Empirical likelihood method for longitudinal data generated from unequally-spaced Lèvy processes

By introducing the notion of “empirical likelihood function of observing sums”, unequally-spaced time series data and longitudinal data generated from Lévy processes can be analyzed. Characteristic function is further incorporated to handle the situations where the density function of the increments is difficult to obtain. In the situations where both characteristic function and the density function are available, it is shown through the simulation examples that the proposed empirical maximum likelihood method does not suffer from significant information loss comparing to the maximum likelihood estimation method. The performances of the proposed method is tested for both equally-spaced and unequally-spaced observations.