Neural network linear forecasts for stock returns Angelos Kanas, страница 9

5.  The weights are updated by the following method: w_i,t=w_i,t−1+n[E/w]+a(w_i,t−1−w_i,t−2), where n is the learning parameter and a is the momentum coefficient. The learning rate captures the contribution of the weight to the objective. Thus, a high learning rate may speed up convergence, but it may also lead to over-correction and failure to converge. By contrast, low learning rate may prolong convergence. The momentum value, a, determines how much of the previous update should be carried on the current stage. The larger the momentum value, the greater the influence of the last update error. The actual value of the weights, once convergence is achieved, may be sensitive to the choice of the learning and momentum parameters. In this study, the value of the learning rate was set equal to 0.5 and the value of momentum equal to 0.8.

6.  For a complete discussion of this model selection procedure and its optimality properties, see Kavalieris (1989).

7.  The inclusion in the linear model of the same explanatory variables does not by itself entail nesting of the linear model by thenonlinear model. The nonlinear ANN model will nest the linear one if all of the three following conditions are met. First, the explanatory variables are the same. Second, in Equation (1) the function f( . ) is not the identity function. Third, in Equation (1), b_i=0.

8.  The forecast encompassing test has an easily derivable distribution when applied to out-of-sample data, but not when applied tothe in-sample data (Donaldson and Kamstra, 1997). Therefore, we present our results only for the out-of-sample forecast encompassing tests.

9.  Using different specifications, Kanas and Yannopoulos (1999) reached similar conclusions.

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