Case Studies in Time Series Forecasting

Duration: 5 min

This module delves into real-world applications of time series forecasting using various methodologies such as ARIMA, SARIMA, Prophet, LSTM, and Transformers. Understanding these case studies is crucial for applying theoretical knowledge to practical problems, enhancing predictive accuracy, and making data-driven decisions.

ARIMA Model Case Study

The ARIMA (AutoRegressive Integrated Moving Average) model is widely used for time series forecasting. It combines autoregression (AR), differencing (I), and moving average (MA) to make data stationary and predict future values. This case study demonstrates how to apply ARIMA to forecast monthly airline passenger numbers.

import pandas as pd
from statsmodels.tsa.arima.model import ARIMA
import matplotlib.pyplot as plt

# Load dataset
data = pd.read_csv('airline_passengers.csv', parse_dates=True, index_col='Month')

# Fit ARIMA model
model = ARIMA(data, order=(5,1,0))
model_fit = model.fit()

# Forecast
forecast = model_fit.forecast(steps=12)

# Plot
plt.plot(data)
plt.plot(forecast, color='red')
plt.show()

Try it in Google Colab:

A plot showing the original time series data and the forecasted values for the next 12 months.

LSTM Model Case Study

Long Short-Term Memory (LSTM) networks are a type of recurrent neural network capable of learning order dependence in sequence prediction problems. This case study illustrates how to use LSTM to forecast daily stock prices, highlighting the model's ability to capture long-term dependencies.

import numpy as np
import pandas as pd
from sklearn.preprocessing import MinMaxScaler
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import LSTM, Dense
import matplotlib.pyplot as plt

# Load dataset
data = pd.read_csv('stock_prices.csv', parse_dates=True, index_col='Date')

# Scale data
scaler = MinMaxScaler(feature_range=(0, 1))
scaled_data = scaler.fit_transform(data)

# Prepare data
x_train, y_train = [], []
for i in range(60, len(scaled_data)):
    x_train.append(scaled_data[i-60:i, 0])
    y_train.append(scaled_data[i, 0])
x_train, y_train = np.array(x_train), np.array(y_train)
x_train = np.reshape(x_train, (x_train.shape[0], x_train.shape[1], 1))

# Build LSTM model
model = Sequential()
model.add(LSTM(units=50, return_sequences=True, input_shape=(x_train.shape[1], 1)))
model.add(LSTM(units=50))
model.add(Dense(1))

model.compile(loss='mean_squared_error', optimizer='adam')
model.fit(x_train, y_train, epochs=1, batch_size=1, verbose=2)

# Forecast
inputs = data[len(data)-len(x_train)-60:].values
inputs = inputs.reshape(-1,1)
inputs = scaler.transform(inputs)

x_test = []
for i in range(60, inputs.shape[0]):
    x_test.append(inputs[i-60:i, 0])
x_test = np.array(x_test)
x_test = np.reshape(x_test, (x_test.shape[0], x_test.shape[1], 1))
predicted_stock_price = model.predict(x_test)
predicted_stock_price = scaler.inverse_transform(predicted_stock_price)

# Plot
plt.plot(data['Close'], label='Actual Stock Price')
plt.plot(predicted_stock_price, color='red', label='Predicted Stock Price')
plt.xlabel('Time')
plt.ylabel('Stock Price')
plt.legend()
plt.show()

💡 Tip: When using LSTM for time series forecasting, ensure your data is properly scaled and your sequences are correctly formatted to avoid common pitfalls.

Key Concepts

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