On the forecasting of high‐frequency financial time series based on ARIMA model improved by deep learning

• DOI: http://doi.org/10.1002/for.2677
• Author: Jing Han,Zhenwei Li,Yuping Song
• Published date: 01 November 2020
• Date: 01 November 2020

RESEARCH ARTICLE

On the forecasting of high-frequency financial time series

based on ARIMA model improved by deep learning

Zhenwei Li

1

| Jing Han

2

| Yuping Song

1

1

School of Finance and Business,

Shanghai Normal University, Shanghai,

PR China

2

School of Finance and Management,

Shanghai University of International

Business and Economics, Shanghai, PR

China

Correspondence

Yuping Song, School of Finance and

Business, Shanghai Normal University,

Shanghai, 200234, PR China.

Email: songyuping@shnu.edu.cn

Funding information

Academic Innovation Team of Shanghai

Normal University, Grant/Award

Number: 310-AC7031-19-004228; Key

Subject of Quantitative Economics of

Shanghai Normal University, Grant/

Award Number: 310-AC7031-19-004221;

Academic Innovation Team, Grant/Award

Number: 310-AC7031-19-004228; Key

Subject of Quantitative Economics, Grant/

Award Number: 310-AC7031-19-004221;

General Research Fund of Shanghai

Normal University, Grant/Award

Number: SK201720; Youth Academic

Backbone Cultivation Project of Shanghai

Normal University, Grant/Award

Number: 310-AC7031-19-003021; National

Statistical Science Research Project,

Grant/Award Number: 2018LZ05;

Ministry of Education, Humanities and

Social Sciences project, Grant/Award

Number: 18YJCZH153; National Natural

Science Foundation of China, Grant/

Award Number: 11901397

Abstract

Through empirical research, it is found that the traditional autoregressive inte-

grated moving average (ARIMA) model has a large deviation for the forecast-

ing of high-frequency financial time series. With the improvement in storage

capacity and computing power of high-frequency financial time series, this

paper combines the traditional ARIMA model with the deep learning model to

forecast high-frequency financial time series. It not only preserves the theoreti-

cal basis of the traditional model and characterizes the linear relationship, but

also can characterize the nonlinear relationship of the error term according to

the deep learning model. The empirical study of Monte Carlo numerical simu-

lation and CSI 300 index in China show that, compared with ARIMA, support

vector machine (SVM), long short-term memory (LSTM) and ARIMA-SVM

models, the improved ARIMA model based on LSTM not only improves the

forecasting accuracy of the single ARIMA model in both fitting and forecast-

ing, but also reduces the computational complexity of only a single deep learn-

ing model. The improved ARIMA model based on deep learning not only

enriches the models for the forecasting of time series, but also provides effec-

tive tools for high-frequency strategy design to reduce the investment risks of

stock index.

KEYWORDS

ARIMA model, high-frequency financial time series, LSTM model, SVM model

1|INTRODUCTION

According to the historical data, an appropriate forecast-

ing model can be constructed to capture the fluctuating

signals of the underlying time series and characterize

their trend, which can provide a reliable basis for

investors’decision making. For example, through accu-

rate forecasting of the stock index, investors can roughly

grasp the overall trend of the market to effectively cap-

ture trading opportunity and make reasonable

asset allocations. As for the forecasting models of time

series, based on classical models such as autoregressive

Received: 17 June 2019 Revised: 13 December 2019 Accepted: 22 February 2020

DOI: 10.1002/for.2677

Journal of Forecasting. 2020;39:1081–1097. wileyonlinelibrary.com/journal/for © 2020 John Wiley & Sons, Ltd. 1081

(AR; Yule, 1927) and moving average (MA;

Walker, 1931), the autoregressive moving average model

(ARMA) and autoregressive integrated moving average

model (ARIMA) were proposed (Box, Jenkins, Reinsel, &

Ljung, 2015). After making the original nonstationary

time series to be stationary after d-order difference, the

ARIMA model then can estimate and test the stationary

sequence. It has become one of the more widely used

methods in the study of forecasting models for time

series. The ARIMA model has been used to predict sales

of retail footwear products in one step and multiple steps

and it was found that the ARIMA model had a good fit-

ness for the forecasting of time series (Ramos, Santos, &

Rebelo, 2015).

For financial time series, using the autocorrelation

function, more scholars have verified that financial time

series were time varying (Ding, Granger, & Engle, 1993),

and that the financial data presented the characteristics

of nonlinearity (Chevallier & Sévi, 2012; Giot, Laurent, &

Petitjean, 2010; Slim & Dahmene, 2016). The time-

varying and nonlinear properties and the large stochastic

volatility of the sample data in the financial market have

posed certain difficulties for quantitative forecasting

based on only a single model. Many scholars have

improved the ARIMA model to enhance the accuracy of

forecasting. Based on the linear error correction model,

the ARIMA model was modified by using the support

vector machine (SVM) model to forecast financial time

series and improve forecasting accuracy (Van Gestel

et al., 2006). Particle swarm optimization (PSO) was

adopted to modify the ARIMA-SVM combination model

and to improve the accuracy of forecasting for time series

(de Oliveira & Ludermir, 2014). Accuracy of predictive

power demand was improved by the error correction

model based on PSO optimal Fourier and seasonal

ARIMA (Wang, Wang, Zhao, & Dong, 2012). By consider-

ing a hybrid correction method based on the ARIMA

model, SVM, and cuckoo search algorithm (CSA), the

ARIMA model was modified to predict the power load

(Kavousi-Fard & Kavousi-Fard, 2013).

The above research was mainly focused on daily or

weekly low-frequency data for modeling and forecasting.

However, with the development of science and technol-

ogy, the era of big data had arrived and the storage and

computing power for high-frequency data were

improved. In addition, by using intraday high-frequency

data to estimate volatility, Andersen, Bollerslev, Diebold,

and Labys (2003) found that high-frequency data con-

tained more market information than low-frequency

data, which could improve the accuracy of estimation.

High-frequency data could provide more arbitrage space

and more possibilities for strategy design (Hanson &

Hall, 2012). High-frequency financial time series also

changed the philosophy of investment strategy design

and the investor's investment style. Up to 2012, the total

transaction volume of high-frequency transactions

accounted for 50–80% of the total transaction volume of

US equity (Barrales, 2012; Laughlin, Aguirre, &

Grundfest, 2014), and the proportion reached 45% in

Europe, 40% in Japan, and about 12% in other Asian

countries (Menkveld, 2014). In 2014, the development of

high-frequency trading made even greater progress.

Through the study of a large number of financial inter-

mediaries, Biais and Foucault (2014) confirmed that in

the process of running capital for financial intermedi-

aries, although they were not named as high-frequency

transactions, they were also consistent with the charac-

teristics of high-frequency trading strategies.

ARIMA models and their modified models in the

existing literature are mostly used in the nonfinancial

field, and sample frequencies for forecasting have been

relatively low. However, with the increase in frequency

of financial data, high-frequency data are highly

nonlinear (Jobson & Korkie, 1981) and nonnormal

(Jacquier, Polson, & Rossi, 2002). Owing to these charac-

teristics of high-frequency data that do not conform to

the traditional low-frequency model hypothesis, the fore-

casting error for high frequency data based on low-

frequency financial time series model has gradually

become larger. How to modify the ARIMA model and

migrate it to high-frequency forecasting has a significant

and practical research value. Currently, few studies have

used the deep learning method to correct the ARIMA

model error or to improve the forecasting accuracy of

high-frequency financial data. Therefore, this paper aims

to modify the traditional ARIMA model by using the

machine-derived deep learning long short-term memory

(LSTM) model. Compared with the machine learning

SVM model and other modified models, the deep learn-

ing corrected model not only can reduce the error of the

forecasting model and improve forecasting accuracy, but

it can also reduce model complexity and improve predic-

tive performance. Methodologically, the ARIMA-LSTM

model not only preserves the stability and interpretability

of the traditional ARIMA model, but also absorbs the

long memory of the deep learning model for time series.

Practically, the ARIMA-LSTM model can reduce the

complexity of the deep learning correction process, and

guarantee timeliness for high-frequency financial time

series.

Section 2 introduces relevant models. In Section 3 a

Monte Carlo numerical simulation is constructed to dis-

cover the space that can be improved by the traditional

ARIMA model, and then we combine machine learning

such as SVM and deep learning such as LSTM to correct

the residuals. Finally, empirical high-frequency data of

1082 LI ET AL.