The Least Squares Method (LSM) is reliable and prevalent means to solve prediction problems in applied research and in econometrics particularly. It is used in the case when the function is represented by its observations. Commonly used statistical form of LSM is called Regression Analysis (RA). It is necessary to say, that RA is only statistical shape for representing the link between the components in observations. So using RA terminology of LSM for solution of function estimating problem, and correspondingly, – prediction problem, is only the form for problem discussing.
It is opportune to note, that the LSM is equivalent to Maximum Likelihood Method for classic normal regression. This method is widely used in econometric problems. The development of technical capabilities of LSM for solution of optimization and predictive application tasks is proposed. Some examples of the least squares method for macroeconomic models parameters identification are given in. Linear regression (LA) within RA has the advantage of having a closed form solution of parameter estimation
Problem and prediction problem. Real valued functions of vector argument are the object of investigation in RA in general and in LA in particular. Such suppositions are due to technical capabilities of technique for solving optimization problems in LSM. This technique is in the essence an investigation of extremum necessary conditions. This remark is entirely true for yet another widely used assumption, namely, full column rank assumption for appropriate matrix, which ensure uniqueness of parameter estimation. It’s interesting that another technique: Moore – Penrose pseudo inverse (M-Ppi) provides a comprehensive study and solution of parameter estimation problem.
And the remark in conclusion. Obvious advantage of matrixes LSM, besides the explicit closed estimation form, is the fact that matrixes observations preserve relationships between the characteristics of phenomenon under consideration. Examples of matrix least square method in macroeconomic and business problems with different types of relations between input and output data and different degree data discretization are given in.