INFERENCE FOR THE PARAMETERS OF A DISCRETE‐TIME SQUARE‐ROOT PROCESS
Author(s) -
Frydman Halina
Publication year - 1994
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.1994.tb00056.x
Subject(s) - estimator , mathematics , asymptotic analysis , square root , asymptotic distribution , consistency (knowledge bases) , inference , unit root , square (algebra) , econometrics , statistics , computer science , discrete mathematics , geometry , artificial intelligence
This paper is concerned with asymptotic properties of the maximum likelihood estimators for the discrete‐time square‐root process. This process and its generalizations are employed in financial literature as models for movements of asset prices. the considered process is nonergodic and therefore standard maximum likelihood theory does not apply. the nonstandard asymptotic theory is developed. Strong consistency of the estimators is established, joint asymptotic distribution of the properly normalized estimators is obtained and confidence intervals for the parameters are constructed. the results of the small simulation study are reported.