Forecasting the Direction of Daily Changes in the India VIX Index Using Machine Learning
Abstract
:1. Introduction
2. Literature Review
 How can we forecast the binary daytoday movements of the India VIX using machine learning classifiers?
 How can we measure the performance of the classifiers?
 How can we say whether classifiers have similar performances?
 How do we know whether the models’ performances are acceptable?
 To forecast the binary daytoday movements of the India VIX, a standard classifier called logistic regression and 11 ensemble machine learning classifiers are trained.
 To measure the predictability of the classifiers, several metrics are applied.
 To distinguish the classifiers’ predictability, a statistical test is performed.
 To judge the predictability of the models in the context of the stock market, the performance of the developed models is compared with the past studies, and additionally, a basic classifier called logistic regression is trained for comparison.
3. Research Methodology
3.1. Description of the Models Used
3.2. Feature Computation Techniques
3.3. Data Transformation
3.4. Performance Evaluation
4. Modelling Procedure
4.1. Data Collection
4.2. Data PreProcessing
4.3. Preparation of Feature Variables
4.4. Feature Scaling
4.5. Target Variable
4.6. Execution of the Model
4.7. Optimal Models
5. Findings
6. Conclusions
7. Practical Implications
 Traders: When volatility is expected to increase sharply, intraday trades run the risk of stoplosses, quickly becoming triggered. To mitigate such risk, traders can either reduce their leverage or widen their stoplosses accordingly.
 Hedgers: For derivative contracts, such as a future contract where marttomarket (MTM) is executed daily, institutional investors and proprietary desks face the risk of MTM being executed and, thereby, generating losses. To manage such risks, they can increase their hedge when volatility is expected to be higher and viceversa.
 Volatility traders: They can take advantage of high validity by taking the long position on straddles and low validity by taking the short position on straddles. Implied volatility also anticipates options prices. When the volatility is expected to rise, the options price becomes more valuable, and when the volatility is expected to subside, the options price becomes less valuable. More precisely, the expected move in the implied volatility is used in conjunction with the outlook on the trend of the underlying index for volatility trading and hedging, as depicted in Table 9.
 Derivative trading: when the implied volatility index (the India VIX) is about to increase, buying calls on the India VIX is a better hedge than buying puts on the underlying stock index (the NIFTY 50 Index) because the implied volatility index is more sensitive. Hence, if the India VIX level is anticipated to be higher, buying calls on the India VIX and selling calls on the NIFTY 50 Index are recommended.
 Portfolio managers: The VIX also helps in selecting stocks to rebalance a portfolio. Portfolio managers can increase exposure to highbeta stocks when volatility is about to bounce from its peak level. Similarly, portfolio managers can increase exposure to lowbeta stocks when volatility is about to bounce from its bottom level.
8. Academic Contributions
9. Limitations and Future Scope
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Logistic regression: penalty=‘elasticnet’, l1_ratio=0.3, solver=‘saga’, C=0.1, max_iter=20, tol=1e08 
Random Forest: n_estimators=180, criterion=‘entropy’, max_depth=5, min_samples_split=2, min_samples_leaf=5, min_weight_fraction_leaf=0.01, max_features=29, min_impurity_decrease=0.01, max_leaf_nodes=7, max_samples=0.85, bootstrap=True, oob_score=True 
Extra Trees: n_estimators=100, criterion=‘entropy’, max_depth=7, min_samples_split=17, min_samples_leaf=5, min_weight_fraction_leaf=0.001, max_leaf_nodes=19, max_features=29, min_impurity_decrease=0.001, bootstrap=True, oob_score=True 
Bagging: n_estimators=310, max_samples=0.85, max_features=32, bootstrap=True, bootstrap_features=False

AdaBoost: n_estimators=221, algorithm=‘SAMME’, learning_rate=0.01

Stacking: passthrough=True, estimators=[e1, e2], final_estimator=e3

Voting: voting=‘soft’, estimators=[e1, e2]

Stochastic GBoosting: n_estimators=111, loss=‘deviance, learning_rate=0.5, subsample=0.45, criterion=‘friedman_mse, max_depth=2, min_samples_split=2, min_samples_leaf=2, min_weight_fraction_leaf=0.4, min_impurity_decrease=0.4, max_features=32, max_leaf_nodes=2, 
Hist GBoosting: max_iter=300, loss=‘binary_crossentropy’, max_depth=2, min_samples_leaf=46, max_leaf_nodes=2, learning_rate=0.012, l2_regularization=1e15, max_bins=200, tol=1e8 
XGBoost: n_estimators=90, max_depth=4, learning_rate=0.01, objective=‘binary:logistic’, eval_metric=‘error’, booster=‘gbtree’, tree_method=‘approx’, gamma=13.6, reg_alpha=1.0, reg_lambda=1e14, min_child_weight=7.7, subsample=0.55, colsample_bytree=0.9, importance_type=‘gain’, 
LightGBM: n_estimators=625, objective=‘binary’, max_depth=2, num_leaves=3, learning_rate=0.001, subsample=0.05, colsample_bytree=0.95, boosting_type=‘gbdt’, reg_alpha=1.0, reg_lambda=10.0, min_child_weight=1e08, min_child_samples=80, 
CatBoost: n_estimators=3000, max_depth=4, learning_rate=0.001, min_child_samples=4, reg_lambda=30, bootstrap_type=‘Bayesian’, bagging_temperature=0, rsm=0.8, leaf_estimation_method=‘Gradient’, boosting_type=‘Plain’, langevin=True, score_function=‘L2’ 
Logistic Regression  Random Forest  Extra Trees  
Precision  Recall  f1Score  Precision  Recall  f1Score  Precision  Recall  f1Score  Support  
0  0.67  0.68  0.68  0.70  0.70  0.70  0.68  0.67  0.67  168 
1  0.59  0.58  0.59  0.62  0.62  0.62  0.59  0.61  0.60  132 
macro avg  0.63  0.63  0.63  0.66  0.66  0.66  0.64  0.64  0.64  300 
weighted avg  0.64  0.64  0.64  0.67  0.67  0.67  0.64  0.64  0.64  300 
Bagging  AdaBoost  Stacking  
Precision  Recall  f1Score  Precision  Recall  f1Score  Precision  Recall  f1Score  Support  
0  0.70  0.70  0.70  0.69  0.67  0.68  0.70  0.74  0.72  168 
1  0.62  0.61  0.62  0.60  0.61  0.60  0.64  0.60  0.62  132 
macro avg  0.66  0.66  0.66  0.64  0.64  0.64  0.67  0.67  0.67  300 
weighted avg  0.66  0.66  0.66  0.65  0.65  0.65  0.67  0.68  0.68  300 
Voting  Stochastic GBoosting  Hist GBoosting  
Precision  Recall  f1Score  Precision  Recall  f1Score  Precision  Recall  f1Score  Support  
0  0.69  0.70  0.70  0.67  0.68  0.68  0.68  0.73  0.70  168 
1  0.62  0.61  0.61  0.59  0.57  0.58  0.62  0.57  0.59  132 
macro avg  0.65  0.65  0.65  0.63  0.63  0.63  0.65  0.65  0.65  300 
weighted avg  0.66  0.66  0.66  0.63  0.63  0.63  0.65  0.66  0.65  300 
XGBoost  LightGBM  CatBoost  
Precision  Recall  f1Score  Precision  Recall  f1Score  Precision  Recall  f1Score  Support  
0  0.70  0.70  0.70  0.70  0.70  0.70  0.70  0.71  0.71  168 
1  0.62  0.61  0.62  0.62  0.61  0.62  0.62  0.61  0.62  132 
macro avg  0.66  0.66  0.66  0.66  0.66  0.66  0.66  0.66  0.66  300 
weighted avg  0.66  0.66  0.66  0.66  0.66  0.66  0.67  0.67  0.67  300 
References
 Aliyeva, Aysel. 2022. Predicting Stock Prices Using Random Forest and Logistic Regression Algorithms. In 11th International Conference on Theory and Application of Soft Computing, Computing with Words and Perceptions and Artificial Intelligence—ICSCCW2021. Edited by Rafik A. Aliev, Janusz Kacprzyk, Witold Pedrycz, Mo Jamshidi, Mustafa Babanli and Fahreddin M. Sadikoglu. Lecture Notes in Networks and Systems. Cham: Springer International Publishing, pp. 95–101. [Google Scholar] [CrossRef]
 Alvarez Vecino, Pol. 2019. A Machine Learning Approach to Stock Screening with Fundamental Analysis. Master’s thesis, Universitat Politècnica de Catalunya, de Catalunya, Spain. Available online: https://upcommons.upc.edu/handle/2117/133070 (accessed on 28 May 2022).
 Bai, Bing, Guiling Li, Senzhang Wang, Zongda Wu, and Wenhe Yan. 2021. Time Series Classification Based on MultiFeature Dictionary Representation and Ensemble Learning. Expert Systems with Applications 169: 114162. [Google Scholar] [CrossRef]
 Bai, Yunfei, and Charlie Xiaowu Cai. 2022. Predicting VIX with Adaptive Machine Learning. SSRN Electronic Journal. [Google Scholar] [CrossRef]
 Ballestra, Luca Vincenzo, Andrea Guizzardi, and Fabio Palladini. 2019. Forecasting and Trading on the VIX Futures Market: A Neural Network Approach Based on Open to Close Returns and Coincident Indicators. International Journal of Forecasting 35: 1250–62. [Google Scholar] [CrossRef]
 Bantwa, Ashok. 2017. A Study on India Volatility Index (VIX) and Its Performance as Risk Management Tool in Indian Stock Market. SSRN Scholarly Paper. Rochester, NY, USA. Available online: https://papers.ssrn.com/abstract=3732839 (accessed on 28 May 2022).
 Batool, Maryam, Huma Ghulam, Muhammad Azmat Hayat, Muhammad Zahid Naeem, Abdullah Ejaz, Zulfiqar Ali Imran, Cristi Spulbar, Ramona Birau, and Tiberiu Horațiu Gorun. 2021. How COVID19 Has Shaken the Sharing Economy? An Analysis Using Google Trends Data. Economic ResearchEkonomska Istraživanja 34: 2374–86. [Google Scholar] [CrossRef]
 Bouri, Elie, Anshul Jain, P. C. Biswal, and David Roubaud. 2017a. Cointegration and Nonlinear Causality amongst Gold, Oil, and the Indian Stock Market: Evidence from Implied Volatility Indices. Resources Policy 52: 201–6. [Google Scholar] [CrossRef]
 Bouri, Elie, David Roubaud, Rania Jammazi, and Ata Assaf. 2017b. Uncovering Frequency Domain Causality between Gold and the Stock Markets of China and India: Evidence from Implied Volatility Indices. Finance Research Letters 23: 23–30. [Google Scholar] [CrossRef]
 Breiman, Leo. 1996. Bagging Predictors. Machine Learning 24: 123–40. [Google Scholar] [CrossRef] [Green Version]
 Breiman, Leo. 2001. Random Forests. Machine Learning 45: 5–32. [Google Scholar] [CrossRef] [Green Version]
 Carr, Peter. 2017. Why Is VIX a Fear Gauge? Risk and Decision Analysis 6: 179–85. [Google Scholar] [CrossRef]
 Chakrabarti, Prasenjit, and K. Kiran Kumar. 2020. HighFrequency ReturnImplied Volatility Relationship: Empirical Evidence from Nifty and India VIX. The Journal of Developing Areas 54. [Google Scholar] [CrossRef]
 Chandra, Abhijeet, and M. Thenmozhi. 2015. On Asymmetric Relationship of India Volatility Index (India VIX) with Stock Market Return and Risk Management. Decision 42: 33–55. [Google Scholar] [CrossRef]
 Chaudhuri, Tamal Datta, and Indranil Ghosh. 2016. Forecasting Volatility in Indian Stock Market Using Artificial Neural Network with Multiple Inputs and Outputs. arXiv arXiv:1604.05008. [Google Scholar] [CrossRef]
 Chen, Tianqi, and Carlos Guestrin. 2016. XGBoost: A Scalable Tree Boosting System. Paper presented at 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA, August 13–17; pp. 785–94. [Google Scholar] [CrossRef] [Green Version]
 Dai, Zhifeng, Huiting Zhou, Fenghua Wen, and Shaoyi He. 2020. Efficient Predictability of Stock Return Volatility: The Role of Stock Market Implied Volatility. The North American Journal of Economics and Finance 52: 101174. [Google Scholar] [CrossRef]
 Dixit, Gaurav, Dipayan Roy, and Nishant Uppal. 2013. Predicting India Volatility Index: An Application of Artificial Neural Network. International Journal of Computer Applications 70: 22–30. [Google Scholar] [CrossRef]
 Dorogush, Anna Veronika, Vasily Ershov, and Andrey Gulin. 2018. CatBoost: Gradient Boosting with Categorical Features Support. arXiv arXiv:1810.11363. [Google Scholar]
 Fernandes, Marcelo, Marcelo C. Medeiros, and Marcel Scharth. 2014. Modeling and Predicting the CBOE Market Volatility Index. Journal of Banking & Finance 40: 1–10. [Google Scholar] [CrossRef]
 Ferri, César, José HernándezOrallo, and R. Modroiu. 2009. An Experimental Comparison of Performance Measures for Classification. Pattern Recognition Letters 30: 27–38. [Google Scholar] [CrossRef]
 Florian, Radu. 2002. Named Entity Recognition as a House of Cards: Classifier Stacking. Available online: https://apps.dtic.mil/sti/citations/ADA459582 (accessed on 28 May 2022).
 Freund, Yoav, and Robert E. Schapire. 1996. Experiments with a new boosting algorithm. icml 96: 148–156. Available online: https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=d186abec952c4348870a73640bf849af9727f5a4 (accessed on 28 May 2022).
 Freund, Yoav, and Robert E. Schapire. 1997. A DecisionTheoretic Generalization of OnLine Learning and an Application to Boosting. Journal of Computer and System Sciences 55: 119–39. [Google Scholar] [CrossRef] [Green Version]
 Friedman, Jerome H. 2002. Stochastic Gradient Boosting. Computational Statistics & Data Analysis 38: 367–78. [Google Scholar] [CrossRef]
 Geurts, Pierre, Damien Ernst, and Louis Wehenkel. 2006. Extremely Randomized Trees. Machine Learning 63: 3–42. [Google Scholar] [CrossRef] [Green Version]
 Grima, Simon, Letife Özdemir, Ercan Özen, and Inna Romānova. 2021. The Interactions between COVID19 Cases in the USA, the VIX Index and Major Stock Markets. International Journal of Financial Studies 9: 26. [Google Scholar] [CrossRef]
 Guryanov, Aleksei. 2019. HistogramBased Algorithm for Building Gradient Boosting Ensembles of Piecewise Linear Decision Trees. In Analysis of Images, Social Networks and Texts. Edited by Wil M. P. van der Aalst, Vladimir Batagelj, Dmitry I. Ignatov, Michael Khachay, Valentina Kuskova, Andrey Kutuzov, Sergei O. Kuznetsov, Irina A. Lomazova, Natalia Loukachevitch, Amedeo Napoli and et al. Lecture Notes in Computer Science. Cham: Springer International Publishing, pp. 39–50. [Google Scholar] [CrossRef]
 Haghighi, Sepand, Masoomeh Jasemi, Shaahin Hessabi, and Alireza Zolanvari. 2018. PyCM: Multiclass Confusion Matrix Library in Python. Journal of Open Source Software 3: 729. [Google Scholar] [CrossRef] [Green Version]
 Han, Yechan, Jaeyun Kim, and David Enke. 2023. A Machine Learning Trading System for the Stock Market Based on NPeriod MinMax Labeling Using XGBoost. Expert Systems with Applications 211: 118581. [Google Scholar] [CrossRef]
 Hastie, Trevor, Saharon Rosset, Ji Zhu, and Hui Zou. 2009. MultiClass AdaBoost. Statistics and Its Interface 2: 349–60. [Google Scholar] [CrossRef] [Green Version]
 Ho, Tin Kam. 1998. The Random Subspace Method for Constructing Decision Forests. IEEE Transactions on Pattern Analysis and Machine Intelligence 20: 832–44. [Google Scholar] [CrossRef] [Green Version]
 Hoang Vuong, Pham, Trinh Tan Dat, Tieu Khoi Mai, Pham Hoang Uyen, and Pham The Bao. 2022. StockPrice Forecasting Based on XGBoost and LSTM. Computer Systems Science and Engineering 40: 237–46. [Google Scholar] [CrossRef]
 Ji, Qiang, Elie Bouri, and David Roubaud. 2018. Dynamic Network of Implied Volatility Transmission among US Equities, Strategic Commodities, and BRICS Equities. International Review of Financial Analysis 57: 1–12. [Google Scholar] [CrossRef]
 Kambeu, Edson. 2019. Trading Volume as a Predictor of Market Movement: An Application of Logistic Regression in the R Environment. International Journal of Finance & Banking Studies (21474486) 8: 57–69. [Google Scholar] [CrossRef]
 Ke, Guolin, Qi Meng, Thomas Finley, Taifeng Wang, Wei Chen, Weidong Ma, Qiwei Ye, and TieYan Liu. 2017. Lightgbm: A Highly Efficient Gradient Boosting Decision Tree. Advances in Neural Information Processing Systems 30: 3149–57. [Google Scholar]
 Kumar, Parul, Sunil Kumar, and R. K. Sharma. 2022. An Impact of FPI Inflows, Nifty Returns, and S&P Returns on India VIX Volatility. World Review of Science, Technology and Sustainable Development 18: 289–308. [Google Scholar]
 Labiad, Badre, Abdelaziz Berrado, and Loubna Benabbou. 2016. Machine Learning Techniques for Short Term Stock Movements Classification for Moroccan Stock Exchange. Paper present at the 2016 11th International Conference on Intelligent Systems: Theories and Applications (SITA), Mohammedia, Morocco, October 19–20; pp. 1–6. [Google Scholar]
 Ledolter, Johannes, and Søren Bisgaard. 2011. Challenges in Constructing Time Series Models from Process Data. Quality and Reliability Engineering International 27: 165–78. [Google Scholar] [CrossRef]
 Livieris, Ioannis E., Theodore Kotsilieris, Stavros Stavroyiannis, and P. Pintelas. 2020. Forecasting Stock Price Index Movement Using a Constrained Deep Neural Network Training Algorithm. Intelligent Decision Technologies 14: 313–23. [Google Scholar] [CrossRef]
 Louppe, Gilles, and Pierre Geurts. 2012. Ensembles on Random Patches. In Machine Learning and Knowledge Discovery in Databases. Edited by Peter A. Flach, Tijl De Bie and Nello Cristianini. Lecture Notes in Computer Science. Berlin/Heidelberg: Springer, vol. 7523, pp. 346–61. [Google Scholar] [CrossRef] [Green Version]
 Mall, M., S. Mishra, P. K. Mishra, and B. B. Pradhan. 2011. A Study on Relation between India VIX and Nifty Returns. International Research Journal of Finance and Economics 69: 178–84. [Google Scholar]
 Molaei, Soheila Mehr, and Mohammad Reza Keyvanpour. 2015. An Analytical Review for Event Prediction System on Time Series. Paper present at the 2015 2nd International Conference on Pattern Recognition and Image Analysis (IPRIA), Rasht, Iran, March 11–12; pp. 1–6. [Google Scholar] [CrossRef]
 Naik, Nagaraj, and Biju R. Mohan. 2019. Stock Price Movements Classification Using Machine and Deep Learning TechniquesThe Case Study of Indian Stock Market. In Engineering Applications of Neural Networks. Edited by John Macintyre, Lazaros Iliadis, Ilias Maglogiannis and Chrisina Jayne. Communications in Computer and Information Science. Cham: Springer International Publishing, pp. 445–52. [Google Scholar] [CrossRef]
 Onan, Mustafa, Aslihan Salih, and Burze Yasar. 2014. Impact of Macroeconomic Announcements on Implied Volatility Slope of SPX Options and VIX. Finance Research Letters 11: 454–62. [Google Scholar] [CrossRef] [Green Version]
 Patro, S. Gopal Krishna, and Kishore Kumar Sahu. 2015. Normalization: A Preprocessing Stage. arXiv arXiv:1503.06462. [Google Scholar] [CrossRef]
 Phillips, Peter C. B. 2005. Challenges of Trending Time Series Econometrics. Mathematics and Computers in Simulation 68: 401–16. [Google Scholar] [CrossRef] [Green Version]
 Prasad, Akhilesh, Priti Bakhshi, and Arumugam Seetharaman. 2022. The Impact of the U.S. Macroeconomic Variables on the CBOE VIX Index. Journal of Risk and Financial Management 15: 126. [Google Scholar] [CrossRef]
 RamosPérez, Eduardo, Pablo J. AlonsoGonzález, and José Javier NúñezVelázquez. 2019. Forecasting Volatility with a Stacked Model Based on a Hybridized Artificial Neural Network. Expert Systems with Applications 129: 1–9. [Google Scholar] [CrossRef]
 Rogers, L. Christopher G., and Stephen E. Satchell. 1991. Estimating Variance From High, Low and Closing Prices. The Annals of Applied Probability 1: 504–12. [Google Scholar] [CrossRef]
 Rogers, L. Christopher G., Stephen E. Satchell, and Y. Yoon. 1994. Estimating the Volatility of Stock Prices: A Comparison of Methods That Use High and Low Prices. Applied Financial Economics 4: 241–47. [Google Scholar] [CrossRef]
 Ruta, Dymitr, and Bogdan Gabrys. 2005. Classifier Selection for Majority Voting. Information Fusion 6: 63–81. [Google Scholar] [CrossRef]
 Sadorsky, Perry. 2021. A Random Forests Approach to Predicting Clean Energy Stock Prices. Journal of Risk and Financial Management 14: 48. [Google Scholar] [CrossRef]
 Saranya, C., and G. Manikandan. 2013. A Study on Normalization Techniques for Privacy Preserving Data Mining. International Journal of Engineering and Technology (IJET) 5: 2701–4. [Google Scholar]
 Serur, Juan Andrés, José Pablo Dapena, and Julián Ricardo Siri. 2021. Decomposing the VIX Index into Greed and Fear. Serie Documentos de TrabajoNro 780. [Google Scholar] [CrossRef]
 Shaikh, Imlak, and Puja Padhi. 2016. On the Relationship between Implied Volatility Index and Equity Index Returns. Journal of Economic Studies 43: 27–47. [Google Scholar] [CrossRef]
 Sokolova, Marina, and Guy Lapalme. 2009. A Systematic Analysis of Performance Measures for Classification Tasks. Information Processing & Management 45: 427–37. [Google Scholar] [CrossRef]
 Tuna, Abdulkadir. 2022. The Effects of Volatilities in Oil Price, Gold Price and Vix Index on Turkish BIST 100 Stock Index in Pandemic Period. İstanbul İktisat DergisiIstanbul Journal of Economics 72: 39–54. [Google Scholar] [CrossRef]
 Ullal, Mithun S., Pushparaj M. Nayak, Ren Trevor Dais, Cristi Spulbar, and Ramona Birau. 2022. Nvestigating the Nexus between Artificial Intelligence and Machine Learning Technologies in the Case of Indian Services Industry. Business: Theory and Practice 23: 323–33. [Google Scholar] [CrossRef]
 Vaswani, Ashish, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Łukasz Kaiser, and Illia Polosukhin. 2017. Attention Is All You Need. In Advances in Neural Information Processing Systems. Long Beach: Curran Associates, vol. 30, pp. 5998–6008. Available online: https://proceedings.neurips.cc/paper/2017/file/3f5ee243547dee91fbd053c1c4a845aaPaper.pdf (accessed on 28 May 2022).
 Wang, Yan, and Yuankai Guo. 2020. Forecasting Method of Stock Market Volatility in Time Series Data Based on Mixed Model of ARIMA and XGBoost. China Communications 17: 205–21. [Google Scholar] [CrossRef]
 Yang, Dennis, and Qiang Zhang. 2000. DriftIndependent Volatility Estimation Based on High, Low, Open, and Close Prices. The Journal of Business 73: 477–92. [Google Scholar] [CrossRef] [Green Version]
 Yang, YanHong, and YingHui Shao. 2020. TimeDependent LeadLag Relationships between the VIX and VIX Futures Markets. The North American Journal of Economics and Finance 53: 101196. [Google Scholar] [CrossRef] [Green Version]
 Yun, Jaeho. 2020. A ReExamination of the Predictability of Stock Returns and Cash Flows via the Decomposition of VIX. Economics Letters 186: 108755. [Google Scholar] [CrossRef]
 Zhang, Yanfang, Chuanhua Wei, and Xiaolin Liu. 2022. Group Logistic Regression Models with Lp,q Regularization. Mathematics 10: 2227. [Google Scholar] [CrossRef]
#  Ensemble Classifier  Reference 

1  Random Forest  Breiman (2001) 
2  Extremely randomised trees (Extra Trees)  Geurts et al. (2006) 
3  Bagging  Breiman (1996); Ho (1998); Louppe and Geurts (2012) 
4  AdaBoost  Freund and Schapire (1996, 1997); Hastie et al. (2009) 
5  Stacking  Florian (2002) 
6  Voting  Ruta and Gabrys (2005) 
7  Stochastic gradient boosting (Stochastic GBoosting)  Friedman (2002) 
8  Histogrambased gradient boosting (Hist GBoosting)  Guryanov (2019) 
9  Extreme Gradient Boosting (XGBoost)  Chen and Guestrin (2016) 
10  Light Gradient Boosted Machine (LightGBM)  Ke et al. (2017) 
11  CatBoost  Dorogush et al. (2018) 
#  Classifier  Location of the Python library 

1  Logistic regression  sklearn.linear_model.LogisticRegression 
2  Random Forest  sklearn.ensemble.RandomForestClassifier 
3  Extra Trees  sklearn.ensemble.ExtraTreesClassifier 
4  Voting  sklearn.ensemble.VotingClassifier 
5  Stacking  sklearn.ensemble.StackingClassifier 
6  Bagging  sklearn.ensemble.BaggingClassifier 
7  AdaBoost  sklearn.ensemble.AdaBoostClassifier 
8  Gradient boosting  sklearn.ensemble.GradientBoostingClassifier 
9  Hist GBoosting  sklearn.ensemble. HistGradientBoostingClassifier 
10  XGBoost  xgboost.XGBClassifier 
11  LightGBM  lightgbm.LGBMClassifier 
12  CatBoost  catboost.CatBoostClassifier 
Predicted Class  

0  1  
Actual class  0  TN (True Negative)  FP (False Positive) 
1  FN (False Negative)  TP (True Positive) 
Index  Features  Descriptions  References 

1  Value of the India VIX (open, high, low and close)  Open, high, low and close values of the India VIX  Ballestra et al. (2019) Dixit et al. (2013) Prasad et al. (2022) 
2  Days of week  0 to 6 for Sunday to Saturday  Dixit et al. (2013) 
3  EWMA  The EWMA of the India VIX with 5, 10, 15 and 20day moving windows  Dixit et al. (2013) 
4  EWMV  EWMV of returns on the NIFTY 50 Index with a 10day moving window  Chaudhuri and Ghosh (2016) 
5  Return on the NIFTY 50 Index  Log returns on NIFTY 50 Index  Bantwa (2017) Carr (2017) Fernandes et al. (2014) Mall et al. (2011) Shaikh and Padhi (2016) 
6  Return on volume of the NIFTY 50 Index  Log return on volume of underlying NIFTY 50 Index  Fernandes et al. (2014) 
7  ATR  ATR (volatility indicator) of the NIFTY 50 Index with a 10day moving window  Included to capture the volatility of the underlying index 
8  DIV  DIV of the NIFTY 50 Index with a 10day moving window  Yang and Zhang (2000) 
9  Return on the S&P 500  Log return on close value of the S&P 500 Index  Onan et al. (2014) 
10  Return on DJIA  Log return on close value of the DJIA Index  Onan et al. (2014) 
11  Changes in VIX  First difference of the closing value of the CBOE VIX Index  Onan et al. (2014) 
Classifier  Class Weights to 0s Label  Class Weights to 1s Label 

Random Forest  0.95  1.18 
Extra Trees  0.95  1.39 
Bagging  0.95  1.16 
AdaBoost  0.95  1.16 
Stacking  0.95  1.15 
Voting  0.95  1.16 
Gradient boosting  0.95  1.19 
Hist GBoosting  0.94  1.14 
XGBoost  0.96  1.10 
LightGBM  0.95  1.09 
Logistic regression  0.95  1.40 
Classifier  Split0 Score  Split1 Score  Mean Score  Std Score 

Logistic regression  0.500206  0.504043  0.502124  0.001919 
Random Forest  0.590954  0.614735  0.602845  0.011891 
Extra Trees  0.466468  0.423695  0.445082  0.021387 
Bagging  0.580314  0.591281  0.585797  0.005484 
AdaBoost  0.611933  0.616224  0.614078  0.002145 
Stacking  0.579413  0.596283  0.587848  0.008435 
Voting  0.578771  0.592769  0.585770  0.006999 
Stochastic GBoosting  0.589778  0.585407  0.587592  0.002185 
Hist GBoosting  0.583003  0.610750  0.596876  0.013873 
XGBoost  0.580665  0.616893  0.598779  0.018114 
LightGBM  0.609343  0.609410  0.609377  0.000033 
CatBoost  0.549842  0.491619  0.520730  0.029111 
Classifier  TN  FP  FN  TP  Accuracy Score  AUC  PrecisionRecall AUC  GMean f1Score 

Logistic regression  114  54  55  77  63.67%  69.04%  66.38%  62.94% 
Random Forest  118  50  50  82  66.67%  67.77%  63.44%  66.06% 
Extra Trees  112  56  52  80  64.00%  68.57%  64.90%  63.47% 
Bagging  118  50  51  81  66.33%  68.11%  64.65%  65.68% 
AdaBoost  113  55  51  81  64.67%  67.98%  62.87%  64.15% 
Stacking  124  44  53  79  67.67%  69.48%  65.48%  66.74% 
Voting  118  50  52  80  66.00%  68.32%  64.54%  65.30% 
Stochastic GBoosting  115  53  57  75  63.33%  68.72%  65.32%  62.47% 
Hist GBoosting  122  46  57  75  65.67%  66.93%  63.73%  64.57% 
XGBoost  118  50  51  81  66.33%  67.42%  63.89%  65.68% 
LightGBM  118  50  51  81  66.33%  67.30%  63.25%  65.68% 
CatBoost  120  48  52  80  66.67%  68.38%  64.07%  65.91% 
Rank  Classifier  Class Score  Overall Score  Accuracy Score 

1  CatBoost  0.4458  0.3972  66.67% 
1  LightGBM  0.4458  0.3972  66.33% 
1  XGBoost  0.4458  0.3972  66.33% 
1  Voting  0.4458  0.3972  66.00% 
1  Stacking  0.4458  0.3972  67.67% 
1  Bagging  0.4458  0.3972  66.33% 
1  Random Forest  0.4458  0.3972  66.67% 
8  Hist GBoosting  0.4125  0.3639  65.67% 
9  AdaBoost  0.3917  0.3639  64.67% 
9  Extra Trees  0.3917  0.3639  64.00% 
11  Stochastic Gboosting  0.3500  0.3639  63.33% 
11  Logistic regression  0.3500  0.3639  63.67% 
Outlook on the Trend of Underlying Index (Nifty 50)  

Bearish  Neutral  Bullish  
Expected move in implied volatility (India VIX)  Decrease  Write calls  Write straddles  Write puts 
Remain unchanged  Write calls and buy puts  Calendar spread  Buy calls and write puts  
Increase  Buy puts  Buy straddle  Buy calls 
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Prasad, A.; Bakhshi, P. Forecasting the Direction of Daily Changes in the India VIX Index Using Machine Learning. J. Risk Financial Manag. 2022, 15, 552. https://doi.org/10.3390/jrfm15120552
Prasad A, Bakhshi P. Forecasting the Direction of Daily Changes in the India VIX Index Using Machine Learning. Journal of Risk and Financial Management. 2022; 15(12):552. https://doi.org/10.3390/jrfm15120552
Chicago/Turabian StylePrasad, Akhilesh, and Priti Bakhshi. 2022. "Forecasting the Direction of Daily Changes in the India VIX Index Using Machine Learning" Journal of Risk and Financial Management 15, no. 12: 552. https://doi.org/10.3390/jrfm15120552