We can detect white noise by using the following tools:

• Line plot: Once we have a line plot, we can have an idea of whether the series has a constant mean and variance
• Autocorrelation plot: Having a correlation plot can give us an inkling as to whether there is an association among lagged variables
• Summary: Checking the mean and variance of the series against the mean and variance of meaningful contiguous blocks of values in the series

Let's do this in Python:

1. First, we will import all the required libraries as follows:

from random import gauss
from random import seed
from pandas import Series
from pandas.tools.plotting import autocorrelation_plot
from matplotlib import pyplot

2. Next, we will set up the white noise series for us to analyze, as follows:

seed(1000)
#creating white noise series
series = [gauss(0.0, 1.0) for i in range(500)]
series = Series(series)

3. Let's take the summary or statistic of it using the following code:

print(series.describe())

We will get the following output:

Here, we can see that the mean is approaching zero and the standard deviation is close to 1.

4. Let's make a line plot now to check out the trend, using the following code:

series.plot()
pyplot.show()

We will get the following output:

The line plot looks totally random, and no trend can be observed here.

5. It's time to make an autocorrelation plot. Let's set one up using the following code:

autocorrelation_plot(series)
pyplot.show()

We will get the following output:

Even in an autocorrelation function plot, the correlation breaches the band of our confidence level. This tells us that it is a white noise series.