本文将小波的方法引入到股票指数的分析和未来趋势的预测中，利用小波的分解和重构，以及其多尺度分析的功能，分析历史数据并提出了一种预测其趋势的方法。主要思想是将原数据当作一维时间信号作小波分解，并逐层重构，将重构序列用余弦函数逼近和预测，再将各层结果整合得到对原信号的逼近和预测。这种方法的特点在于从股指的历史数据中总体把握股指和其收益率的非线性波动特征，从而对未来一段时间进行预测。通过对上证指数1990年底开始至2007年结束这段时间的日收盘指数运用该方法进行分析，得到了股指在十几年内的变化规律具有周期性这一行为特征，在此基础上对未来趋势做出预测，经验证得到了较为理想的结果。

Using wavelet decomposition, reconstruction and multi-scale analysis, we analyze stock data and conclude a method of long-term trend forecasting. The main idea of this approach is to consider stock index data as a one-dimensional time signal and apply wavelet decomposition and reconstruction to original signal, approximate and forecast reconstructed series layer-by-layer by using cosine functions, then conclude final approximation and forecasting of original signal. The advantage of the wavelet long-term trend forecasting approach is that it can reflect long-term trend and non-linear characteristic of the stock index and daily gain rate series fluctuation depending on the historical data, thus we can forecast the stock index in a relatively long future. By applying this wavelet long-term trend forecasting approach to the historical data of Shanghai Composite Index (SCI) daily closing index from 1990 to 2007, we generalize that SCI follows a behavior characteristic of periodic variation during past 16 years. The forecasting of stock index trend is based on the periodic fluctuation and the results turn to be relatively optimal.