  The main object of investigation in this paper is a very general regression
model in optional setting - when an observed process is an optional
semimartingale depending on an unknown parameter. It is well-known that
statistical data may present an information flow/filtration without usual
conditions. The estimation problem is achieved by means of structural least
squares (LS) estimates and their sequential versions. The main results of the
paper are devoted to the strong consistency of such LS-estimates. For
sequential LS-estimates the property of fixed accuracy is proved.
