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New Frontiers in Banking Services Emerging Needs and Tailored Products for Untapped Markets_3

Tham khảo tài liệu 'new frontiers in banking services emerging needs and tailored products for untapped markets_3', tài chính - ngân hàng, tài chính doanh nghiệp phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 3.2 The Nonlinear Estimation Problem 65 and then taking the logsigmoid transformation of the standardized series z __ x 1 1 exp z x x z ơx 3.16 3.17 Which type of scaling function works best depends on the quality of the results. There is no way to decide which scaling function works best on a priori grounds given the features of the data. The best strategy is to estimate the model with different types of scaling functions to find out which one gives the best performance based on in-sample criteria discussed in the following section. 3.2 The Nonlinear Estimation Problem Finding the coefficient values for a neural network or any nonlinear model is not an easy job certainly not as easy as parameter estimation with a linear approximation. A neural network is a highly complex nonlinear system. There may be a multiplicity of locally optimal solutions none of which deliver the best solution in terms of minimizing the differences between the model predictions y and the actual values of y. Thus neural network estimation takes time and involves the use of alternative methods. Briefly in any nonlinear system we need to start the estimation process with initial conditions or guesses of the parameter values we wish to estimate. Unfortunately some guesses may be better than others for moving the estimation process to the best coefficients for the optimal forecast. Some guesses may lead us to a local optimum that is the best forecast in the neighborhood of the initial guess but not the coefficients for giving the best forecast if we look a bit further afield from the initial guesses for the coefficients. Figure 3.1 illustrates the problem of finding globally optimal or globally minimal points on a highly nonlinear surface. As Figure 3.1 shows an initial set of weight values anywhere on the x axis may lie near to a local or global maximum rather than a minimum or near to a saddle point. A minimum or maximum point has a slope or derivative equal to zero. At a maximum point the .