# Stock Market Prediction – Adjusting Time Series Prediction Intervals in Python

Get ready to level up your time-series forecasting game! In this tutorial, we’re going to take things up a notch by showing you how to adjust prediction intervals using Keras recurrent neural networks and Python.

Now, you may remember our previous article on stock market forecasting where we made a forecast for the S&P500 stock market index using a prediction interval of just one day. However, other time-series prediction problems may require us to look further ahead – maybe several days, weeks, or even months. Fear not! We’ve got you covered.

By tweaking our data preparation and model architecture, we can modify the prediction interval and create a single-step forecast for a longer time frame. In this article, we’re going to show you exactly how to do that.

First, we’ll give you a quick rundown of different methods for adjusting the time series prediction interval. Then, we’ll dive into the practical stuff. We’ll use Python to train a simple neural network on stock market data and validate its performance. Once we’re happy with the model, we’ll prepare the data in a way that allows us to forecast a single but more extended step into the future.

Ready to take your time-series forecasting to the next level? Then let’s get started!

## 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.

## Ways of Adjusting Prediction Intervals

When forecasting one step, the prediction interval is the point in time for which a prediction model will simulate the next value. There are three different ways to change the prediction interval:

• Multi-Step Rolling Forecasting: Another way is to train the model on its output. We do this by maintaining the predictions and reusing them as input in the subsequent training run. In this way, the projections range one-time step further ahead with each iteration. After seven iterations, based on daily input time steps, the model will have provided the output for a weekly prediction. We have covered this rolling forecasting approach in a separate tutorial.
• Deep Multi-Output Forecasting: A third option is to create a multi-output model that provides an entire series of predictions with multiple timesteps. We have covered this multi-output forecasting approach in a separate tutorial.
• Single-step forecasting with bigger timesteps: In a single-stage forecasting approach, the input data defines the length of a time step. Changing the size of the input steps will change the output steps to the same extent. For example, a model that uses daily prices as input data will also provide day-to-day forecasts. We will cover this forecasting approach in the following section.

## Predicting the Price of the S&P500 One Week Ahead

Let’s begin with the hands-on part. In this part, we will use Python to create a single-step forecasting model with more extended timesteps. Our model will make projections that reach one week ahead. For this purpose, we reuse most of the code from the previous article on univariate single-step daily forecasting. So we won’t go into all the details and will only speak about the areas in which we must adjust the code. Changes are necessary to data preparation and model architecture.

In the following, we develop a single-variate neural network model that forecasts the S&P500 stock market index. 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, you can follow these steps 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 pandas DataReader to interact with the yahoo finance API.

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 Data

In the following, we will modify the prediction interval of the neural network model we developed in a previous post. As a result, the model will generate predictions for the market price of the S&P500 Index that range one week ahead.

As before, we start loading the stock market data via an API.

```# A tutorial for this file is available at www.relataly.com

import math # Fundamental package for scientific computing with Python
import numpy as np # Additional functions for analysing and manipulating data
import pandas as pd # Date Functions
from datetime import date, timedelta # This function adds plotting functions for calender dates
from pandas.plotting import register_matplotlib_converters # Important package for visualization - we use this to plot the market data
import matplotlib.pyplot as plt # Formatting dates
import matplotlib.dates as mdates # Packages for measuring model performance / errors
from sklearn.metrics import mean_absolute_error, mean_squared_error # Tools for predictive data analysis. We will use the MinMaxScaler to normalize the price data
from sklearn.preprocessing import MinMaxScaler # Deep learning library, used for neural networks
from tensorflow.keras.models import Sequential # Deep learning classes for recurrent and regular densely-connected layers
from tensorflow.keras.layers import LSTM, Dense
from tensorflow.keras.callbacks import EarlyStopping
import tensorflow as tf
import seaborn as sns
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 S&P500 quotes
stockname = 'S&P500'
symbol = '^GSPC'

# 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

```Tensorflow Version: 2.5.0
Num GPUs: 0
[*********************100%***********************]  1 of 1 completed
Open		High		Low			Close		Adj Close	Volume
Date
2009-12-31	1126.599976	1127.640015	1114.810059	1115.099976	1115.099976	2076990000
2010-01-04	1116.560059	1133.869995	1116.560059	1132.989990	1132.989990	3991400000
2010-01-05	1132.660034	1136.630005	1129.660034	1136.520020	1136.520020	2491020000
2010-01-06	1135.709961	1139.189941	1133.949951	1137.140015	1137.140015	4972660000
2010-01-07	1136.270020	1142.459961	1131.319946	1141.689941	1141.689941	5270680000```

### Step #2 Adjusting the Shape of the Input Data and Exploration

We have a DataFrame that contains the daily price quotes for the S&P 500. Next, we prepare the data to include the weekly price quotes. If we want our model to provide weekly price predictions, we need to change the data so that the input contains weekly price quotes. A simple way to achieve this is to iterate through the rows and only keep every 7th row.

```# Changing the data structure to a dataframe with weekly price quotes
df["index1"] = range(1, len(df) + 1)
rownumber = df.shape
lst = list(range(rownumber))
list_of_relevant_numbers = lst[0::7]
df_weekly = df[df["index1"].isin(list_of_relevant_numbers)]
```	Open	High	Low	Close	Adj Close	Volume	index1
Date
2010-01-11	1145.959961	1149.739990	1142.020020	1146.979980	1146.979980	4255780000	7
2010-01-21	1138.680054	1141.579956	1114.839966	1116.479980	1116.479980	6874290000	14
2010-02-01	1073.890015	1089.380005	1073.890015	1089.189941	1089.189941	4077610000	21
2010-02-10	1069.680054	1073.670044	1059.339966	1068.130005	1068.130005	4251450000	28
2010-02-22	1110.000000	1112.290039	1105.380005	1108.010010	1108.010010	3814440000	35```

After this, we quickly create a line plot to validate that everything looks as expected.

```# Creating a Lineplot
years = mdates.YearLocator()
fig, ax1 = plt.subplots(figsize=(16, 6))
ax1.xaxis.set_major_locator(years)
ax1.legend([stockname], fontsize=12)
plt.title(stockname + ' from '+ start_date + ' to ' + end_date)
sns.lineplot(data=df['Close'], label=stockname, linewidth=1.0)
plt.ylabel('S&P500 Points')
plt.show()```
```			Open		High		Low			Close		Adj Close	Volume		index1
Date
2010-01-11	1145.959961	1149.739990	1142.020020	1146.979980	1146.979980	4255780000	7
2010-01-21	1138.680054	1141.579956	1114.839966	1116.479980	1116.479980	6874290000	14
2010-02-01	1073.890015	1089.380005	1073.890015	1089.189941	1089.189941	4077610000	21
2010-02-10	1069.680054	1073.670044	1059.339966	1068.130005	1068.130005	4251450000	28
2010-02-22	1110.000000	1112.290039	1105.380005	1108.010010	1108.010010	3814440000	35```

### Step #3 Preprocess the Data

Before we can train the neural network, we first need to define the shape of the training data. We use weekly price quotes and define an input_sequence_length of 50 weeks.

```# Feature Selection - Only Close Data
train_df = df.filter(['Close'])
data_unscaled = df.values

# Transform features by scaling each feature to a range between 0 and 1
mmscaler = MinMaxScaler(feature_range=(0, 1))
np_data = mmscaler.fit_transform(data_unscaled)

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

# Set the sequence length - this is the timeframe used to make a single prediction
sequence_length = 25

# Prediction Index
index_Close = train_df.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_length = math.ceil(np_data.shape * 0.8)

# Create the training and test data
train_data = np_data[0:train_data_length, :]
test_data = np_data[train_data_length - 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, train_df):
x, y = [], []
data_len = train_df.shape
for i in range(sequence_length, data_len):
x.append(train_df[i-sequence_length:i,:]) #contains sequence_length values 0-sequence_length * columsn
y.append(train_df[i, index_Close]) #contains the prediction values for validation (3rd column = Close),  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_test[sequence_length-1][index_Close])
print(y_test)```
```(2465, 25, 7) (2465,)
(622, 25, 7) (622,)
0.5509444640253316
0.5509444640253316```

### Step #4 Building a Time Series Prediction Model

The first layer of neurons in our neural network needs to fit the input values from the data. Therefore, we need 50 neurons – one for each input price quote.

We use the following input arguments for the model fit:

• x_train: Vector, matrix, or array of training data. It can also be a list (as in our case) if the model has multiple inputs.
• y_train: Vector, matrix, or array of target data. This is the labeled data the model tries to predict; in other words, these are the results of x_train.
• Epochs: The integer value defines how often the model goes through the training set.
• Batch size: Integer value that defines the number of samples that will be propagated through the network. After each propagation, the network adjusts the weights of the nodes in each layer.
```# Configure the neural network model
model = Sequential()

# Model with n_neurons Neurons
n_neurons = x_train.shape * x_train.shape
print(n_neurons, x_train.shape, x_train.shape)

# Compile the model

# Training the model
epochs = 10
early_stop = EarlyStopping(monitor='loss', patience=2, verbose=1)
history = model.fit(x_train, y_train,
batch_size=16,
epochs=epochs,
callbacks=[early_stop])```
```Epoch 1/10
155/155 [==============================] - 7s 25ms/step - loss: 8.2791e-04
Epoch 2/10
155/155 [==============================] - 4s 24ms/step - loss: 1.3465e-04
Epoch 3/10
155/155 [==============================] - 4s 24ms/step - loss: 1.0998e-04
Epoch 4/10
155/155 [==============================] - 4s 25ms/step - loss: 1.0241e-04
Epoch 5/10
155/155 [==============================] - 4s 24ms/step - loss: 7.4277e-05
Epoch 6/10
155/155 [==============================] - 4s 24ms/step - loss: 6.5786e-05
Epoch 7/10
155/155 [==============================] - 4s 24ms/step - loss: 6.8482e-05
Epoch 8/10
155/155 [==============================] - 4s 24ms/step - loss: 5.0326e-05
Epoch 9/10
155/155 [==============================] - 4s 24ms/step - loss: 4.8574e-05
Epoch 10/10
155/155 [==============================] - 4s 25ms/step - loss: 4.1287e-05```

### Step #5 Evaluate Model Performance

Next, we validate the model by calculating our predictions’ mean-squared and root-mean-squared errors. However, in time series forecasting metrics can be misleading. It is good to double-check model results using illustrations. Therefore, we plot the input sequences and the forecast to see if our model can continue the time series in a plausible way.

```# Get the predicted values
y_pred_scaled = model.predict(x_test)
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 date from which on the date is displayed
display_start_date = "2018-01-01"

# Add the difference between the valid and predicted prices
train = pd.DataFrame(train_df[:train_data_length + 1]).rename(columns={'Close': 'x_train'})
valid = pd.DataFrame(train_df[train_data_length:]).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("Predictions vs Ground Truth")
plt.ylabel(stockname, fontsize=18)
sns.despine();
sns.lineplot(data=df_union_zoom, linewidth=1.0, palette='CMRmap', ax=ax1)
plt.show()```
```Median Absolute Error (MAE): 42.7
Mean Absolute Percentage Error (MAPE): 1.16 %
Median Absolute Percentage Error (MDAPE): 0.92 %```

At the bottom, we can see the differences between predictions and valid data. Positive values signal that the projections were too optimistic. Negative values mean that the predictions were too pessimistic and that the actual value turned out to be higher than the prediction.

### Step #6 Predicting for the Next Week

What can be more satisfying than to see a newly trained model at work? Let’s use our new model to predict next week’s price for the S&P500. We will create a fresh input_sequence with prices from the past N days. Then we scale this input sequence and include it as input in our call to the model.predict() function.

```# Get fresh data until today and create a new dataframe with only the price data

new_df = df

N = sequence_length

# Get the last N steps closing price values and scale the data to be values between 0 and 1
last_N_steps = new_df[-sequence_length:].values
last_N_steps_scaled = mmscaler.transform(last_N_steps)

# Create an empty list and Append past N steps
X_test_new = []
X_test_new.append(last_N_steps_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 week
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 S&P500 at 2022-05-11 was 4001.05
The predicted close price is 4046.300048828125 (+1.12%)```

So for the 9th of April 2020, the model predicts that the S&P500 will close at:

4046.300048828125

Considering today’s (2nd of April 2020) price is 2528 points, our model expects the S&P to gain roughly 124 points in the coming seven days. Of course, this is by no means financial advice. As we have seen before, our model is often wrong.

## Summary

This article has shown how to adjust the prediction intervals for a time series forecasting model. We have created a neural network that predicts the price of the S&P500 one week in advance. Finally, we trained and validated the model and made a forecast for the next week.

Varying the input shape is a quick approach to changing the forecasting time steps. However, increasing the length of the time steps also reduces the amount of data we can use for training and testing. In our case, we still have enough data available. But in other cases, where less information is available, this can become a problem. The preferred method is to use a rolling forecast approach or create a multi-output forecast in such a case.

The links above to Amazon are affiliate links. By buying through these links, you support the Relataly.com blog and help to cover the hosting costs. Using the links does not affect the price.

## Author

• Hi, I am Florian, a Zurich-based Cloud Solution Architect 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.

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2 years ago

hi there,
i did not get the code. first you tried to convert daily data into week data. but in neural model, you utilized daily data. Also did prediction on daily x_test data. then how you predicted next week data?

Ed
2 years ago

in the daily timeframe you could also forecast a price 7 days (or 7 bars ) in the future by adjusting the samples. For instance, see below. I tested it and it works. So it just forecasts 1 bar but 7 bars ahead instead of just 1 bar ahead. Of course the length of the array pred_price_unscaled will also be nfut bars shorter.

Let me know what you think

nfut = 7

def partition_dataset(sequence_length, train_df):
x, y = [], []
data_len = train_df.shape
for i in range(sequence_length, data_len – nfut + 1):
x.append(train_df[i-sequence_length:i,:]) #contains sequence_length values 0-sequence_length * columsn
y.append(train_df[i + nfut – 1, index_Close]) #contains the prediction values for validation (3rd column = Close), for single-step prediction

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

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