We study the role of partial autocorrelations in the reparameterization and parsimonious modeling of a covariance matrix. The work is motivated by and tries to mimic the phenomenal success of the partial autocorrelations function (PACF) in model formulation, removing the positive-definiteness...

A generalized innovation algorithm is used to solve the problems of prediction of future values based on incomplete past and interpolation of missing values of a stationary time series. The emphasis is on the computational aspects and the proposed method is particularly useful when there are...

The multi-variate t distribution provides a viable framework for modelling volatile time-series data; it includes the multi-variate Cauchy and normal distributions as special cases. For multi-variate t autoregressive models, we study the nature of the innovation distribution and the prediction...

Longitudinal studies are prevalent in biological and social sciences where subjects are measured repeatedly over time. Modeling the correlations and handling missing data are among the most challenging problems in analyzing such data. There are various methods for handling missing data, but...

Important results in prediction theory dealing with missing values have been obtained traditionally using difficult techniques based on duality in Hilbert spaces of analytic functions [Nakazi, T., 1984. Two problems in prediction theory. Studia Math. 78, 7-14; Miamee, A.G., Pourahmadi, M., 1988....