# Stock Market Prediction using Multivariate Time Series and Recurrent Neural Networks in Python

Regression models based on recurrent neural networks (RNN) can recognize patterns in time series data, making them an exciting technology for stock market forecasting. What distinguishes these RNNs from traditional neural networks is their architecture, consisting of multiple layers of long-term, short-term memory (LSTM). The LSTM layers allow the model to learn patterns in a time series that occur over different periods and are often difficult for human analysts to detect. We can train such models with one feature (univariate models) or multiple features (multivariate models). Multivariate Models can take more data into account, and if we provide them with relevant features, they can make better predictions. This tutorial shows how to implement a multivariate RNN for stock price prediction in Python. We use the Keras Python library to define the architecture of our regression model and then train this model to predict the NASDAQ index.

The remainder of this tutorial proceeds as follows: We start with a brief intro in which we compare modeling univariate and multivariate time series data. Then we turn to the hands-on part, in which we prepare the multivariate time series data and use it to train a neural network in Python. The model is a recurrent neural network with LSTM layers that forecasts the NASDAQ stock market index. Finally, we evaluate the performance of our model and make a forecast for the next day. Stock market forecasting has become an exciting application area for recurrent neural networks.

Disclaimer: This article does not constitute financial advice. Stock markets can be very volatile and are generally difficult to predict. Predictive models and other forms of analytics applied in this article only serve the purpose of illustrating machine learning use cases.

## Univariate vs. Multivariate Time Series Models

Multivariate models and univariate models differ in the number of their input features. While univariate models consider only a single feature, multivariate models use several input variables (features). In stock market forecasting, we can create additional features from price history. Examples are performance indicators such as moving averages, the RSI, or the Sales Volume. We can also include features from other sources, for example, social media sentiment, weather forecasts, etc. Multivariate models that have additional relevant information available have a chance to outperform univariate models. However, this is only true if the features are relevant and are indicative of future price movements.

Preparing data for training univariate models is more straightforward than for multivariate models. If you are new to time series prediction, you might want to check out my earlier articles. These explain how to develop and evaluate univariate time series models:

#### Univariate Prediction Models

The standard approach in time series regression is to train a model on past values from the time series that the model seeks to predict. The idea is that the value of a time series at time t is closely related to the previous time steps t-1, t-2, t-3, etc. This approach is similar to chart analysis, aiming to identify recurring formations in a price chart that indicates future movements. In both cases, the prediction performance depends on the capacity to identify recurring price formations and draw the correct conclusions.

#### Multivariate Prediction Models

Forecasting the price of a financial asset is a complex task. An endless number of variables can influence the price. Economic cycles, political developments, unforeseen events, psychological factors, market sentiment, and even the weather, all these variables will more or less exert an influence on the price. In addition, many of these variables are interdependent, which makes statistical modeling even more complex. Multivariate models are not able to fully cover the complexity of the market. However, they offer a more detailed abstraction of reality than univariate models.

A univariable forecast model reduces this complexity to a minimum of a single dependent variable. The other dimensions are left out. A multivariate can take several factors into account, but it is still a simplification. For example, a multivariate stock market prediction model can consider the relationship between the closing price and the opening price, moving averages, daily highs, the price of other stocks, and so on.

And even if you have great features, it gets more complex, as patterns and market rules may be subjected to frequent change. Models thus inevitably make mistakes. Nevertheless, to quote Georg Box, “All models are wrong, but some are useful.”

## Implementing a Multivariate Time Series Prediction Model in Python

In the following, we will develop a multivariate recurrent neuronal network in Python for time series prediction. The model will forecast the NASDAQ stock market index.

The development process covers six essential steps:

1. Creating Features and Scaling the Data
2. Splitting the Data into Train and Test
3. Slicing the Data using a sliding window approach
4. Training the model
5. Model Validation
6. Making Predictions and Unscaling them

The code is available on the GitHub repository.

### Prerequisites

Before starting the coding part, make sure that you have set up your Python 3 environment and required packages. If you don’t have an environment set up yet, you can follow the steps in this tutorial to set up the Anaconda environment.

Also, make sure you install all required packages. In this tutorial, we will be working with the following standard packages:

In addition, we will be using Keras (2.0 or higher) with Tensorflow backend, the machine learning library sci-kit-learn, and the pandas-DataReader.

You can install packages using console commands:

• pip install <package name>
• conda install <package name> (if you are using the anaconda packet manager)

### Step #1 Load the Time Series Data

Let’s start by loading price data on the NASDAQ composite index (symbol: ^IXIC) from yahoo.finance.com into our Python project. To download the data, we use Pandas DataReader – a popular Python library that provides functions to extract data from various sources on the web. Alternatively, you can also use the “yfinance” library.

We provide the technical symbol for the NASDAQ index, which is “^IXIC“. Alternatively, you could use other asset symbols, for example, BTC-USD to get price quotes for Bitcoin. In addition, we limit the data in the API request to the timeframe between 2010-01-01 and the current date.

Running the code below will load the data into a new DataFrame object. Be aware that your input data and thus also the predictions will vary depending on when you execute the code.

```# Time Series Forecasting - Multivariate Time Series Models for Stock Market Prediction

import math # Mathematical functions
import numpy as np # Fundamental package for scientific computing with Python
import pandas as pd # Additional functions for analysing and manipulating data
from datetime import date, timedelta, datetime # Date Functions
from pandas.plotting import register_matplotlib_converters # This function adds plotting functions for calender dates
import matplotlib.pyplot as plt # Important package for visualization - we use this to plot the market data
import matplotlib.dates as mdates # Formatting dates
import tensorflow as tf
from sklearn.metrics import mean_absolute_error, mean_squared_error # Packages for measuring model performance / errors
from tensorflow.keras import Sequential # Deep learning library, used for neural networks
from tensorflow.keras.layers import LSTM, Dense, Dropout # Deep learning classes for recurrent and regular densely-connected layers
from tensorflow.keras.callbacks import EarlyStopping # EarlyStopping during model training
from sklearn.preprocessing import RobustScaler, MinMaxScaler # This Scaler removes the median and scales the data according to the quantile range to normalize the price data
import seaborn as sns # Visualization
sns.set_style('white', { 'axes.spines.right': False, 'axes.spines.top': False})

# check the tensorflow version and the number of available GPUs
print('Tensorflow Version: ' + tf.__version__)
physical_devices = tf.config.list_physical_devices('GPU')
print("Num GPUs:", len(physical_devices))

# Setting the timeframe for the data extraction
end_date =  date.today().strftime("%Y-%m-%d")
start_date = '2010-01-01'

# Getting NASDAQ quotes
stockname = 'NASDAQ'
symbol = '^IXIC'

# You can either use webreader or yfinance to load the data from yahoo finance

import yfinance as yf #Alternative package if webreader does not work: pip install yfinance

# Create a quick overview of the dataset

The data looks as expected and contains the following columns:

• High – the daily high
• Low – the daily low
• Open – the opening price
• Close – the closing price
• Volume – the daily trading volume

### Step #2 Explore the Data

Let’s first familiarize ourselves with the data before processing them further. Line plots are an excellent choice to familiarize with time series data. By running the code below, we create lineplots for all columns in our DataFrame.

```# Plot line charts
df_plot = df.copy()

ncols = 2
nrows = int(round(df_plot.shape / ncols, 0))

fig, ax = plt.subplots(nrows=nrows, ncols=ncols, sharex=True, figsize=(14, 7))
for i, ax in enumerate(fig.axes):
sns.lineplot(data = df_plot.iloc[:, i], ax=ax)
ax.tick_params(axis="x", rotation=30, labelsize=10, length=0)
ax.xaxis.set_major_locator(mdates.AutoDateLocator())
fig.tight_layout()
plt.show()```

The line plots look as expected. We continue with preprocessing and feature engineering.

### Step #3 Feature Selection and Scaling

Before we can train the neural network, we need to transform the data into a processable shape. In this section, we perform the following tasks:

• Selecting features
• Scaling the data to a standard value range

First, we will select the features upon which we want to train our neural network. The selection and engineering of relevant feature variables is a complex topic. We could also create additional features such as moving averages, but I want to keep things simple. Therefore, we select features that are already present in our data. If you want to learn more about feature engineering for stock market prediction, check out the relataly feature engineering tutorial.

Running the code below selects the features. We add a dummy column to our record called “Predictions,” which will help us later when we need to reverse the scaling of our data.

```# Indexing Batches
train_df = df.sort_values(by=['Date']).copy()

# List of considered Features
FEATURES = ['High', 'Low', 'Open', 'Close', 'Volume'
]

print('FEATURE LIST')
print([f for f in FEATURES])

# Create the dataset with features and filter the data to the list of FEATURES
data = pd.DataFrame(train_df)
data_filtered = data[FEATURES]

# We add a prediction column and set dummy values to prepare the data for scaling
data_filtered_ext = data_filtered.copy()
data_filtered_ext['Prediction'] = data_filtered_ext['Close']

# Print the tail of the dataframe
data_filtered_ext.tail()```

Another necessary step in data preparation for neural networks is the scaling of the input data. Scaling will increase training times and improve model accuracy. The scikit-learn package offers different scaling approaches. We use the MinMaxScaler to scale the input data to a range between 0 and 1.

A model that is trained on scaled data will also produce scalled predictions. Therefore, when we make predictions later with our model, we must not forget to scale the predictions back. The scaler_model will adapt to the shape of the data (6 dimensional). However, our predictions will be one-dimensional. Because, the scaler has a fixed input shape, we cannot simply reuse it for unscaling our model predictions. To unscale the predictions later, we create an additional scaler that works on a single feature column (scaler_pred).

```# Get the number of rows in the data
nrows = data_filtered.shape

# Convert the data to numpy values
np_data_unscaled = np.array(data_filtered)
np_data = np.reshape(np_data_unscaled, (nrows, -1))
print(np_data.shape)

# Transform the data by scaling each feature to a range between 0 and 1
scaler = MinMaxScaler()
np_data_scaled = scaler.fit_transform(np_data_unscaled)

# Creating a separate scaler that works on a single column for scaling predictions
scaler_pred = MinMaxScaler()
df_Close = pd.DataFrame(data_filtered_ext['Close'])
np_Close_scaled = scaler_pred.fit_transform(df_Close)```

Out: (2619, 6)

### Step #4 Transforming the Data

Next, we train our multivariate regression model based on a three-dimensional data structure. The first dimension is the sequences, the second dimension is the time steps (mini-batches), and the third dimension is the features. The illustration below shows the steps to bring the multivariate data into a shape that our neural model can process during training. We must keep this form and perform the same steps when using the model to create a forecast.

An essential step in the preparation process is slicing the data into multiple input data sequences with associated target values. We write a simple Python script that uses a “sliding window.” This approach moves a window through the time series data, adding a sequence of multiple data points to the input data with each step. We store the target value (e.g., Closing Price) following this sequence in a separate target data set. Then we push the window one step further and repeat these activities. This process results in a data set with many input sequences (mini-batches), each with a corresponding target value in the target record. This process applies both to the training and the test data.

We will apply the sliding window approach to our data. The result is a training set (x_train) that contains 2258 input sequences, and each has 50 steps and six features. The corresponding target dataset (y_train) contains 2258 target values.

```# Set the sequence length - this is the timeframe used to make a single prediction
sequence_length = 50

# Prediction Index
index_Close = data.columns.get_loc("Close")

# Split the training data into train and train data sets
# As a first step, we get the number of rows to train the model on 80% of the data
train_data_len = math.ceil(np_data_scaled.shape * 0.8)

# Create the training and test data
train_data = np_data_scaled[0:train_data_len, :]
test_data = np_data_scaled[train_data_len - sequence_length:, :]

# The RNN needs data with the format of [samples, time steps, features]
# Here, we create N samples, sequence_length time steps per sample, and 6 features
def partition_dataset(sequence_length, data):
x, y = [], []
data_len = data.shape
for i in range(sequence_length, data_len):
x.append(data[i-sequence_length:i,:]) #contains sequence_length values 0-sequence_length * columsn
y.append(data[i, index_Close]) #contains the prediction values for validation,  for single-step prediction

# Convert the x and y to numpy arrays
x = np.array(x)
y = np.array(y)
return x, y

# Generate training data and test data
x_train, y_train = partition_dataset(sequence_length, train_data)
x_test, y_test = partition_dataset(sequence_length, test_data)

# Print the shapes: the result is: (rows, training_sequence, features) (prediction value, )
print(x_train.shape, y_train.shape)
print(x_test.shape, y_test.shape)

# Validate that the prediction value and the input match up
# The last close price of the second input sample should equal the first prediction value
print(x_train[sequence_length-1][index_Close])
print(y_train)```

### Step #5 Train the Multivariate Prediction Model

Once we have the data prepared and ready, we can train our model. The architecture of our neural network consists of the following four layers:

• An LSTM layer, which takes our mini-batches as input and returns the whole sequence
• Another LSTM layer that takes the sequence from the previous layer but only returns five values
• Dense layer with five neurons
• A final dense layer that outputs the predicted value

The number of neurons in the first layer must equal the size of a minibatch of the input data. Each minibatch in our dataset consists of a matrix with 50 steps and six features. Thus, the input layer of our recurrent neural network consists of 300 neurons. Keeping this architecture in mind is essential because, later, we need to bring the data into the same shape when we want to predict a new dataset. Running the code below creates the model architecture and compiles the model.

```# Configure the neural network model
model = Sequential()

# Model with n_neurons = inputshape Timestamps, each with x_train.shape variables
n_neurons = x_train.shape * x_train.shape
print(n_neurons, x_train.shape, x_train.shape)

# Compile the model

Running the code below starts the training process.

```# Training the model
epochs = 50
batch_size = 16
early_stop = EarlyStopping(monitor='loss', patience=5, verbose=1)
history = model.fit(x_train, y_train,
batch_size=batch_size,
epochs=epochs,
validation_data=(x_test, y_test)
)

#callbacks=[early_stop])```

Let’s take a quick look at the loss curve.

```# Plot training & validation loss values
fig, ax = plt.subplots(figsize=(16, 5), sharex=True)
sns.lineplot(data=history.history["loss"])
plt.title("Model loss")
plt.ylabel("Loss")
plt.xlabel("Epoch")
ax.xaxis.set_major_locator(plt.MaxNLocator(epochs))
plt.legend(["Train", "Test"], loc="upper left")
plt.grid()
plt.show()```

The loss drops quickly to a lower plateau, which signals that the model has improved throughout the training process.

### Step #6 Evaluate Model Performance

Once we have trained the neural network regression model, we want to measure its performance. As mentioned in section 3, we first have to reverse the scaling of the predictions. Afterwards, we calculate different error metrics, MAE, MAPE, and MDAPE. Then we will compare the predictions in a line plot with the actual values. For more information on measuring the performance of regression models, see this relataly article.

```# Get the predicted values
y_pred_scaled = model.predict(x_test)

# Unscale the predicted values
y_pred = scaler_pred.inverse_transform(y_pred_scaled)
y_test_unscaled = scaler_pred.inverse_transform(y_test.reshape(-1, 1))

# Mean Absolute Error (MAE)
MAE = mean_absolute_error(y_test_unscaled, y_pred)
print(f'Median Absolute Error (MAE): {np.round(MAE, 2)}')

# Mean Absolute Percentage Error (MAPE)
MAPE = np.mean((np.abs(np.subtract(y_test_unscaled, y_pred)/ y_test_unscaled))) * 100
print(f'Mean Absolute Percentage Error (MAPE): {np.round(MAPE, 2)} %')

# Median Absolute Percentage Error (MDAPE)
MDAPE = np.median((np.abs(np.subtract(y_test_unscaled, y_pred)/ y_test_unscaled)) ) * 100
print(f'Median Absolute Percentage Error (MDAPE): {np.round(MDAPE, 2)} %')```

The MAPE is 22.15, which means that the mean of our predictions deviates from the actual values by 3.12%. The MDAPE is 2.88 % and a bit lower than the mean, thus indicating there are some outliers among the prediction errors. 50% of the predictions deviate by more than 2.88%, and 50% differ by less than 2.88% from the actual values.

Next, we create a line plot showing the forecast and compare it to the actual values. Adding a bar plot to the chart helps highlight the deviations of the predictions from the actual values. Running the code below creates the line plot.

```# The date from which on the date is displayed
display_start_date = "2019-01-01"

# Add the difference between the valid and predicted prices
train = pd.DataFrame(data_filtered_ext['Close'][:train_data_len + 1]).rename(columns={'Close': 'y_train'})
valid = pd.DataFrame(data_filtered_ext['Close'][train_data_len:]).rename(columns={'Close': 'y_test'})
valid.insert(1, "y_pred", y_pred, True)
valid.insert(1, "residuals", valid["y_pred"] - valid["y_test"], True)
df_union = pd.concat([train, valid])

# Zoom in to a closer timeframe
df_union_zoom = df_union[df_union.index > display_start_date]

# Create the lineplot
fig, ax1 = plt.subplots(figsize=(16, 8))
plt.title("y_pred vs y_test")
plt.ylabel(stockname, fontsize=18)
sns.set_palette(["#090364", "#1960EF", "#EF5919"])
sns.lineplot(data=df_union_zoom[['y_pred', 'y_train', 'y_test']], linewidth=1.0, dashes=False, ax=ax1)

# Create the bar plot with the differences
df_sub = ["#2BC97A" if x > 0 else "#C92B2B" for x in df_union_zoom["residuals"].dropna()]
ax1.bar(height=df_union_zoom['residuals'].dropna(), x=df_union_zoom['residuals'].dropna().index, width=3, label='residuals', color=df_sub)
plt.legend()
plt.show()```

The line plot shows that the forecast is close to the actual values but partially deviates from it. The deviations between actual values and predictions are called residiuals. For our mode, they seem to be most significant during periods of increased market volatility and least during periods of steady market movement, which makes sense, because sudden movements are generally more difficult to predict.

### Step #7 Predict Next Day’s Price

After training the neural network, we want to forecast the stock market for the next day. For this purpose, we extract a new dataset from the Yahoo-Finance API and preprocess it the same way we did for model training.

We trained our model with mini-batches of 50 time-steps and six features. Thus, we also need to provide the model with 50-time steps when making the forecast. As before, we transform the data into the shape of 1 x 50 x 6, whereby the last figure is the number of feature columns. After generating the forecast, we unscale the stock market predictions back to the original range of values.

```df_temp = df[-sequence_length:]
new_df = df_temp.filter(FEATURES)

N = sequence_length

# Get the last N day closing price values and scale the data to be values between 0 and 1
last_N_days = new_df[-sequence_length:].values
last_N_days_scaled = scaler.transform(last_N_days)

# Create an empty list and Append past N days
X_test_new = []
X_test_new.append(last_N_days_scaled)

# Convert the X_test data set to a numpy array and reshape the data
pred_price_scaled = model.predict(np.array(X_test_new))
pred_price_unscaled = scaler_pred.inverse_transform(pred_price_scaled.reshape(-1, 1))

# Print last price and predicted price for the next day
price_today = np.round(new_df['Close'][-1], 2)
predicted_price = np.round(pred_price_unscaled.ravel(), 2)
change_percent = np.round(100 - (price_today * 100)/predicted_price, 2)

plus = '+'; minus = ''
print(f'The close price for {stockname} at {end_date} was {price_today}')
print(f'The predicted close price is {predicted_price} ({plus if change_percent > 0 else minus}{change_percent}%)')```

The close price for NASDAQ on 2021-06-27 was 14360.39. The predicted closing price is 14232.8095703125 (-0.9%)

## Summary

This tutorial has shown multivariate time series modeling for stock market prediction in Python. We trained a neural network regression model for predicting the NASDAQ index. Before training our model, we performed several steps to prepare the data. The steps included splitting the data and scaling them. In addition, we created and tested various new features from the original time series data to account for the multivariate modeling approach. You now have the knowledge and code at hand to conduct furtherexperiments with the features of your choice.

Multivariate time series forecasting is a complex topic. You might want to take the time to retrace the different steps. Especially the transformation of the data can be challenging. The best way to learn is to practice. Therefore I encourage you to develop more time series models and experiment with other data sources.

If you want to give feedback or have remarks or, feel free to share them in the comments.

Another interesting approach to stock market prediction uses candlestick images and convolutional neural networks. If this topic interests you, check out the following article: Deep reinforcement learning stock market trading, utilizing a CNN with candlestick images

## Author

• Hi, I am Florian, a Zurich-based consultant for AI and Data. Since the completion of my Ph.D. in 2017, I have been working on the design and implementation of ML use cases in the Swiss financial sector. I started this blog in 2020 with the goal in mind to share my experiences and create a place where you can find key concepts of machine learning and materials that will allow you to kick-start your own Python projects.

### 10 thoughts on “Stock Market Prediction using Multivariate Time Series and Recurrent Neural Networks in Python”

1. Well done – informative and easy to understand.
thank you

2. I think your x_train including the target column “Close” isn’t it?

• Hello Iqmal, yes, that is correct. The code example forecasts the closing price of the next day. Therefore, it is ok to use the previous day’s closing price as a feature.

If you do not want to use the closing price, you can remove it from the list of features in step 3.

3. Hello,

I basically copy/pasted your code and ran the model. I was not able to get anything below 6% MAE Error rate and went even as high as 14%. Any advice on how to optimize the model?

THanks!

4. Hi, Florian, great post! This has really helped me.

I have 2 questions regarding the train_data and test_data, and inclusion of a validation dataset.

1. With separating the data into train_data and test_data with the code:

train_data = np_data_scaled[0:train_data_len, :]
test_data = np_data_scaled[train_data_len – sequence_length:, :]

Does this create data leakage as the test_data will include data from the train set, or is this prevented due to the use of a sliding window?

2. With respect to question 1, how can I include a validation set for hyperparameter tuning?

Many thanks!

5. https://www.relataly.com/time-series-forecasting-changing-prediction-horizon/169/

gives the error:

Sorry, but the page you were trying to view does not exist.
It looks like this was the result of either:

Can you update the reference link? Thanks!

6. how it is predicting for next ,you are taking data till same day and predicting for the same day.

7. • 