Application and Comparison of Multiple Machine Learning Models in Finance

Hindawi
Scientific Programming
Volume 2022, Article ID 9613554, 9 pages
https://doi.org/10.1155/2022/9613554

Research Article
Application and Comparison of Multiple Machine Learning
Models in Finance

 Yali Jiang
 Guangxi Vocational College of Technology and Business, Guangxi 530015, China

 Correspondence should be addressed to Yali Jiang; 1931110371@stmail.ntu.edu.cn

 Received 27 January 2022; Revised 19 February 2022; Accepted 26 February 2022; Published 24 March 2022

 Academic Editor: Tongguang Ni

 Copyright © 2022 Yali Jiang. This is an open access article distributed under the Creative Commons Attribution License, which
 permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

 Accurate and effective financial data analysis is very important for investors to avoid risks and formulate profitable investment
 strategies. Therefore, the analysis of financial data has important research significance. However, the financial market is a complex
 nonlinear dynamic system affected by many factors. It is very challenging to analyze the financial data according to the obtained
 information. Among them, stock selection is the most typical financial data mining problem. The core of stock selection is to
 design a systematic scoring mechanism to quantitatively score stocks so as to more intuitively reflect the investment value of
 stocks. The scoring mechanism is based on the assumption that stocks with higher scores have higher investment value and stocks
 with lower scores have lower investment value. The stock selection model proposed in this paper mainly includes two steps: stock
 prediction and stock scoring. First, construct stock predictors and use machine learning forecasting methods to predict the future
 price of each stock. Second, construct a stock scoring mechanism to evaluate each stock through the predictive factors and
 financial factors in the previous step. Finally, select high-scoring stocks and make equal-weight investments. This paper applies the
 model to the empirical study of the A-share market, verifies its feasibility and effectiveness, and makes a systematic comparison
 with other benchmark models.

1. Introduction Faced with confusing, high-dimensional, and huge
 amounts of historical stock information, it is a reasonable
With the development of the market economy, the issuance and efficient way to analyze and process with the help of
and trading of stocks occurred, and both promoted the computers, which frees stock analysts from tedious work and
development of the market economy. In recent years, stocks concentrates on analyzing key issues [3]. The high-speed
have shown their tenacious vitality, and the stock market has processing capability of the computer makes it possible to
gradually become an indispensable part of the entire fi- provide customers with more comprehensive and accurate
nancial industry, especially the securities industry. In order forecasts in a short period of time. In addition, algorithms
to develop the national economy better and faster, as my can provide insights into the forecasting problem from novel
country continues to enter the deep water zone of reforms, perspectives to achieve better forecasting results, which are
the reforms in the financial sector are gradually deepening beyond the reach of human analysis. Model algorithms such
[1]. Predicting the development of stocks has always been the as machine learning and deep learning are suitable for the
direction of research and exploration by scholars from all analysis of high-dimensional big data, and the use of
walks of life. Predicting the development of stocks is a computers to customize auxiliary software for stock fore-
branch of prediction. The premise is to use scientific casting for different service objects has become a research
methods and methods, and it is necessary to know the hotspot [4]. This paper will combine neural networks and
development laws of financial markets, understand eco- support vector machines, two of the most widely used
nomics, and fully grasp the law of development of the fi- machine learning models, and propose improvements to
nancial market and the current stage of development [2]. provide novel solutions to problems such as model mixing

2 Scientific Programming

and stock forecasting [5]. According to the existing stock
 X1 y1
analysis and prediction methods, the participation of the
whole people can be maximized, and it is not necessary to
have sufficient financial expertise to participate in stock
investment. For research topics with special properties such X2 y2
as time series and high-dimensional stock historical data, . . . . .
many forecasting methods can be used for reference [6]. . . . . .
 . . . . .
Therefore, the research topic of stock forecasting has very
important significance from both theoretical and application Xn ym
perspectives and meets the current needs. Input layer Hidden layer Output layer
 Figure 1: BP neural network structure diagram.
2. Preliminary Study
2.1. Problem Definition. The total data set D � {X, Y} is iterations, the prediction model is obtained, and then the
composed of the input factor X and the real label Y cor- price of a + b + c (c ≥ 1) at a certain time in the future is
responding to the input factor X, and the prediction result Y predicted. The nonlinear relationship of the price Ya+b+c
is obtained by using the model F(·) to predict the data set D. time series at the predicted time can be expressed by the
When designing a specific prediction scheme, the input following formula:
factor X and label Y can be differentiated according to the
prediction model F(·) and the purpose of prediction. Xa+b+c � f Xa , Xa+1 , . . . . . . , Xa+b . (1)
Therefore, the input factor X can be time series data, text
 The fitting model f is obtained through the training set
data, binary features, and so on, and the label Y can be a
 time series Xa + Xb + · · · + Xa+b, and the unvalued value is
specific value, classification result, and so on.
 predicted from this.
 Obviously, financial stock forecasting is a complex
problem, which has the following five characteristics: (1) it is
appropriate to use machine learning to analyze and predict
 2.3. Support Vector Machine Regression. Support vector
financial stocks., and the input sources for stock prediction
 machine (SVM) was first proposed by Vapnik et al. [10]
are huge, high-dimensional, and heterogeneous, and ma-
 Based on the “structural risk minimization” criterion, the
chine learning algorithms are particularly good at processing
 optimal hyperplane is constructed to separate the two types
such data [7]; (2) indirect factors such as real-time data on
 of samples to the greatest extent. Support vector machine
the Internet and public sentiment will also affect the pre-
 regression (SVR) is an extension of SVM [11]. The basic
diction results; (3) when considering numerical data as an
 principle of SVR is similar to SVM, but its purpose is dif-
input feature, the basic transaction data and the technical
 ferent. It aims to construct an optimal classification plane to
indicators calculated from the basic transaction data are
 minimize the error of all samples from the classification
huge and need to be selected, and in addition, the two
 plane [12].
features may affect each other; (4) each stock has its own
 There are n training samples, where xi is the input
specific development law, and the trained model algorithm is
 variable and yi is the output variable. SVR can be regarded as
not necessarily applicable to the data sets of other stocks; and
 a quadratic programming problem, as shown in the fol-
(5) for the prediction output, it can be divided into classi-
 lowing equation:
fication prediction and regression prediction according to
the purpose of prediction. Classification and regression 1
 min ‖w‖2 ,
forecasts not only reflect trends and stock price forecasts but 2 (2)
also provide new ideas for investment strategies and price �� ��
reversal points [8]. subject to��yi − w · xi + b �� < ε, i � 1, . . . , n,

 where ξ represents the boundary of the prediction error.
2.2. BP Neural Network. The neural network model is In order to ensure the generalization ability of the model,
currently the most widely used neural network. At the same slack variables ξ i and ξ ∗i are introduced to modify equation
time, the neural network has the ability to predict only after (2), namely,
training and learning and can adapt to the prediction re- 1 n
quirements, obtain the structure of learning knowledge, and min ‖w‖2 + C ξ i + ξ ∗i , (3)
 2 i�1
map the nonlinearity to linear functions [9]. The main
structure diagram and flowchart are shown in Figures 1 and
2. ⎪
 ⎧
 ⎪ y − w, xi − b ≤ ε + ξ i ,
 ⎨ i ∗
 When the BP neural network predicts stocks, the time subject to⎪ w, xi + b − yi ≤ ε + ξ i , (4)
 ⎪
 ⎩ ∗
series i{X} is regarded as the input value of the input layer, ξ i , ξ i ≥ 0,
and a part of it is selected for training. The price {Yi}
obtained from the training result is compared with the where C is the penalty factor, which is the maximum
actual price and adjusted by feedback. After multiple tolerance error.

Scientific Programming 3

 NO

 Error and direction
 Calculate the input Running
 Network Take a sample and Calculate the propagation,
 Start and output of each out of learning
 initialization forward the input output error adjustment of weights
 layer of neurons samples?
 and thresholds

 NO

 The number of Calculate the
 Accuracy meets
 YES iterations reaches average error E of
 End requirements
 the upper limit? the network

 YES

 Figure 2: Flow chart of BP neural network implementation.

 In order to solve equations (3) and (4), the Lagrange total of 17 trading factors are used to predict the future price
function is introduced and transformed into a dual problem of stocks. The 17 trading factors can be roughly divided into
as follows: 4 categories. Volume and price factors include the previous
 n n day’s closing price, trading volume, opening price, average
 1
L � ‖w‖2 + C ξ i + ξ ∗i − λi ε + ξ i − yi + w, xi + b price, closing price, lowest price, turnover, and highest price
 2 i�1 i [14]. Valuation factors include P/B ratio, P/B ratio, P/E ratio,
 and P/S ratio [15]. Risk factors include ups and downs of
 n
 yuan, ups and downs, and turnover rate. Scale factors in-
 − λ∗i ε + ξ ∗i + yi − w, xi − b 
 i
 clude total market capitalization and total equity. The
 predicted stock price P i,t+1 is transformed into the predicted
 n stock return through equation (10):
 − ηi ξ i + η∗i ξ ∗i , ∊ ηi , η∗i , ξ i , ξ ∗i ≥ 0.
 
 i�1 i,t+1 � Pi,t+1 − Pi,t ,
 R (8)
 (5) Pi,t
 Solve the Lagrange equation and get the optimal solution where R i,1 represents the predicted return of stock i in
w and b∗ as follows:
 ∗
 the period. Furthermore, normalize R i,t+1 to obtain Y
 i,t+1 ,
 
 and the process is shown in equation (11). Yi,t+1 will be used
 n
 w∗ � λi − λ∗i xi , as a predictor for the stock scoring in the second step.
 i 
 ∗ ∗ (6) i,t+1 � Ri,t+1 − Rt+1 ,
 Y (9)
 b � yi − w , xi − ε, 0 ≤ λi ≤ C, i � 1, . . . , n, t+1
 D
 −
 b∗ � yi − w∗ , xi + ε, 0 ≤ λ∗i ≤ C, i � 1, . . . , n. i � N i,t /N is the average value of the pre-
 where R R
 �����������
 x∈1
 −
 t � X
 dictor and D 2
 i�1 (Ri,t − R ) /N is the standard devi-
3. The Design of the Financial Stock Selection t
 ation of the predictor, where N is the number of stocks.
 Model Based on Machine Learning Models
3.1. Stock Prediction Model Framework. The stock selection
model proposed in this article mainly includes two steps: 3.2.2. Financial Stock Scoring. In addition to predictive
stock prediction (used to construct predictive factors) and factors, financial factors Vi,j,r (j � 1, . . . , 12) have also been
stock scoring (used to evaluate stock value) [13–15]. The introduced into our stock selection model. These factors are
overall framework is shown in Figure 3. widely used in existing stock selection models, and they usually
 reflect the company’s operating conditions. For example, ROE
 usually reflects the company’s profitability; debt to equity ratio
3.2. Financial Stock Forecast and Scoring (DE) usually reflects the company’s bar ratio; current ratio
 (CR) usually reflects the company’s liquidity; and inventory
3.2.1. Financial Stock Forecast. In order to construct pre-
 turnover rate (ITR) usually reflects the company’s operating
dictors, we predict the returns of all stocks. In the period of t,
 efficiency and operating income [16]. The growth rate OIG
use zi,k,t (k � 1, 2, . . . , 17) transaction data to predict the
 usually reflects the company’s growth and so on. As with
stock price in period t+1 as follows [13]:
 forecasted earnings, standardize them as follows [17]:
 i,t+1 � f zi,1,t , zi,2,t , . . . , zi,17,t ,
 P (7) −
 Yi,j,t � Vi,j,t − Vj,t
 where P i,t+1 is the predicted price of stock i in period t + 1 , (10)
and zi,k,t is the k-th transaction data of stock i in period t. A Dj,t

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 step 1: Step 2:
 Stock forecast Stock score

 enter Transaction data Predictor Financial factor
 Zi, k, t Ŷi,t+1 Yi,j,t

 method ELM DE

 Weights 0 Weights1 Weights J
 W0 W1 ... Wj
 Forecast price
 P̂i, t+1

 Future earnings Stock i score
 J
 P̂ – P̂ Si,t =W0Ŷi,t+1+ j=1 WjYi,j,t
 Output R̂i, t+1 = i, t+1 i
 P̂i

 standardization Stock picking
 R̂i, t+1 → Ŷi,t+1 Si,t≥Q0.95,t

 Figure 3: Framework diagram of the stock selection model.

 −
 where Vj,t � N
 i�1 Vi,j,j /N �������������
 is the average �value of fi- portfolio return of the top stocks in the t period com-
 − prehensive score and the stocks after the m period com-
nancial factors and Dj,t � N 2
 i�1 (Vt,j,t − Vj,t, ) /N is the prehensive score.
standard deviation of the financial factor, where N is the
number of stocks. 1 T
 min F � − Spreadt ,
 The stock’s i score in the period of t, si,t , can be described wj T t�1
as a linear combination of predictive factors and financial (13)
factors as follows: m N
 ri,t�1 Rt+1 ri,t − ri,t�N−m+1 Rt+1 ri,t 
 Spreadt � .
 J m
 i,t+1 + Wj Yi,j,t ,
 si,t � W0 Y (11)
 j�1

 where W0 represents the weight of the predictive factor, 3.3. Evaluation Indicator. Root mean square error (RMSE),
Wj represents the weight of the j financial factor, and si,t mean absolute percentage error (MAPE), and directional
represents the comprehensive score of the stock in the period. statistics (D-STAT) are often used to evaluate the effec-
 Each stock is sorted according to its comprehensive tiveness of prediction models. This article also uses the above
score from high to low, denoting ri,j ∈ {1, 2, . . . , N}, if three indicators to evaluate the effectiveness of various
si,t ≥ sk,t , then ri,1 ≤ rk, where i, k ∈ {1, 2, . . . , N} represents prediction models in this article as follows [18]:
any two separate stocks. In each period, the top m stocks are ���������������
 2
selected for equal-weight investment. The portfolio returns N Pi,t − 
 Pi,t 
 1
are as follows: RMSE � ,
 N · T′ i�1 l�1
 1 m
 Rt+1 � R r , 
 m r �1 t+1 i,t N T′ i,t 
 i,j (12) 1 Pi,1 − P , (14)
 MAPE � 
 N · T′ i�1 t�1 Pi,t 
 ri,t � 1, 2, . . . , m,
 N T ′
 where m is the number of stocks that the investor hopes 1
 Dstat � ai,t ,
to choose and Rt+1 (ri,t ) is the t return of the stocks selected N · T′ i�1 t�1
during the period sorting in period t + 1. Rt+1 is the average
return of stocks selected according to the model in t + 1. where T is the number of test periods, N is the number of
 This research introduces Spread as the objective stocks, Pi,t is the price of stock i in period t, P i,t is the
function (fitness function) of the model. The objective predicted price of the stock, and when
function (fitness function) is defined as the long-short i,t − Pi,t−1 ) > 0, ai,t � 1; otherwise it is 0. In
 (Pi,t − Pi,t−1 )(P

Scientific Programming 5

addition, the running time of the model is also an important 4.2. Benchmark Model Comparison. As shown in Table 2,
indicator for evaluating the performance of the model. It will this article introduces a variety of benchmark models, in-
cover the entire time of the training period and the test cluding different prediction models (marked as M1), dif-
period. ferent factorial designs (marked as M2), different
 Choosing high-quality stocks for equal-weight invest- optimization algorithms (marked as M3), and different
ment means constructing an equal-weight investment fitness functions (marked as M4). Among them, M0 is the
portfolio. Portfolio income can most intuitively reflect the stock selection model proposed in this article. Next, we will
effectiveness of the stock selection model. The higher the introduce the construction methods of various benchmark
portfolio return, the better the effect of the stock selection models in detail.
model. Therefore, this paper adopts the average return of all In each benchmark method, in order to ensure the
investment portfolios during the test period as one of the fairness of comparison, each type of benchmark model only
evaluation indicators of the stock selection model. In ad- changes its unique variable. For type M1, BP neural network
dition, portfolio risk is also a key concern. SharpeRatio is a (BPNN) and support vector machine regression (SVR) are
commonly used indicator to describe portfolio risk. This two classic forecasting models, which are widely used in
article also uses SharpeRatio as one of the evaluation in- stock forecasting, investment portfolio, and stock selection
dicators of the stock selection model. The specific calculation research. Therefore, this article will introduce these two
formula is as follows [19]: prediction models as the benchmark model. For type M2,
 − f
 the model proposed in this paper contains two types of
 ′ E R t − R i factors, namely, basic factors and predictive factors, which
 1 T −
 AR � Rt+1 , Sharpe Ratio � . (15) are denoted as A0. Two new designs are now introduced as
 T′ t�1 σ
 the benchmark model of this article. Design A1 means that
 where R1 is the average return of the portfolio in the t only financial factors are considered but not predictive
period, that is, the average value of the
 f factors, and design A2 means that only predictive factors are
 − strategy return; Ri is the
 f
risk-free return in the t period; E[Rt − Ri ] is the expectation; considered but not financial factors. For type M3, the more
and σ is the portfolio volatility, that is, the strategy return. popular intelligent optimization algorithm in the stock se-
 lection model is introduced as the benchmark model of this
 article, namely, genetic algorithm GA and particle swarm
3.4. Hyperparameter Setting. All parameters involved in the algorithm PSO. For type M4, in the stock selection model
model and benchmark model proposed in this paper refer based on the intelligent optimization algorithm, four
to previous studies, as shown in Table 1. Regardless of commonly used optimization objective functions (fitness
whether it is an optimization model or a prediction model, functions) are used as the benchmark model of this article,
there are random variables or parameters, and different namely, information coefficient (IC), equity (CR), long-
optimization values will be generated every time the model short combination winning rate (IFHR), and absolute win
is run (the output result cannot be guaranteed to be the rate (WIN).
optimal result). Therefore, all models are run 30 times for
each case, and their average value is used as the final output 1 T ′ 
 cov ri,t, , ri,t
 IC � − �������������,
result. T t�1 var r var r′ 
 i,t i,t

4. Experimental Test and Result Comparison T −
 CR � − 1 + Rt+1 ,
4.1. Experimental Data Set. The trading volume and total i�1 m
 1 T ⎝ ri,t �1 sgn Rt+1 ri,t − Mt+1 
market value of China’s A-share market in the global fi- IFHR � − ⎛
 T t�1 2m
nancial market are increasing day by day, and its status is
increasing day by day. Therefore, the A-share band field is N
 r �N−m+1 sgn Rt+1 ri,t − Mi+1 ⎠
selected as the experimental sample of this article. There are − i,t ⎞,
a total of 2,473 stocks as candidate stocks for the invest- 2m
ment portfolio, which excludes financial industry stocks −
 T Rt+1 
with different balance sheet structures and specially pro- 1
 WIN � − sgn, (16)
cessed stocks ST that may be unstable. In the existing stock T t�1
forecasting models, this chapter will introduce the acqui-
sition, processing, and cleaning of data sources from two where T is the number of training periods, ri,t is the
aspects of stock index data and text data. Among them, ranking of stock i in the t-th period, ri,t is the stock’s income
stock index data refers to data related to stock trading. The ranking in t + 1 period, cov(·) is the covariance, var(·) is the
text data mainly consists of news data. The trading data variance, m is to select the number of stocks, and Rt+1 is the
used for stock forecasting and the financial data of stock average return of the stock selection strategy in the t + 1
scoring are all quarterly data, and they all come from the period. It outputs 1 when it is x > 0; otherwise, it outputs 0.
Wind database. See Table 1 for benchmark model design.

6 Scientific Programming

 Table 1: Parameter settings of this model and benchmark model.
Optimization Parameter Value Method of prediction Parameter Value
 P 30 N 0.1∗N_train
DE Cr 0.5 ELM TF sig
 F 0.6 n 10
 P 50 ep 3,000
GA cr 0.6 lr 0.1
 BPNN
 mr 0.5 mc 0.4
 P 40 K RBF
PSO c1 � c2 1.495 r {2−15, 2−13, . . ., 213, . . ., 215}
 SVR
 wn [0.4, 0.9] C {2−15, 2−13, . . ., 213, . . ., 215}
Note: c and C are traversed from the grid of 2−15 , 2−13 , . . . , 213 , 215 to obtain values. N− train is the number of training periods of the extreme learning
machine. For other parameter descriptions, please refer to the description of symbols and abbreviations.

 Table 2: Benchmark model design.
Type Describe Predictive model Factorial design Optimization Fitness function
M0 Stock selection model ELM A0 DE Spread
 BPNN A0 DE Spread
M1 Benchmark model: different forecasting models
 SVR A0 DE Spread
 ELM A1 DE Spread
M2 Benchmark model: different factorial designs
 ELM A2 DE Spread
 ELM A0 PSO Spread
M3 Benchmark model: different optimization algorithms
 ELM A0 GA Spread
 ELM A0 DE IC
 ELM A0 DE CR
M4 Benchmark model: different fitness functions
 ELM A0 DE IFHR
 ELM A0 DE WIN

4.2.1. Comparison of Different Prediction Models (M1). Table 3: Comparison results of different forecasting methods in the
When constructing predictors, this article uses the extreme stock selection model.
learning machine ELM to predict stock prices. In order to Model ELM BPNN SVR
prove the effectiveness of ELM in stock forecasting, two Module A: performance of stock-picking model
classic forecasting methods, BP neural network (BPNN) and AR 0.0998 0.0877 0.0799
support vector machine regression (SVR), are introduced as SharpeRatio 0.4054 0.2997 0.3049
benchmark models. Table 3 shows the prediction results. Max. 0.4199 0.4089 0.4278
Among them, Prob.(R1) is the probability that the stock Min. −0.3178 −0.3203 −0.3049
selection model of this article will have a higher quarterly Prob.(R1) 0.6554 0.4712 0.5083
return than the quarterly earnings of R1; Prob.(R2) is the Prob.(R2) 0.7831 0.7500 0.7521
probability that the quarterly earnings of the stock selection HitRatio 0.7603 0.7580 0.5813
model of this article will be higher than the quarterly Module B: t test(H0: ARELM ≤ ARBenchmark )
earnings of R2; and Max. is the average value of the max- Positive test (p value) 0.3121 0.2014 0.4179
imum return of the stock selection model of this article; Min. t-stat NA 18.1433 13.2240
 p value NA

Scientific Programming 7

normality test, and the values of all models are less than 5%. Table 4: Comparison results of different factorial designs in the
It shows that at the 95% confidence level, the stock selection stock selection model.
model based on ELM is better than the benchmark model. Model A0 A1 A2 R1 R2
This proves that the predictive factors constructed by ELM Module A: model performance
can better assist stock selection decision-making. AR 0.1102 0.0765 0.0799 0.8403 0.0398
 Module C shows the evaluation indicators of all fore- SharpeRatio 0.4010 0.2997 0.3012 0.2988 0.1798
casting methods. Obviously, the method of using ELM to Max. 0.4587 0.4099 0.4010 0.3789 0.3594
predict stock prices crushes all benchmark models in com- Min. −0.2998 −0.3201 −0.3587 −0.3099 −0.3178
puting time, directional accuracy D-STAT, prediction accu- Prob.(R1) 0.6549 0.4378 0.5001 NA 0.0000
racy MAPE, and RMSE. In the research of this article, ELM Prob.(R2) 0.8001 0.7603 0.7554 1.0000 NA
has more prominent predictive abilities. Similarly, in order to HitRatio 0.7602 0.7812 0.7399 0.7849 0.5645
statistically prove that the prediction results based on the Module B: t-test(H0: ARDF ≤ ARBenchmark )
extreme learning machine ELM are significantly better than Normality test
 0.2998 0.0489 0.3379 NA NA
other benchmark models, this section conducts the Die- (p value)
bold–Mariano test (DM test) on each benchmark model. The t stat NA 20.5879 14.1339 25.8999 57.0004
 p value NA

8 Scientific Programming

 Table 5: Comparison results of different optimization algorithms in the stock selection model.
 Training set Test set t-test (H0: ARDF ≤ ARBenchmark )
Model
 AR SharpRatio AR SharpRatio Normality test (p value) t-stat p value
DE 0.1201 0.1311 0.1078 0.3644 0.2988 NA NA
PSO 0.1887 0.1088 0.1244 0.3577 0.4999 3.7994 0.0002
GA 0.1001 0.1022 0.1012 0.3578 0.1994 4.3829

Scientific Programming 9

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