Using ARIMA Model To Fit And Predict Index Of Stock Price Based On Wavelet De-Noising

Analysis and prediction of the stock price index(SPI)has been a hot research topic for decades.To accommodate the non-stationarity and strong noise in the SPI data,we use wavelet method for denoising and autoregressive integrated moving average model(ARIMA)for prediction.The seven-day moving average of closing time SPI data in four Asian stock markets,i.e.,Hong Kong Hang Seng Index(HSI),Taiwan Weighted Index(TAIEX),Shanghai Composite Index(SSE)and Shenzhen Component Index(SZSE)are analyzed.First,we use wavelet multi-resolution analysis to conduct wavelet fast decomposition for the SPI time series,and obtain trend coefficient sequences and detail coefficient sequences.After that.we reconstruct the de-noising SPI time series by soft-thresholding at each level.With the de-noised signal obtained,we build ARIMA model to fit it.Our results show that,for more developed market indexes such as HSI and TAIEX,noise can be removed effectively using wavelet method.Combination of ARIMA model with wavelet de-noising has better prediction results than using ARIMA model alone.Simulation results show that:The more developed markets,the better such new model is used.The fitted and predicted details show that developed market(HSI&TAIEX)have better regulations,and the market participants have higher level of operation and education,the short-term trading behaviors of investors are more rational.Above all,noise can be separated from high frequency signal more easily in more developed market,and valuable high-frequency signals are preserved and generate a positive role in the subsequent predictive modeling process,relative to the developing markets(SSE&SZSE).This is in accordance with current situation of these markets.More developed markets have better predictability as they have better regulations and more experienced investors;for less developed markets,many investors are inexperienced and their behaviors are more dramatically influenced by many factors.The research is helpful for investors to judge the situation of the stock market and make corresponding measures correctly.