{ "source_file": "0930", "source_platform": "Medium", "author": "Serafeim Loukas, PhD", "title_listed": "Time-Series Forecasting: Predicting Stock Prices Using An ARIMA Model", "keywords": "", "domain": "数据处理", "content_type": "深度技术解析", "is_paid_flag": "否", "url": "https://towardsdatascience.com/time-series-forecasting-predicting-stock-prices-using-an-arima-model-2e3b3080bd70/", "publish_date": "2020-07-23", "corpus_stage": "", "notes": "", "id": "4adb27b6472f", "collected_at": "2026-10-02T08:16:18", "title": "Time-Series Forecasting: Predicting Stock Prices Using An ARIMA Model | Towards Data Science", "body_markdown": "![Revisit consent button](../images/body-df29beacd7496220cc94.svg)\nWe value your privacy\nWe use cookies to enhance your browsing experience, serve personalised ads or content, and analyse our traffic. 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It also helps in adverstising on the website.\n\n\n * Cookie\nedgebucket\n * Duration\nsession\n * Description\nReddit sets this cookie to save the information about a log-on Reddit user, for the purpose of advertisement recommendations and updating the content.\n\n\n * Cookie\ndid\n * Duration\n1 year\n * Description\nArbor sets this cookie to show targeted ads to site visitors.This cookie expires after 2 months or 1 year.\n\n\nUncategorised\nOther uncategorised cookies are those that are being analysed and have not been classified into a category as yet.\nNo cookies to display.\nReject All Save My Preferences Accept All\nToggle Search[](https://towardsdatascience.com/)Toggle Mobile Navigation\n[](https://towardsdatascience.com/)\nPublish AI, ML & data-science insights to a global community of data professionals.\nSign in[Submit an Article](https://write.insightmediagroup.io)\n[Latest](https://towardsdatascience.com/latest/)[Editor's Picks](https://towardsdatascience.com/tag/editors-pick/)[Newsletter](https://towardsdatascience.com/tag/the-variable/)[ShipAI](https://towardsdatascience.com/shipai/)\n* * *\n[Write For TDS](https://towardsdatascience.com/submissions/)\n[LinkedIn](https://www.linkedin.com/company/towards-data-science/)[X](https://x.com/TDataScience)Toggle Search\n[Data Science](https://towardsdatascience.com/category/data-science/)\n# Time-Series Forecasting: Predicting Stock Prices Using An ARIMA Model\nIn this post I show you how to predict the TESLA stock price using a forecasting ARIMA model\n[Serafeim Loukas, PhD](https://towardsdatascience.com/author/seralouk/)\nJuly 23, 20206 min read\n![ARIMA model performance on the test set](../images/000.png)\nARIMA model performance on the test set\n## 1. Introduction\n### 1.1. Time-series & forecasting models\n**Time-series forecasting** models are the models that are capable to **predict** **future values** based on **previously** **observed** **values**. Time-series forecasting is widely used for **non-stationary data**. **Non-stationary data** are called the data whose statistical properties e.g. the mean and standard deviation are not constant over time but instead, these metrics vary over time.\nThese non-stationary input data (used as input to these models) are usually called **time-series.** Some examples of time-series include the temperature values over time, stock price over time, price of a house over time etc. So, the input is a **signal** (time-series) that is **defined by observations taken sequentially in time**.\n> A time series is a sequence of observations taken sequentially in time.\n![An example of a time-series. Plot created by the author in Python.](../images/001.png)\nAn example of a time-series. Plot created by the author in Python.\n**Observation: Time-series** data is recorded on a **discrete** **time** **scale**.\n**Disclaimer** : There have been attempts to predict stock prices using time series analysis algorithms, though they still cannot be used to place bets in the real market. This is just a tutorial article that does not intent in any way to \"direct\" people into buying stocks.\n* * *\nIf you're passionate about diving deeper into machine learning with Python and sklearn, I highly recommend checking out [**this book**](https://amzn.to/3t4YB2d); it's a game-changer in breaking down complex topics into digestible insights.\n> [**Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques...**](https://amzn.to/3t4YB2d)\n* * *\n## 2. The AutoRegressive Integrated Moving Average (ARIMA) model\nA famous and widely used forecasting method for time-series prediction is the **AutoRegressive Integrated Moving Average (ARIMA)** model. **ARIMA** models are capable of capturing a suite of different standard temporal structures in time-series data.\n### Terminology\nLet's break down these terms:\n * **AR: < Auto Regressive >** means that the model **uses the dependent relationship between an observation and some predefined number of lagged observations** (also known as \"time lag\" or \"lag\").\n * **I: < Integrated >** means that the model employs **differencing of raw observations** (e.g. it subtracts an observation from an observation at the previous time step) in order to make the time-series **stationary.MA** :\n * _**MA: < Moving Average >**_ means that the model exploits the **relationship between the residual error and the observations.**\n\n\n### Model parameters\nThe standard ARIMA models expect as input parameters 3 arguments i.e. p,d,q.\n * **p** is the **number of lag observations.**\n * **d** is the **degree of differencing.**\n * **q** is the **size/width of the moving average window.**\n\n\n* * *\n * **NEW** : After a great deal of hard work and staying behind the scenes for quite a while, we're excited to now offer our expertise through a platform, the \"[**Data Science Hub**](https://www.patreon.com/TheDataScienceHub\\))\" on Patreon (). This hub is our way of providing you with **bespoke consulting services** and comprehensive **responses to all your inquiries** , ranging from Machine Learning to strategic data analytics planning.\n * Another resource. Learn Data Science and ML with the help of an 🤖 AI-powered tutor. Start here h[ttps://aigents.co/learn ](https://aigents.co/learn)choose a topic and he will show up where you need him. No paywall, no signups, no ads.\n\n\n* * *\n## 3. Getting the stock price history data\nThanks to **Yahoo finance** we can get the data for **free**. Use the following link to get the stock price history of **TESLA** : [https://finance.yahoo.com/quote/TSLA/history?period1=1436486400&period2=1594339200&interval=1d&filter=history&frequency=1d](https://finance.yahoo.com/quote/TSLA/history?period1=1436486400&period2=1594339200&interval=1d&filter=history&frequency=1d)\nYou should see the following:\n![](../images/body-4632f022c0c2ea7a4a71.png)\nClick on the **Download** and save the **.csv** file locally on your computer.\nThe data are from **2015** till now (**2020**) !\n* * *\n## 4. Python working example\n_Modules needed: Numpy, Pandas,_ Statsmodels _, Scikit-Learn_\n**4.1. Load & inspect the data**\nOur **imports** :\ntext\n\n```\nimport numpy as np \nimport pandas as pd \nimport matplotlib.pyplot as plt\nfrom pandas.plotting import lag_plot\nfrom pandas import datetime\nfrom statsmodels.tsa.arima_model import ARIMA\nfrom sklearn.metrics import mean_squared_error\n```\n\nNow let's **load** the TESLA stock history **data** :\ntext\n\n```\ndf = pd.read_csv(\"TSLA.csv\")\ndf.head(5)\n```\n\n![](../images/body-6891cf82dea41f5aeba9.png)\n * Our target variable will be the **Close** value.\n\n\n### Before building the ARIMA model, let's see if there is some cross-correlation in out data.\ntext\n\n```\nplt.figure()\nlag_plot(df['Open'], lag=3)\nplt.title('TESLA Stock - Autocorrelation plot with lag = 3')\nplt.show()\n```\n\n![TESLA Stock - Autocorrelation plot with lag = 3](../images/002.png)\nTESLA Stock - Autocorrelation plot with lag = 3\nWe can now confirm that **ARIMA** is going to be a good model to be applied to this type of data (there is auto-correlation in the data).\nFinally, let's **plot the stock price evolution over time.**\ntext\n\n```\nplt.plot(df[\"Date\"], df[\"Close\"])\nplt.xticks(np.arange(0,1259, 200), df['Date'][0:1259:200])\nplt.title(\"TESLA stock price over time\")\nplt.xlabel(\"time\")\nplt.ylabel(\"price\")\nplt.show()\n```\n\n![](../images/body-47c2d97345e32166d9a9.png)\n**4.2. Build the predictive ARIMA model**\nNext, let's **divide** the data into a **training** (70 % ) and **test** (30%) set. For this tutorial we select the following **ARIMA parameters: p=4, d=1 and q=0.**\ntext\n\n```\ntrain_data, test_data = df[0:int(len(df)*0.7)], df[int(len(df)*0.7):]\n```\n\ntext\n\n```\ntraining_data = train_data['Close'].values\ntest_data = test_data['Close'].values\n```\n\ntext\n\n```\nhistory = [x for x in training_data]\nmodel_predictions = []\nN_test_observations = len(test_data)\n```\n\ntext\n\n```\nfor time_point in range(N_test_observations):\n model = ARIMA(history, order=(4,1,0))\n model_fit = model.fit(disp=0)\n output = model_fit.forecast()\n yhat = output[0]\n model_predictions.append(yhat)\n true_test_value = test_data[time_point]\n history.append(true_test_value)\n```\n\ntext\n\n```\nMSE_error = mean_squared_error(test_data, model_predictions)\nprint('Testing Mean Squared Error is {}'.format(MSE_error))\n```\n\n### Summary of the code\n * We split the training dataset into train and test sets and we use the train set to fit the model, and generate a prediction **for each element on the test set**.\n * **A rolling forecasting procedure is required given the dependence on observations in prior time steps for differencing and the AR model. To this end, we re-create the ARIMA model after each new observation is received.**\n * Finally, we manually keep track of all observations in a list called **history** that is seeded with the training data and to which new observations are appended at each iteration.\n\n\nTesting Mean Squared Error is 741.0594879572484\n> The MSE of the test set is quite large denoting that the precise prediction is a hard problem. However, this is the average squared value across all the test set predictions. Let's **visualize** the predictions to understand the performance of the model more.\ntext\n\n```\ntest_set_range = df[int(len(df)*0.7):].index\n```\n\ntext\n\n```\nplt.plot(test_set_range, model_predictions, color='blue', marker='o', linestyle='dashed',label='Predicted Price')\n```\n\ntext\n\n```\nplt.plot(test_set_range, test_data, color='red', label='Actual Price')\n```\n\ntext\n\n```\nplt.title('TESLA Prices Prediction')\nplt.xlabel('Date')\nplt.ylabel('Prices')\nplt.xticks(np.arange(881,1259,50), df.Date[881:1259:50])\nplt.legend()\nplt.show()\n```\n\n![ARIMA model performance on the test set](../images/003.png)\nARIMA model performance on the test set\n### Not so bad right?\nOur ARIMA model results in appreciable results. This model offers a good prediction accuracy and to be relatively fast compared to other alternatives, in terms of training/fitting time and complexity.\nThat's all folks ! Hope you liked this article!\n* * *\nIf you're passionate about diving deeper into machine learning with Python and sklearn, I highly recommend checking out [**this book**](https://amzn.to/3t4YB2d); it's a game-changer in breaking down complex topics into digestible insights.\n> [**Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques...**](https://amzn.to/3t4YB2d)\n* * *\n## Stay tuned & support this effort\nIf you liked and found this article useful, **follow** me to be able to see all my new posts.\nQuestions? Post them as a comment and I will reply as soon as possible.\nWe offer our expertise through a platform, the \"[**Data Science Hub**](https://www.patreon.com/TheDataScienceHub\\))\" on Patreon (). This hub is our way of providing you with **bespoke consulting services** and comprehensive **responses to all your inquiries** , ranging from Machine Learning to strategic data analytics planning.\n* * *\n## My previous articles that you might also like:\n[**LSTM Time-Series Forecasting: Predicting Stock Prices Using An LSTM Model**](https://towardsdatascience.com/lstm-time-series-forecasting-predicting-stock-prices-using-an-lstm-model-6223e9644a2f)\n> [**LSTM Time-Series Forecasting: Predicting Stock Prices Using An LSTM Model**](https://towardsdatascience.com/lstm-time-series-forecasting-predicting-stock-prices-using-an-lstm-model-6223e9644a2f)\n[**Time-Series Forecasting: Predicting Stock Prices Using Facebook's Prophet Model**](https://towardsdatascience.com/time-series-forecasting-predicting-stock-prices-using-facebooks-prophet-model-9ee1657132b5)\n> [**Time-Series Forecasting: Predicting Stock Prices Using Facebook's Prophet Model**](https://towardsdatascience.com/time-series-forecasting-predicting-stock-prices-using-facebooks-prophet-model-9ee1657132b5)\n* * *\n## References\n[1] \n* * *\n## Other posts\n> [**The Best FREE Data Science Resources: FREE Books & Online Courses**](https://medium.com/@seralouk/the-best-free-data-science-resources-free-books-online-courses-9c4a2df194e5)\n> [**ROC Curve Explained using a COVID-19 hypothetical example: Binary & Multi-Class Classification...**](https://towardsdatascience.com/roc-curve-explained-using-a-covid-19-hypothetical-example-binary-multi-class-classification-bab188ea869c)\n> [**Support Vector Machines (SVM) clearly explained: A python tutorial for classification problems...**](https://towardsdatascience.com/support-vector-machines-svm-clearly-explained-a-python-tutorial-for-classification-problems-29c539f3ad8)\n> [**PCA clearly explained - How, when, why to use it and feature importance: A guide in Python**](https://towardsdatascience.com/pca-clearly-explained-how-when-why-to-use-it-and-feature-importance-a-guide-in-python-7c274582c37e)\n> [**Everything you need to know about Min-Max normalization in Python**](https://towardsdatascience.com/everything-you-need-to-know-about-min-max-normalization-in-python-b79592732b79)\n> [**How Scikit-Learn's StandardScaler works**](https://towardsdatascience.com/how-and-why-to-standardize-your-data-996926c2c832)\n## Register Now to Continue Reading\n### Unlock Towards Data Science with a Free Account\nAll articles on Towards Data Science are available to registered users. 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It also helps in adverstising on the website.\n\n\n * Cookie\nedgebucket\n * Duration\nsession\n * Description\nReddit sets this cookie to save the information about a log-on Reddit user, for the purpose of advertisement recommendations and updating the content.\n\n\n * Cookie\ndid\n * Duration\n1 year\n * Description\nArbor sets this cookie to show targeted ads to site visitors.This cookie expires after 2 months or 1 year.\n\n\nUncategorised\nOther uncategorised cookies are those that are being analysed and have not been classified into a category as yet.\nNo cookies to display.\nReject All Save My Preferences Accept All\nToggle Search[](https://towardsdatascience.com/)Toggle Mobile Navigation\n[](https://towardsdatascience.com/)\nPublish AI, ML & data-science insights to a global community of data professionals.\nSign in[Submit an Article](https://write.insightmediagroup.io)\n[Latest](https://towardsdatascience.com/latest/)[Editor's Picks](https://towardsdatascience.com/tag/editors-pick/)[Newsletter](https://towardsdatascience.com/tag/the-variable/)[ShipAI](https://towardsdatascience.com/shipai/)\n* * *\n[Write For TDS](https://towardsdatascience.com/submissions/)\n[LinkedIn](https://www.linkedin.com/company/towards-data-science/)[X](https://x.com/TDataScience)Toggle Search\n[Data Science](https://towardsdatascience.com/category/data-science/)\n# Time-Series Forecasting: Predicting Stock Prices Using An ARIMA Model\nIn this post I show you how to predict the TESLA stock price using a forecasting ARIMA model\n[Serafeim Loukas, PhD](https://towardsdatascience.com/author/seralouk/)\nJuly 23, 20206 min read\n![ARIMA model performance on the test set](https://assets.insightmediagroup.io/media/wp-content/uploads/2020/07/1H2tmwTA1cZYQ7h4TPNdQkA.png)\nARIMA model performance on the test set\n## 1. Introduction\n### 1.1. Time-series & forecasting models\n**Time-series forecasting** models are the models that are capable to **predict** **future values** based on **previously** **observed** **values**. Time-series forecasting is widely used for **non-stationary data**. **Non-stationary data** are called the data whose statistical properties e.g. the mean and standard deviation are not constant over time but instead, these metrics vary over time.\nThese non-stationary input data (used as input to these models) are usually called **time-series.** Some examples of time-series include the temperature values over time, stock price over time, price of a house over time etc. So, the input is a **signal** (time-series) that is **defined by observations taken sequentially in time**.\n> A time series is a sequence of observations taken sequentially in time.\n![An example of a time-series. Plot created by the author in Python.](https://assets.insightmediagroup.io/media/wp-content/uploads/2020/07/1SULcaLxjHsAVmhxG7Xo0cA.png)\nAn example of a time-series. Plot created by the author in Python.\n**Observation: Time-series** data is recorded on a **discrete** **time** **scale**.\n**Disclaimer** : There have been attempts to predict stock prices using time series analysis algorithms, though they still cannot be used to place bets in the real market. This is just a tutorial article that does not intent in any way to \"direct\" people into buying stocks.\n* * *\nIf you're passionate about diving deeper into machine learning with Python and sklearn, I highly recommend checking out [**this book**](https://amzn.to/3t4YB2d); it's a game-changer in breaking down complex topics into digestible insights.\n> [**Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques...**](https://amzn.to/3t4YB2d)\n* * *\n## 2. The AutoRegressive Integrated Moving Average (ARIMA) model\nA famous and widely used forecasting method for time-series prediction is the **AutoRegressive Integrated Moving Average (ARIMA)** model. **ARIMA** models are capable of capturing a suite of different standard temporal structures in time-series data.\n### Terminology\nLet's break down these terms:\n * **AR: < Auto Regressive >** means that the model **uses the dependent relationship between an observation and some predefined number of lagged observations** (also known as \"time lag\" or \"lag\").\n * **I: < Integrated >** means that the model employs **differencing of raw observations** (e.g. it subtracts an observation from an observation at the previous time step) in order to make the time-series **stationary.MA** :\n * _**MA: < Moving Average >**_ means that the model exploits the **relationship between the residual error and the observations.**\n\n\n### Model parameters\nThe standard ARIMA models expect as input parameters 3 arguments i.e. p,d,q.\n * **p** is the **number of lag observations.**\n * **d** is the **degree of differencing.**\n * **q** is the **size/width of the moving average window.**\n\n\n* * *\n * **NEW** : After a great deal of hard work and staying behind the scenes for quite a while, we're excited to now offer our expertise through a platform, the \"[**Data Science Hub**](https://www.patreon.com/TheDataScienceHub\\))\" on Patreon (). This hub is our way of providing you with **bespoke consulting services** and comprehensive **responses to all your inquiries** , ranging from Machine Learning to strategic data analytics planning.\n * Another resource. Learn Data Science and ML with the help of an 🤖 AI-powered tutor. Start here h[ttps://aigents.co/learn ](https://aigents.co/learn)choose a topic and he will show up where you need him. No paywall, no signups, no ads.\n\n\n* * *\n## 3. Getting the stock price history data\nThanks to **Yahoo finance** we can get the data for **free**. Use the following link to get the stock price history of **TESLA** : [https://finance.yahoo.com/quote/TSLA/history?period1=1436486400&period2=1594339200&interval=1d&filter=history&frequency=1d](https://finance.yahoo.com/quote/TSLA/history?period1=1436486400&period2=1594339200&interval=1d&filter=history&frequency=1d)\nYou should see the following:\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2020/07/1ClLXfFKG6zL3RsZI1jrZaw.png)\nClick on the **Download** and save the **.csv** file locally on your computer.\nThe data are from **2015** till now (**2020**) !\n* * *\n## 4. Python working example\n_Modules needed: Numpy, Pandas,_ Statsmodels _, Scikit-Learn_\n**4.1. Load & inspect the data**\nOur **imports** :\ntext\n\n```\nimport numpy as np \nimport pandas as pd \nimport matplotlib.pyplot as plt\nfrom pandas.plotting import lag_plot\nfrom pandas import datetime\nfrom statsmodels.tsa.arima_model import ARIMA\nfrom sklearn.metrics import mean_squared_error\n```\n\nNow let's **load** the TESLA stock history **data** :\ntext\n\n```\ndf = pd.read_csv(\"TSLA.csv\")\ndf.head(5)\n```\n\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2020/07/1Mz1MFVelLRXGUMMZI1SCDA.png)\n * Our target variable will be the **Close** value.\n\n\n### Before building the ARIMA model, let's see if there is some cross-correlation in out data.\ntext\n\n```\nplt.figure()\nlag_plot(df['Open'], lag=3)\nplt.title('TESLA Stock - Autocorrelation plot with lag = 3')\nplt.show()\n```\n\n![TESLA Stock - Autocorrelation plot with lag = 3](https://assets.insightmediagroup.io/media/wp-content/uploads/2020/07/1mWYgxguPhVFPkjZBG1GvNQ.png)\nTESLA Stock - Autocorrelation plot with lag = 3\nWe can now confirm that **ARIMA** is going to be a good model to be applied to this type of data (there is auto-correlation in the data).\nFinally, let's **plot the stock price evolution over time.**\ntext\n\n```\nplt.plot(df[\"Date\"], df[\"Close\"])\nplt.xticks(np.arange(0,1259, 200), df['Date'][0:1259:200])\nplt.title(\"TESLA stock price over time\")\nplt.xlabel(\"time\")\nplt.ylabel(\"price\")\nplt.show()\n```\n\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2020/07/1-MWDEvYgLLdomHL7KmHCzQ.png)\n**4.2. Build the predictive ARIMA model**\nNext, let's **divide** the data into a **training** (70 % ) and **test** (30%) set. For this tutorial we select the following **ARIMA parameters: p=4, d=1 and q=0.**\ntext\n\n```\ntrain_data, test_data = df[0:int(len(df)*0.7)], df[int(len(df)*0.7):]\n```\n\ntext\n\n```\ntraining_data = train_data['Close'].values\ntest_data = test_data['Close'].values\n```\n\ntext\n\n```\nhistory = [x for x in training_data]\nmodel_predictions = []\nN_test_observations = len(test_data)\n```\n\ntext\n\n```\nfor time_point in range(N_test_observations):\n model = ARIMA(history, order=(4,1,0))\n model_fit = model.fit(disp=0)\n output = model_fit.forecast()\n yhat = output[0]\n model_predictions.append(yhat)\n true_test_value = test_data[time_point]\n history.append(true_test_value)\n```\n\ntext\n\n```\nMSE_error = mean_squared_error(test_data, model_predictions)\nprint('Testing Mean Squared Error is {}'.format(MSE_error))\n```\n\n### Summary of the code\n * We split the training dataset into train and test sets and we use the train set to fit the model, and generate a prediction **for each element on the test set**.\n * **A rolling forecasting procedure is required given the dependence on observations in prior time steps for differencing and the AR model. To this end, we re-create the ARIMA model after each new observation is received.**\n * Finally, we manually keep track of all observations in a list called **history** that is seeded with the training data and to which new observations are appended at each iteration.\n\n\nTesting Mean Squared Error is 741.0594879572484\n> The MSE of the test set is quite large denoting that the precise prediction is a hard problem. However, this is the average squared value across all the test set predictions. Let's **visualize** the predictions to understand the performance of the model more.\ntext\n\n```\ntest_set_range = df[int(len(df)*0.7):].index\n```\n\ntext\n\n```\nplt.plot(test_set_range, model_predictions, color='blue', marker='o', linestyle='dashed',label='Predicted Price')\n```\n\ntext\n\n```\nplt.plot(test_set_range, test_data, color='red', label='Actual Price')\n```\n\ntext\n\n```\nplt.title('TESLA Prices Prediction')\nplt.xlabel('Date')\nplt.ylabel('Prices')\nplt.xticks(np.arange(881,1259,50), df.Date[881:1259:50])\nplt.legend()\nplt.show()\n```\n\n![ARIMA model performance on the test set](https://assets.insightmediagroup.io/media/wp-content/uploads/2020/07/1n8t9uJTLkuk-T1gW6u_7tA.png)\nARIMA model performance on the test set\n### Not so bad right?\nOur ARIMA model results in appreciable results. This model offers a good prediction accuracy and to be relatively fast compared to other alternatives, in terms of training/fitting time and complexity.\nThat's all folks ! Hope you liked this article!\n* * *\nIf you're passionate about diving deeper into machine learning with Python and sklearn, I highly recommend checking out [**this book**](https://amzn.to/3t4YB2d); it's a game-changer in breaking down complex topics into digestible insights.\n> [**Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques...**](https://amzn.to/3t4YB2d)\n* * *\n## Stay tuned & support this effort\nIf you liked and found this article useful, **follow** me to be able to see all my new posts.\nQuestions? Post them as a comment and I will reply as soon as possible.\nWe offer our expertise through a platform, the \"[**Data Science Hub**](https://www.patreon.com/TheDataScienceHub\\))\" on Patreon (). This hub is our way of providing you with **bespoke consulting services** and comprehensive **responses to all your inquiries** , ranging from Machine Learning to strategic data analytics planning.\n* * *\n## My previous articles that you might also like:\n[**LSTM Time-Series Forecasting: Predicting Stock Prices Using An LSTM Model**](https://towardsdatascience.com/lstm-time-series-forecasting-predicting-stock-prices-using-an-lstm-model-6223e9644a2f)\n> [**LSTM Time-Series Forecasting: Predicting Stock Prices Using An LSTM Model**](https://towardsdatascience.com/lstm-time-series-forecasting-predicting-stock-prices-using-an-lstm-model-6223e9644a2f)\n[**Time-Series Forecasting: Predicting Stock Prices Using Facebook's Prophet Model**](https://towardsdatascience.com/time-series-forecasting-predicting-stock-prices-using-facebooks-prophet-model-9ee1657132b5)\n> [**Time-Series Forecasting: Predicting Stock Prices Using Facebook's Prophet Model**](https://towardsdatascience.com/time-series-forecasting-predicting-stock-prices-using-facebooks-prophet-model-9ee1657132b5)\n* * *\n## References\n[1] \n* * *\n## Other posts\n> [**The Best FREE Data Science Resources: FREE Books & Online Courses**](https://medium.com/@seralouk/the-best-free-data-science-resources-free-books-online-courses-9c4a2df194e5)\n> [**ROC Curve Explained using a COVID-19 hypothetical example: Binary & Multi-Class Classification...**](https://towardsdatascience.com/roc-curve-explained-using-a-covid-19-hypothetical-example-binary-multi-class-classification-bab188ea869c)\n> [**Support Vector Machines (SVM) clearly explained: A python tutorial for classification problems...**](https://towardsdatascience.com/support-vector-machines-svm-clearly-explained-a-python-tutorial-for-classification-problems-29c539f3ad8)\n> [**PCA clearly explained - How, when, why to use it and feature importance: A guide in Python**](https://towardsdatascience.com/pca-clearly-explained-how-when-why-to-use-it-and-feature-importance-a-guide-in-python-7c274582c37e)\n> [**Everything you need to know about Min-Max normalization in Python**](https://towardsdatascience.com/everything-you-need-to-know-about-min-max-normalization-in-python-b79592732b79)\n> [**How Scikit-Learn's StandardScaler works**](https://towardsdatascience.com/how-and-why-to-standardize-your-data-996926c2c832)\n## Register Now to Continue Reading\n### Unlock Towards Data Science with a Free Account\nAll articles on Towards Data Science are available to registered users. 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