# Multitask Learning Based on Least Squares Support Vector Regression for Stock Forecast

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Least Squares Support Vector Regression

## 3. Extension of Multitask Learning Least Squares Support Vector Regression

#### 3.1. MTL-LS-SVR

#### 3.2. EMTL-LS-SVR

#### 3.3. Krylov-Cholesky Algorithm

- (1)
- Convert the linear system (7) or (13) to the following form using Krylov methods:$$\left[\begin{array}{cc}{Q}_{m\times m}& {0}_{m\times 1}\\ {0}_{m\times 1}^{T}& s\end{array}\right]\left[\begin{array}{c}{\left({Q}^{-1}H{b}_{0}+\alpha \right)}_{m\times 1}\\ {b}_{0}\end{array}\right]=\left[\begin{array}{c}{Y}_{m\times 1}\\ {H}^{T}{Q}^{-1}Y\end{array}\right]$$
- (2)
- Apply the Cholesky factorization method to decompose $Q$ into $Q=L{L}^{T}$, and the elements ${l}_{ij}$ of the lower-triangular matrix $L$ can be determined from $Q$;
- (3)
- Calculate ${L}^{-1}$, and thus ${\left({L}^{T}\right)}^{-1}={\left({L}^{-1}\right)}^{T}$, ${Q}^{-1}={\left({L}^{-1}\right)}^{T}{L}^{-1}$;
- (4)
- Solve $R$, $\tau $ from $QR=H$ and $Q\tau =Y$, respectively, and record the corresponding solution ${R}^{*}$ and ${\tau}^{*}$;
- (5)
- Calculate $s={H}^{T}{R}^{*}$;
- (6)
- Obtain the optimal solution: ${b}_{0}^{*}=\frac{1}{s}{H}^{T}{\tau}^{*}$ and $\alpha *={\tau}^{*}-R*{b}_{0}^{*}$.

## 4. Experiments

- 1)
- ${K}_{0}$ is a linear kernel and ${K}_{t}$ is a polynomial kernel.
- 2)
- ${K}_{0}$ is a linear kernel and ${K}_{t}$ is a radial basis function kernel.
- 3)
- ${K}_{0}$ is a polynomial kernel and ${K}_{t}$ is a radial basis function kernel.

#### 4.1. Parameter Selection

#### 4.2. Evaluation Criteria

#### 4.3. Forecast of Security of Stock Market Investment Environment

^{a}SZSE Composite Index (SZI),

^{b}Growth Enterprise Index (CNT),

^{c}and SSE SME Composite Index (SZSMEPI).

^{d}From the development history of the Chinese stock market, the crash effect of a rapid change from a bull market to a bear market was worse than for some international events, such as the Middle East Respiratory Syndrome Coronavirus (MERS-CoV) in 2012, and the 2019-nCoV out-broken in early 2020. Therefore, we selected an entire evolutionary period from a bull market to a bear market in Chinese stock market, with historical data including 1352 trading days, from 25 June 2013, to 4 January 2019. The data from each trading day were used as a sample point, with nine indicators: opening index, highest index value, lowest index value, closing index, index changing margin, index changing ratio, trading volume, trading amount, and previous day’s closing price. The four major stock market indices together compose the stock market of China, and they are affected by factors such as national policies, trade, and the international situation. We regard the above four stock indices as four subtasks, which are distinctive but interrelated, and which conform to the rules of multitask learning method.

^{a}- http://quotes.money.163.com/trade/lsjysj_zhishu_000001.html (accessed on 1 May 2021)
^{b}- http://quotes.money.163.com/trade/lsjysj_zhishu_399001.html (accessed on 1 May 2021)
^{c}- http://quotes.money.163.com/trade/lsjysj_zhishu_399006.html (accessed on 1 May 2021)
^{d}- http://quotes.money.163.com/trade/lsjysj_zhishu_399005.html (accessed on 1 May 2021)

#### 4.4. Forecasting Opening Prices of Five Major Banks

^{e}Agricultural Bank of China (ABC),

^{f}Bank of China (BOC),

^{g}China Construction Bank CCB),

^{h}and Bank of Communications (BCM)

^{i}from 1 January 2014 to 10 July 2019. The data included eleven attribute indicators: opening price, highest price, lowest price, closing price, price changing margin, price changing ratio, trading volume, trading amount, trading amplitude, trading turnover rate, and previous day’s closing price. Therefore, five interrelated but different learning tasks were trained simultaneously, and used to confirm the accuracy of our proposed models. In the experiment, the opening price of the day is the dependent variable, and the remaining ten indicators of the previous day are independent variables. The stock (opening) prices on 1346 trading days are shown in Figure 8. It can be seen that the opening prices of the five major banks almost always fluctuated in the same direction, confirming a strong internal correlation among them.

^{e}- http://quotes.money.163.com/trade/lsjysj_601398.html (accessed on 1 May 2021)
^{f}- http://quotes.money.163.com/trade/lsjysj_601288.html (accessed on 1 May 2021)
^{g}- http://quotes.money.163.com/trade/lsjysj_601988.html (accessed on 1 May 2021)
^{h}- http://quotes.money.163.com/trade/lsjysj_601939.html (accessed on 1 May 2021)
^{i}- http://quotes.money.163.com/trade/lsjysj_601328.html (accessed on 1 May 2021)

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Predictions of different regression models on opening index for SSEC (

**a**) Original figure, (

**b**) Enlarged figure.

**Figure 5.**Predictions of different regression models on opening index for SZI (

**a**) Original figure, (

**b**) Enlarged figure.

**Figure 6.**Predictions of different regression models on opening index for CNT (

**a**) Original figure, (

**b**) Enlarged figure.

**Figure 7.**Predictions of different regression models on opening index for SZSMEPI (

**a**) Original figure, (

**b**) Enlarged figure.

**Figure 9.**Predictions of different regression models on stock opening price for ICBC (

**a**) Original figure, (

**b**) Enlarged figure.

**Figure 10.**Predictions of different regression models on stock opening price for ABC (

**a**) Original figure, (

**b**) Enlarged figure.

**Figure 11.**Predictions of different regression models on stock opening price for BOC (

**a**) Original figure, (

**b**) Enlarged figure.

**Figure 12.**Predictions of different regression models on stock opening price for CCB (

**a**) Original figure, (

**b**) Enlarged figure.

**Figure 13.**Predictions of different regression models on stock opening price for BCM (

**a**) Original figure, (

**b**) Enlarged figure.

Stock Index | Algorithm | MAE | RMSE | SSE/SST | SSR/SST | (C,σ,λ,d) |
---|---|---|---|---|---|---|

SSEC | SVR | 8.7363 ± 0.6100 | 15.0791 ± 2.9735 | 0.0007 ± 0.0003 | 0.9992 ± 0.0041 | (55,3.85,~,~) |

LS-SVR | 9.8034 ± 0.9884 | 17.1879 ± 3.0598 | 0.0008 ± 0.0003 | 0.9961 ± 0.0064 | (100,1.85,~,~) | |

MTPSVR | 10.299 ± 1.7081 | 18.9993 ± 2.9656 | 0.0010 ± 0.0003 | 0.9990 ± 0.0090 | (80,3.45,0.21,~) | |

MTLS-SVR | 9.083 ± 1.8565 | 16.5463 ± 3.6839 | 0.0008 ± 0.0004 | 1.0038 ± 0.0070 | (70,2.65,1.26,~) | |

MTL-LS-SVR | 7.0850 ± 1.2081 | 12.1375 ± 2.9656 | 0.0005 ± 0.0003 | 1.0134 ± 0.0090 | (100,2.25,0.11,~) | |

EMTL-LS-SVR(L + P) | 8.7002 ± 1.8565 | 13.1821 ± 3.6839 | 0.0006 ± 0.0004 | 1.0180 ± 0.0070 | (85,~,1.81,2) | |

EMTL-LS-SVR(L + R) | 8.2580 ± 0.9870 | 14.5139 ± 2.2211 | 0.0006 ± 0.0002 | 1.0152 ± 0.0067 | (95,2.65,1.31,~) | |

EMTL-LS-SVR(P + R) | 7.9055 ± 1.4195 | 12.1985 ± 3.3330 | 0.0004 ± 0.0003 | 1.0147 ± 0.0065 | (100,1.85,0.86,2) | |

SZI | SVR | 34.307 ± 3.2894 | 60.0911 ± 10.263 | 0.0010 ± 0.0003 | 1.0027 ± 0.0070 | (55,3.85,~,~) |

LS-SVR | 39.772 ± 4.1398 | 65.2855 ± 10.649 | 0.0012 ± 0.0004 | 0.9983 ± 0.0066 | (85,0.65,~,~) | |

MTPSVR | 41.355 ± 7.7932 | 70.3547 ± 14.535 | 0.0013 ± 0.0005 | 1.0042 ± 0.0101 | (80,3.45,0.21,~) | |

MTLS-SVR | 35.049 ± 4.8879 | 58.0722 ± 7.9587 | 0.0010 ± 0.0002 | 1.0010 ± 0.0102 | (70,2.65,1.26,~) | |

MTL-LS-SVR | 30.323 ± 7.7932 | 47.9612 ± 14.535 | 0.0008 ± 0.0005 | 1.0238 ± 0.0101 | (100,2.25,0.11,~) | |

EMTL-LS-SVR(L + P) | 31.789 ± 4.8879 | 48.0880 ± 7.9587 | 0.0006 ± 0.0002 | 1.0305 ± 0.0102 | (85,~,1.81,2) | |

EMTL-LS-SVR(L + R) | 31.278 ± 3.6882 | 50.9115 ± 6.5526 | 0.0007 ± 0.0002 | 1.0134 ± 0.0060 | (95,2.65,1.31,~) | |

EMTL-LS-SVR(P + R) | 34.269 ± 6.7111 | 57.4735 ± 12.680 | 0.0008 ± 0.0005 | 1.0268 ± 0.0096 | (100,1.85,0.86,2) | |

CNT | SVR | 6.6680 ± 0.6043 | 13.3354 ± 2.0972 | 0.0007 ± 0.0002 | 1.0035 ± 0.0081 | (65,3.05,~,~) |

LS-SVR | 9.6897 ± 0.8728 | 17.6334 ± 2.2048 | 0.0012 ± 0.0003 | 0.9974 ± 0.0139 | (100,1.05,~,~) | |

MTPSVR | 10.483 ± 1.5874 | 17.1729 ± 2.1407 | 0.0012 ± 0.0003 | 1.0006 ± 0.0088 | (80,3.45,0.21,~) | |

MTLS-SVR | 9.3258 ± 1.2721 | 15.4848 ± 1.8014 | 0.0010 ± 0.0003 | 0.9985 ± 0.0090 | (70,2.65,1.26,~) | |

MTL-LS-SVR | 8.8047 ± 1.5874 | 12.9715 ± 2.1407 | 0.0008 ± 0.0003 | 1.0121 ± 0.0088 | (100,2.25,0.11,~) | |

EMTL-LS-SVR(L + P) | 7.5338 ± 1.2721 | 12.0025 ± 1.8014 | 0.0005 ± 0.0003 | 1.0152 ± 0.0090 | (85,~,1.81,2) | |

EMTL-LS-SVR(L + R) | 7.6653 ± 0.7791 | 13.2993 ± 1.3632 | 0.0007 ± 0.0002 | 1.0170 ± 0.0095 | (95,2.65,1.31,~) | |

EMTL-LS-SVR(P + R) | 8.1940 ± 1.8366 | 12.9907 ± 2.5260 | 0.0008 ± 0.0003 | 1.0162 ± 0.0110 | (100,1.85,0.86,2) | |

SZSMEPI | SVR | 24.642 ± 1.6220 | 42.3225 ± 5.7639 | 0.0010 ± 0.0002 | 1.0015 ± 0.0058 | (80,1.45,~,~) |

LS-SVR | 26.818 ± 1.7986 | 42.5460 ± 5.2053 | 0.0011 ± 0.0002 | 0.9979 ± 0.0068 | (100,0.95,~,~) | |

MTPSVR | 28.393 ± 4.8609 | 47.7573 ± 10.486 | 0.0013 ± 0.0006 | 0.9975 ± 0.0100 | (80,3.45,0.21,~) | |

MTLS-SVR | 25.043 ± 3.2029 | 42.4982 ± 7.4606 | 0.0011 ± 0.0003 | 1.0019 ± 0.0052 | (70,2.65,1.26,~) | |

MTL-LS-SVR | 19.548 ± 2.3609 | 30.7638 ± 10.486 | 0.0006 ± 0.0006 | 1.0170 ± 0.0100 | (100,2.25,0.11,~) | |

EMTL-LS-SVR(L + P) | 20.723 ± 3.2029 | 35.2842 ± 7.4606 | 0.0006 ± 0.0003 | 1.0105 ± 0.0052 | (85,~,1.81,2) | |

EMTL-LS-SVR(L + R) | 22.228 ± 1.6492 | 34.3454 ± 3.9592 | 0.0007 ± 0.0001 | 1.0146 ± 0.0062 | (95,2.65,1.31,~) | |

EMTL-LS-SVR(P + R) | 20.014 ± 4.2357 | 32.6555 ± 8.3170 | 0.0007 ± 0.0004 | 1.0157 ± 0.0071 | (100,1.85,0.86,2) |

Bank Stock Price | Algorithm | MAE | RMSE | SSE/SST | SSR/SST | (C,σ,λ,d) |
---|---|---|---|---|---|---|

ICBC | SVR | 0.0144 ± 0.0012 | 0.0245 ± 0.0049 | 0.0008 ± 0.0003 | 0.9980 ± 0.0050 | (80,2.25,~,~) |

LS-SVR | 0.0196 ± 0.0015 | 0.0276 ± 0.0070 | 0.0010 ± 0.0005 | 0.9968 ± 0.0070 | (70,0.65,~,~) | |

MTPSVR | 0.0252 ± 0.0025 | 0.0263 ± 0.0060 | 0.0011 ± 0.0005 | 0.9939 ± 0.0124 | (75,2.25,0.06,~) | |

MTLS-SVR | 0.0263 ± 0.0032 | 0.0278 ± 0.0075 | 0.0010 ± 0.0008 | 0.9978 ± 0.0157 | (75,3.05,1.81,~) | |

MTL-LS-SVR | 0.0145 ± 0.0025 | 0.0220 ± 0.0060 | 0.0006 ± 0.0005 | 1.0109 ± 0.0124 | (90,3.45,0.91,~) | |

EMTL-LS-SVR(L + P) | 0.0164 ± 0.0032 | 0.0230 ± 0.0075 | 0.0007 ± 0.0008 | 1.0487 ± 0.0157 | (100,~,1.61,2) | |

EMTL-LS-SVR(L + R) | 0.0156 ± 0.0037 | 0.0232 ± 0.0092 | 0.0006 ± 0.0008 | 1.0088 ± 0.0115 | (100,1.45,1.41,~) | |

EMTL-LS-SVR(P + R) | 0.0143 ± 0.0012 | 0.0203 ± 0.0063 | 0.0005 ± 0.0005 | 1.0146 ± 0.0086 | (85,1.45,0.46,2) | |

ABC | SVR | 0.0098 ± 0.0009 | 0.0171 ± 0.0033 | 0.0013 ± 0.0005 | 0.9989 ± 0.0032 | (50,3.45,~,~) |

LS-SVR | 0.0110 ± 0.0008 | 0.0184 ± 0.0027 | 0.0015 ± 0.0004 | 0.9964 ± 0.0046 | (90,1.45,~,~) | |

MTPSVR | 0.0137 ± 0.0021 | 0.0211 ± 0.0040 | 0.0019 ± 0.0007 | 1.0038 ± 0.0216 | (75,2.25,0.06,~) | |

MTLS-SVR | 0.0124 ± 0.0019 | 0.0216 ± 0.0062 | 0.0021 ± 0.0014 | 0.9975 ± 0.0101 | (75,3.05,1.81,~) | |

MTL-LS-SVR | 0.0100 ± 0.0021 | 0.0150 ± 0.0040 | 0.0010 ± 0.0007 | 1.0505 ± 0.0216 | (90,3.45,0.91,~) | |

EMTL-LS-SVR(L + P) | 0.0101 ± 0.0019 | 0.0147 ± 0.0028 | 0.0008 ± 0.0005 | 1.0141 ± 0.0101 | (100,~,1.61,2) | |

EMTL-LS-SVR(L + R) | 0.0105 ± 0.0015 | 0.0167 ± 0.0034 | 0.0011 ± 0.0006 | 1.0130 ± 0.0117 | (100,1.45,1.41,~) | |

EMTL-LS-SVR(P + R) | 0.0096 ± 0.0009 | 0.0149 ± 0.0033 | 0.0009 ± 0.0006 | 1.0253 ± 0.0111 | (85,1.45,0.46,2) | |

BOC | SVR | 0.0120 ± 0.0013 | 0.0250 ± 0.0055 | 0.0019 ± 0.0008 | 0.9998 ± 0.0084 | (70,3.85,~,~) |

LS-SVR | 0.0134 ± 0.0015 | 0.0262 ± 0.0056 | 0.0021 ± 0.0009 | 0.9973 ± 0.0069 | (95,2.25,~,~) | |

MTPSVR | 0.0164 ± 0.0030 | 0.0278 ± 0.0061 | 0.0024 ± 0.0010 | 0.9991 ± 0.0210 | (75,2.25,0.06,~) | |

MTLS-SVR | 0.0153 ± 0.0019 | 0.0272 ± 0.0060 | 0.0025 ± 0.0011 | 0.9971 ± 0.0122 | (75,3.05,1.81,~) | |

MTL-LS-SVR | 0.0128 ± 0.0030 | 0.0189 ± 0.0061 | 0.0011 ± 0.0010 | 1.0424 ± 0.0210 | (90,3.45,0.91,~) | |

EMTL-LS-SVR(L + P) | 0.0113 ± 0.0019 | 0.0177 ± 0.0060 | 0.0009 ± 0.0011 | 1.0209 ± 0.0122 | (100,~,1.61,2) | |

EMTL-LS-SVR(L + R) | 0.0118 ± 0.0021 | 0.0190 ± 0.0070 | 0.0010 ± 0.0012 | 1.0159 ± 0.0176 | (100,1.45,1.41,~) | |

EMTL-LS-SVR(P + R) | 0.0118 ± 0.0015 | 0.0182 ± 0.0062 | 0.0010 ± 0.0011 | 1.0433 ± 0.0162 | (85,1.45,0.46,2) | |

CCB | SVR | 0.0203 ± 0.0018 | 0.0376 ± 0.0055 | 0.0010 ± 0.0003 | 0.9979 ± 0.0042 | (50,3.85,~,~) |

LS-SVR | 0.0264 ± 0.0014 | 0.0510 ± 0.0048 | 0.0016 ± 0.0003 | 0.9946 ± 0.0048 | (85,0.65,~,~) | |

MTPSVR | 0.0238 ± 0.0056 | 0.0432 ± 0.0070 | 0.0013 ± 0.0004 | 0.9956 ± 0.0246 | (75,2.25,0.06,~) | |

MTLS-SVR | 0.0245 ± 0.0073 | 0.0509 ± 0.0142 | 0.0015 ± 0.0011 | 0.9961 ± 0.0133 | (75,3.05,1.81,~) | |

MTL-LS-SVR | 0.0208 ± 0.0056 | 0.0327 ± 0.0070 | 0.0007 ± 0.0004 | 1.0558 ± 0.0246 | (90,3.45,0.91,~) | |

EMTL-LS-SVR(L + P) | 0.0224 ± 0.0073 | 0.0330 ± 0.0142 | 0.0007 ± 0.0011 | 1.0134 ± 0.0133 | (100,~,1.61,2) | |

EMTL-LS-SVR(L + R) | 0.0225 ± 0.0031 | 0.0374 ± 0.0055 | 0.0009 ± 0.0003 | 1.0098 ± 0.0121 | (100,1.45,1.41,~) | |

EMTL-LS-SVR(P + R) | 0.0208 ± 0.0024 | 0.0316 ± 0.0046 | 0.0006 ± 0.0005 | 1.0118 ± 0.0097 | (85,1.45,0.46,2) | |

BCM | SVR | 0.0204 ± 0.0021 | 0.0430 ± 0.0069 | 0.0021 ± 0.0006 | 0.9970 ± 0.0162 | (80,2.85,~,~) |

LS-SVR | 0.0245 ± 0.0025 | 0.0483 ± 0.0067 | 0.0027 ± 0.0007 | 0.9924 ± 0.0154 | (75,1.85,~,~) | |

MTPSVR | 0.0278 ± 0.0028 | 0.0565 ± 0.0082 | 0.0031 ± 0.0008 | 0.9916 ± 0.0205 | (75,2.25,0.06,~) | |

MTLS-SVR | 0.0259 ± 0.0039 | 0.0418 ± 0.0121 | 0.0025 ± 0.0013 | 0.9996 ± 0.0163 | (75,3.05,1.81,~) | |

MTL-LS-SVR | 0.0203 ± 0.0028 | 0.0333 ± 0.0082 | 0.0011 ± 0.0008 | 1.0370 ± 0.0205 | (90,3.45,0.91,~) | |

EMTL-LS-SVR(L + P) | 0.0220 ± 0.0039 | 0.0352 ± 0.0121 | 0.0014 ± 0.0013 | 1.0404 ± 0.0163 | (100,~,1.61,2) | |

EMTL-LS-SVR(L + R) | 0.0195 ± 0.0053 | 0.0308 ± 0.0103 | 0.0013 ± 0.0010 | 1.0270 ± 0.0187 | (100,1.45,1.41,~) | |

EMTL-LS-SVR(P + R) | 0.0191 ± 0.0022 | 0.0278 ± 0.0089 | 0.0012 ± 0.0008 | 1.0242 ± 0.0138 | (85,1.45,0.46,2) |

Algorithm | Metric | SSEC | SZI | CNT | SZSMEPI | ICBC | ABC | BOC | CCB | BCM | p-Value |
---|---|---|---|---|---|---|---|---|---|---|---|

SVR | MAE | 5 | 5 | 1 | 5 | 2 | 2 | 4 | 1 | 4 | 3.222 |

RMSE | 5 | 6 | 5 | 5 | 5 | 5 | 5 | 5 | 6 | 5.222 | |

LS-SVR | MAE | 7 | 7 | 7 | 7 | 6 | 6 | 6 | 8 | 6 | 6.667 |

RMSE | 7 | 7 | 8 | 7 | 7 | 6 | 6 | 8 | 7 | 7 | |

MTPSVR | MAE | 8 | 8 | 8 | 8 | 7 | 8 | 8 | 6 | 8 | 7.667 |

RMSE | 8 | 8 | 7 | 8 | 6 | 7 | 8 | 6 | 8 | 7.333 | |

MTLS-SVR | MAE | 6 | 6 | 6 | 6 | 8 | 7 | 7 | 7 | 7 | 6.667 |

RMSE | 6 | 5 | 6 | 6 | 8 | 8 | 7 | 7 | 5 | 6.444 | |

MTL-LS-SVR | MAE | 4 | 3 | 2 | 3 | 5 | 4 | 1 | 4 | 5 | 3.444 |

RMSE | 3 | 2 | 1 | 4 | 3 | 1 | 1 | 3 | 4 | 2.444 | |

EMTL-LS-SVR(L + P) | MAE | 3 | 2 | 3 | 4 | 4 | 5 | 3 | 5 | 2 | 3.444 |

RMSE | 4 | 3 | 4 | 3 | 4 | 4 | 4 | 4 | 2 | 3.556 | |

EMTL-LS-SVR(L + R) | MAE | 2 | 4 | 4 | 2 | 1 | 1 | 2 | 2 | 1 | 2.111 |

RMSE | 2 | 4 | 3 | 2 | 1 | 2 | 2 | 1 | 1 | 2 | |

EMTL-LS-SVR(P + R) | MAE | 1 | 1 | 5 | 1 | 3 | 3 | 5 | 3 | 3 | 2.778 |

RMSE | 1 | 1 | 2 | 1 | 2 | 3 | 3 | 2 | 3 | 2 |

**Table 4.**Comparison results between EMTL-LS-SVR(L + R) and other algorithms on average rank deviations.

Title 1 | MAE | Tag | RMSE | Tag |
---|---|---|---|---|

SVR | 1.111 | 0 | 3.222 | 1 ^{*} |

LS-SVR | 4.556 | 1 ^{**} | 5 | 1 ^{***} |

MTPSVR | 5.556 | 1 ^{***} | 5.333 | 1 ^{***} |

MTLS-SVR | 4.556 | 1 ^{**} | 4.444 | 1 ^{**} |

MTL-LS-SVR | 1.333 | 0 | 0.444 | 0 |

EMTL-LS-SVR(L + P) | 1.333 | 0 | 1.556 | 0 |

EMTL-LS-SVR(P + R) | 0.667 | 0 | 0 | 0 |

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**MDPI and ACS Style**

Zhang, H.-C.; Wu, Q.; Li, F.-Y.; Li, H.
Multitask Learning Based on Least Squares Support Vector Regression for Stock Forecast. *Axioms* **2022**, *11*, 292.
https://doi.org/10.3390/axioms11060292

**AMA Style**

Zhang H-C, Wu Q, Li F-Y, Li H.
Multitask Learning Based on Least Squares Support Vector Regression for Stock Forecast. *Axioms*. 2022; 11(6):292.
https://doi.org/10.3390/axioms11060292

**Chicago/Turabian Style**

Zhang, Heng-Chang, Qing Wu, Fei-Yan Li, and Hong Li.
2022. "Multitask Learning Based on Least Squares Support Vector Regression for Stock Forecast" *Axioms* 11, no. 6: 292.
https://doi.org/10.3390/axioms11060292