Stock index is an indicator that describes the changes in the total price level of the stock market, and it is susceptible to many dynamic factors, with such characteristics as high dimension, uncertainty, non-linearity, time delay, complexity, etc., resulting in abnormal and missing values in stock index data, which will lead to instability or unreliability of the stock index tracking model. In order to solve these problems, we take the historical stock index as the input, model the internal dynamic changes of features, and learn the change rule. Firstly, we introduce an attention mechanism, that is, to assign different weights to the implicit state of the long short term memory network (LSTM) through mapping weights and learning parameters. We further propose a stock index data preprocessing model of the LSTM based on the attention mechanism. Secondly, the group method of data handling type neural networks (GMDH-NN) is a self-organizing data mining technology, which is especially suitable for modeling complex systems. So we choose a discrete form of Kolmogorov-Gabor ( K-G ) polynomial of the first-order as the reference function of GMDH-NN to establish the general relationship between input and output variables. We further present a deep evolutionary GMDH polynomial neural network (DGMDH) to perform stock index tracking. Moreover, for a high-dimensional stock index dataset, the traditional external criterion can no longer meet the needs of reality, so we propose a tracking error external criterion (TEEC) for stock indices, which is based on the difference between allocation yield and target yield. The TEEC provides better information for selecting the optimal complex DGMDH model. Our experiments clearly show the effectiveness of our methodology.