Recursive Least Squares

There appears to be a substantial amount of criticism levelled these days at the deleterious effect that computers are having on the algebraic (especially manipulative) skills of students. Clearly computers do have an important part to play in a subject such as statistics but the article by Searle (1983) reminds us that sensible algebraic pre-planning can often improve the accuracy of estimation procedures many of which will be carried out by computer. There are a wide variety of problems in the real world (steering supertankers, short-term prediction of power loads and economic planning are typical examples) which students are happy to discuss and where there is a rapid awareness that model structures are updated regularly as new data becomes available. When the model structure is well understood and data becomes available a t regular intervals of time, and particularly where the requirement is for rapid updating, then recursive or online procedures are most useful. Many recursive algorithms require substantial algebraic manipulation to make them easy to implement on a computer. Once this manipulation is completed however, the updating can be carried out rapidly and data storage is minimal.