1. White Noise
Although people define white noise slightly differently, a general definition
2. What is White Noise?
is that it is a series with mean that is constant with time, a variance that is also constant with time, and zero autocorrelation at all lags. There are several special cases of White Noise. For example, if the data is white noise but also has a normal, or Gaussian, distribution, then it is called Gaussian White Noise.
3. Simulating White Noise
numpy random normal creates an array of normally distributed random numbers. The loc argument is the mean and the scale argument is the standard deviation. This is one way to generate a white noise series.
4. What Does White Noise Look Like?
And here is a plot of the white noise series.
5. Autocorrelation of White Noise
And all the autocorrelations of a white noise series are zero. The returns on the stock market are pretty close to a white noise process.
6. Stock Market Returns: Close to White Noise
Here is the autocorrelation function for the S&P500. Notice that there are pretty much no lags where the autocorrelation is significantly different from zero.
7. Let's practice!
Time to put this into practice.