Application Of Functional Time Series Analysis Method In High-frequency Stock Price Forecasting

With the rapid development of the Internet and the rapid transmission of information,the data that carries the information can be frequently recorded and saved.At present,a large amount of data can be recorded in a nearly continuous manner.This kind of data carries more information than the data recorded at a long time interval,but it also has some problems,such as long calculation time and efficiency low and if handled carelessly,it may cause dimensionality disasters,etc.Driven by advances in technology,such data have attracted many statisticians to study them.The method of analyzing discrete observation data as elements in an infinite-dimensional function space is called functional data analysis,and its analysis object is curve rather than discrete data.At present,functional data analysis methods have been widely used in many scientific fields such as environment,meteorology,ecology,psychology,etc.However,the financial field such as stock price forecasting has few applications in this field.In recent years,investing in stocks and funds has attracted a large number of people.The volatility of stock market prices has become a hot topic of discussion.Scholars are also constantly studying how to minimize investment risks while ensuring the rate of return.However,due to too many factors affecting stock prices,there is not a completely appropriate model to fit the fluctuation of stock prices and predict it.In this paper,the functional data analysis method is applied to several highfrequency stock price data,and the functional principal component prediction method,the functional weighted principal component prediction method,the functional dynamic principal component analysis and factor analysis combined with the second dimension reduction prediction method are used to predict the stock price in one step.This article uses two data sets to analyze the applicability,advantages and disadvantages of these three forecasting methods under different conditions in the stock market.The two data sets are:22 days and 5 minutes of HFT price sample data of 20 stocks randomly selected in the same period of time;In the three stock market conditions of consolidation,decline and rise,6 stock samples were selected respectively,and a total of 18 stocks were collected for 5 minutes of high-frequency trading price data within 21 days.This article compares the performance of these three methods in high-frequency time series from the perspective of prediction accuracy and model time complexity.Three methods are used to predict 38 stocks.According to the prediction results,it can be concluded that in terms of prediction accuracy:If the stock market is in an unknown volatility state,the functional weighted principal component prediction method has better prediction accuracy for the stock market trading price on the next day.If the stock market is in a consolidation state,the second dimension reduction forecasting method is more accurate to the stock price prediction of the next day;If the stock market is in a state of decline,the prediction accuracy of the functional weighted principal component method is better.If the stock market is in a rising state,one of three methods can be used to predict the price of the stock.In terms of the time complexity of the models:The quadratic dimension reduction prediction method is more operable,and the prediction time is the shortest,and the prediction time of the functional weighted principal component is the longest,which is about 25 times that of the quadratic dimension reduction method.