Nvidia's Stock Returns Prediction Using Machine Learning Techniques for Time Series Forecasting Problem

Chlebus, Marcin; Dyczko, Michał; Woźniak, Michał

doi:10.2478/ceej-2021-0004

Figures & Tables

Algorithm of model buildingSource: Author

Nvidia stock returns on in-sample setSource: Authors calculations

Nvidia stock returns on out-of-sample setSource: Authors calculations

Results of Ljung-Box test for in-sample set and out-of-sample set. Notes: Figure presents results of Ljung-Box test of white-noise hypothesis of Nvidia's stock returns on in-sample set and out-of-sample setSource: Authors calculations

ACF and PACF for in-sample and out-of-sample sets. Notes: Figure presents autocorrelation and partial autocorrelation plots of Nvidia's stock returns on in-sample and out-of-sample setsSource: Authors calculations

Performance on test set of the best model in research – SVR (based on stationary variables)Source: Authors calculations

Results of Augmented Dickey-Fuller test for in-sample set and out-of-sample set

Test statistic (in sample)	p-value (in sample)	Test statistic (out of sample)	p-value (out of sample)
−11.01	<0.0001	−11.09	<0.0001

Results of singular models on validation and test set (based on stationary variables)

Model (number of attributes)	Set	Hyperparameters	RMSE	MAE	MedAE
SVR (20)	Validation	C=0.005206Epsilon=0.087308	0.026924	0.019478	0.014985
SVR (20)	Test	C=0.005206epsilon=0.087308	0.036014	0.024916	0.016682
KNN (20)	Validation	Power of Minkowski metric=2k=7Weight function=uniform	0.026328	0.020331	0.016199
KNN (20)	Test	Power of Minkowski metric=2k=7Weight function=uniform	0.039305	0.025935	0.017202
XGBoost (27)	Validation	Max depth:7Subsample: 0.760762Colsample by tree: 0.199892Lambda: 0.345263Gamma: 0.000233Learning rate: 0.2	0.027622	0.020678	0.016553
XGBoost (27)	Test	Max depth:7Subsample: 0.760762Colsample by tree: 0.199892Lambda: 0.345263Gamma: 0.000233Learning rate: 0.2	0.038848	0.027218	0.019782
LGBM (43)	Validation	Number of leaves:58Min data in leaf:21ETA: 0.067318Max drop: 52L1 regularization: 0.059938L2 regularization: 0.050305	0.025905	0.018803	0.014339
LGBM (43)	Test	Number of leaves:58Min data in leaf:21ETA: 0.067318Max drop: 52L1 regularization: 0.059938L2 regularization: 0.050305	0.038870	0.026283	0.016467
LSTM (20)	Validation	H₁	0.026565	0.019741	0.014537
LSTM (20)	Test	H₁	0.036705	0.024918	0.016772

Performance of ensemble models on test set (based on all models)

Number of models	Models (weight)	RMSE	MAE	MedAE
2	S+NS SVR (0.504057), S+NS LightGBM (0.495943)	0.03873	0.025882	0.017714
3	S+NS SVR (0.337508), S+NS LightGBM (0.332075), S LightGBM (0.330417)	0.038593	0.025959	0.017321
4	S+NS SVR (0.255711), S+NS LightGBM (0.251594), S LightGBM (0.250338), S KNN (0.242357)	0.038436	0.025665	0.017152
5	S+NS SVR (0.206542), S+NS LightGBM (0.203217), S LightGBM (0.202202), S KNN (0.195756), S LSTM (0.192283)	0.037734	0.025267	0.016599
6	S+NS SVR (0.173976), S+NS LightGBM (0.171176), S LightGBM (0.170321), S KNN (0.164891), S LSTM (0.161965), S SVR (0.157671)	0.03681	0.024751	0.01743
7	S+NS SVR (0.150427), S+NS LightGBM (0.148006), S LightGBM (0.147266), S KNN (0.142572), S LSTM (0.140042), S SVR (0.136329), S+NS KNN (0.135359)	0.036871	0.024897	0.016953
8	S+NS SVR (0.133177), S+NS LightGBM (0.131034), S LightGBM (0.130379), S KNN (0.126223), S LSTM (0.123983), S SVR (0.120696), S+NS KNN (0.119837), S XGBoost (0.114672)	0.036746	0.024681	0.01647
9	S+NS SVR (0.119825), S+NS LightGBM (0.117896), S LightGBM (0.117307), S KNN (0.113568), S LSTM (0.111553), S SVR (0.108595), S+NS KNN (0.107822), S XGBoost (0.103175), S+NS XGBoost (0.100259)	0.036898	0.024757	0.01645
10	S+NS SVR (0.109125), S+NS LightGBM (0.107368), S LightGBM (0.106832), S KNN (0.103426), S LSTM (0.101591), S SVR (0.098897), S+NS KNN (0.098193), S XGBoost (0.093961), S+NS XGBoost (0.091305), S+NS LSTM (0.089302)	0.036899	0.024915	0.016466

Performance of best models on test set (ensemble and primary models)

Metric	Best stationary ensemble model	Best stationary + non-stationary ensemble model	Best ensemble model based on all models	Best stationary model – SVR	Best stationary + non-stationary model − LGBM	Naive model
RMSE	0.036106	0.038053	0.036746	0.036014	0.037284	0.050244
MAE	0.024094	0.026068	0.024681	0.024916	0.026295	0.034908
MedAE	0.015307	0.016645	0.01647	0.016682	0.017959	0.022378

Performance of ensemble models on test set (models based on stationary and non-stationary variables)

Number of models	Models (weight)	RMSE	MAE	MedAE
2	SVR (0.504057), LightGBM (0.495943)	0.038730	0.025882	0.017714
3	SVR (0.346773), LightGBM (0.341191), KNN (0.312036)	0.038314	0.026003	0.016682
4	SVR (0.268786), LightGBM (0.264459), KNN (0.241861), XGBoost (0.224895)	0.038301	0.025793	0.016876
5	SVR (0.220323), LightGBM (0.216777), KNN (0.198253), XGBoost (0.184346), LSTM (0.180301)	0.038053	0.026068	0.016645

Performance of models on test set (based on stationary and non-stationary variables)

Metric	SVR	KNN	XGBoost	LSTM	LGBM	Best ensemble model	Naive model
RMSE	0.041904	0.039313	0.040685	0.039593	0.037284	0.038053	0.050244
MAE	0.025875	0.026863	0.026906	0.028891	0.026295	0.026068	0.034908
MedAE	0.017279	0.018946	0.016939	0.020576	0.017959	0.016645	0.022378

Performance of ensemble models on test set (models based on stationary variables)

Number of models	Models (weight)	RMSE	MAE	MedAE
2	LightGBM (0.508099), KNN (0.491901)	0.038571	0.025784	0.017147
3	LightGBM (0.342575), KNN (0.331655), LSTM (0.32577)	0.037403	0.025111	0.015704
4	LightGBM (0.260092), KNN (0.251801), LSTM (0.247333), SVR (0.240775)	0.036181	0.024366	0.01599
5	LightGBM (0.211671), KNN (0.204923), LSTM (0.201287), SVR (0.19595),XGBoost (0.18617)	0.036106	0.024094	0.015307

Results of singular models on validation and test set (based on stationary and non-stationary variables)

Model (number of attributes)	Set	Hyperparameters	RMSE	MAE	MedAE
SVR (27)	Validation	C=0.005317, epsilon=0.092179	0.025632	0.019126	0.015488
SVR (27)	Test	C=0.005317, epsilon=0.092179	0.041904	0.025875	0.017279
KNN (40)	Validation	Power of Minkowski metric=1k=6Weight function=uniform	0.027021	0.020110	0.013813
KNN (40)	Test	Power of Minkowski metric=1k=6Weight function=uniform	0.039313	0.026863	0.018946
XGBoost (74)	Validation	Max depth:3Subsample: 0.840403Colsample by tree: 0.605006Lambda: 4.461698Gamma: 0.000808Learning rate: 0.105	0.028021	0.021604	0.020396
XGBoost (74)	Test	Max depth:3Subsample: 0.840403Colsample by tree: 0.605006Lambda: 4.461698Gamma: 0.000808Learning rate: 0.105	0.040685	0.026906	0.016939
LGBM (80)	Validation	Number of leaves:32Min data in leaf:38ETA: 0.099519Max drop: 51L1 regularization: 0.060221L2 regularization: 0.050423	0.025840	0.019361	0.014083
LGBM (80)	Test	Number of leaves:32Min data in leaf:38ETA: 0.099519Max drop: 51L1 regularization: 0.060221L2 regularization: 0.050423	0.037284	0.026295	0.017959
LSTM (20)	Validation	H₂	0.028334	0.021702	0.018201
LSTM (20)	Test	H₂	0.039593	0.028891	0.020576

Hyperparameters tuning algorithm_

1.	For each pair of sets (X_i,Y_i) ∈ S={(train, validation₁), (train ∪ validation₁, validation₂), (train ∪ validation₁∪ validation₂, validation₃)} next operations will be performed:
a.	the possibly largest group of hyperparameters will be selected according to best practice mentioned in literature,
b.	one-step-ahead prediction will be done, providing X_i as train set and Y_i as test set, and then one model with the lowest RMSE will be chosen, with parameters H_i.
As a result, set {H₁, H₂, H₃} is obtained.
2.	For H_i will be executed three predictions on each pair from S. In effect 3 RMSE will be received, from which the average will be calculated – A_i. As a result, set {A₁, A₂, A₃} is obtained.
3.	H_j will be chosen, where A_j = min{A₁, A₂, A₃}. It is the best set of hyperparameters, which is believed to assure stable fit in future forecasts.

Performance of models on test set (based on stationary variables)

Metric	SVR	KNN	XGBoost	LSTM	LGBM	Best ensemble	Naive model
RMSE	0.036014	0.039305	0.038848	0.036705	0.038870	0.036106	0.050244
MAE	0.024916	0.025935	0.027218	0.024918	0.026283	0.024094	0.034908
MedAE	0.016682	0.017202	0.019780	0.016772	0.016467	0.015307	0.022378

Nvidia's Stock Returns Prediction Using Machine Learning Techniques for Time Series Forecasting Problem

Figures & Tables

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Results of Augmented Dickey-Fuller test for in-sample set and out-of-sample set

Results of singular models on validation and test set (based on stationary variables)

Performance of ensemble models on test set (based on all models)

Performance of best models on test set (ensemble and primary models)

Performance of ensemble models on test set (models based on stationary and non-stationary variables)

Performance of models on test set (based on stationary and non-stationary variables)

Performance of ensemble models on test set (models based on stationary variables)

Results of singular models on validation and test set (based on stationary and non-stationary variables)

Hyperparameters tuning algorithm_

Performance of models on test set (based on stationary variables)

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