A Note on the Asymptotic Behavior of the LSE's of the Parameters for Superimposed Exponential Signals in Presence of Stationary Noise

SYNOPTIC ABSTRACT

Superimposed exponential signals play an important role in Statistical Signal Processing and Time series analysis. In this note, the asymptotic behavior of the least squares estimators of the parameters are obtained in presence of stationary noise for the undamped exponential model. It is well known that this model does not satisfy the sufficient conditions of Jennrich (1969), Wu (1981) or Kundu (1991) for the least squares estimators to be consistent even when the errors are independent and identically distributed random variables with mean zero and finite variance. This paper extends some of the earlier works of Hannan (1971, 1973), Walker (1971), Bai, Chen, Krishnaiah, Wu and Zhao (1991), Rao and Zhao (1993), Kundu (1995) and Kundu and Mitra (1996, 2000) in different ways. Some numerical experiments are performed to observe the small sample behavior of the least squares estimators.

Key Words and Phrases:

• Asymptotic covariance
• exponential signals
• stationary noise
• complex normal distribution
• least squares estimators