tailieunhanh - Elsevier, Neural Networks In Finance 2005_2

Tham khảo tài liệu 'elsevier, neural networks in finance 2005_2', tài chính - ngân hàng, ngân hàng - tín dụng phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Part I Econometric Foundations 11 2 What Are Neural Networks Linear Regression Model The rationale for the use of the neural network is forecasting or predicting a given target or output variable y from information on a set of observed input variables x. In time series the set of input variables x may include lagged variables the current variables of x and lagged values of y. In forecasting we usually start with the linear regression model given by the following equation yt ỳ k Xk t kt kt N 0 Ơ2 where the variable et is a random disturbance term usually assumed to be normally distributed with mean zero and constant variance Ơ2 and -k represents the parameters to be estimated. The set of estimated parameters is denoted -k while the set of forecasts of y generated by the model with the coefficient set j3k is denoted by yt . The goal is to select j3k to minimize the sum of squared differences between the actual observations y and the observations predicted by the linear model y. In time series the input and output variables y x have subscript t denoting the particular observation date with the earliest .