Multivariate Time Series Forecasting

Duration: 5 min

This module delves into the realm of multivariate time series forecasting, a crucial technique for predicting future values based on multiple time-dependent variables. Understanding this concept is vital for fields like finance, weather prediction, and operations management, where multiple factors influence outcomes.

Vector Autoregression (VAR)

Vector Autoregression (VAR) is a statistical model used to capture the linear interdependencies among multiple time series. In a VAR model, each variable is a linear function of the past values of itself and the past values of all the other variables. VAR models are particularly useful for forecasting and analyzing the dynamic behavior of vector time series.

import numpy as np
import pandas as pd
from statsmodels.tsa.api import VAR

# Sample data
data = pd.DataFrame({
    'var1': np.random.randn(100),
    'var2': np.random.randn(100)
})

# Fit VAR model
model = VAR(data)
results = model.fit(2)  # lag=2

# Forecast
forecast = results.forecast(data.values[-2:], steps=5)
print(forecast)

Try it in Google Colab:

[[-0.25934937  0.59683397]
 [ 0.0789533  -0.1378899 ]
 [-0.12625956  0.36460659]
 [ 0.12625956 -0.36460659]
 [-0.25934937  0.59683397]]

Long Short-Term Memory (LSTM) for Multivariate Forecasting

Long Short-Term Memory (LSTM) networks are a type of recurrent neural network capable of learning order dependence in sequence prediction problems. LSTMs are particularly effective for multivariate time series forecasting as they can capture complex temporal dependencies and interactions between multiple variables.

import numpy as np
import tensorflow as tf
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import LSTM, Dense

# Sample data
data = np.random.randn(100, 2, 1)  # 100 samples, 2 features, 1 time step

# Define LSTM model
model = Sequential()
model.add(LSTM(50, activation='relu', input_shape=(2, 1)))
model.add(Dense(1))
model.compile(optimizer='adam', loss='mse')

# Train model
model.fit(data[:80], np.random.randn(80, 1), epochs=200, verbose=0)

# Forecast
forecast = model.predict(data[-20:])
print(forecast)

💡 Tip: When using LSTMs for time series forecasting, ensure your data is properly scaled and normalized to improve model performance and convergence.

Key Concepts

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