White Noise

Time Series Analysis in Python

Rob Reider

Adjunct Professor, NYU-Courant Consultant, Quantopian

What is White Noise?

• White Noise is a series with:
  • Constant mean
  • Constant variance
  • Zero autocorrelations at all lags
• Special Case: if data has normal distribution, then Gaussian White Noise

Simulating White Noise

• It's very easy to generate white noise

  import numpy as np
  noise = np.random.normal(loc=0, scale=1, size=500)
  

What Does White Noise Look Like?

plt.plot(noise)

Autocorrelation of White Noise

plot_acf(noise, lags=50)

Stock Market Returns: Close to White Noise

• Autocorrelation Function for the S&P500

Let's practice!

Time Series Analysis in Python