1 Multifactor Modelling with Regularization Dr. Ventsislav Nikolov Senior Software Developer Eurorisk Systems Ltd. 31, General Kiselov Str., 9002 Varna, Bulgaria Е-mail: vnikolov аt eurorisksystems dot com Keywords: Multifactor, Polynomial Formula, Basis Functions, Genetic Algorithm, Least Squares Regression, Regularization 1. INTRODUCTION Suppose we are given a finite number of discrete time series xi called factors. They can represent arbitrary physical, social, financial or other indicators. All factors are with equal length and their values correspond to measurements performed in equal time intervals. One of the series is chosen to be a target factor and some of the others are chosen to be explanatory factors. The aim is to create a formula by which a series can be generated, using the explanatory factors for the given historical period, that should be as close as possible to the given target series, using a chosen criterion [4]. For simplicity such a criterion can be the Euclidean distance between the target and generated factor for all data points. Such a created formula can be used for different purposes in the financial instruments modelling, sensitivity analysis, etc. In the case of predictable explanatory factors and unpredictable target factor analysis can be performed about the influence of the explanatory factors changes to the target factor. The formula can be created in different forms but simplifying the solution the following polynomial form is used: y = β1f1(x1) + β 2f2(x2) + ... + β mfm(xm) + β m+1 (1) where f1, f2, …fm are arbitrary basis functions, and β 1, β 2, … β m are regression coefficients, β m+1 is a free term without explanatory factor. 2. FORMULA GENERATION First of all, the target factor is selected according to the specific purposes. After that the explanatory factors are selected amongst the all available series. In our solution a few alternative approaches can be used as selection of the most correlated factors to the target factor or minimal correlated each other or so on. When both the target and explanatory factors are selected the automatic modelling, stage is performed by repeating the stages of applying basis functions to explanatory factors and after that calculation of the regression coefficients. Taking into account that for all selected factors all basis functions can be applied, there are k m combinations, where k is the number of the basic functions and m is the number of the explanatory factors. Usually in the practice the factors are a few hundred and the functions are a few dozen. Thus, the brute force searching of the best basis functions combination is practically impossible. That is why for