Which of the following statements about white noise processes is false?

The assertion that all white noise processes are non-stationary is incorrect because white noise processes are, in fact, defined as stationary processes. A white noise process is characterized by having a constant mean, constant variance, and no autocorrelation at any lag other than zero. This means that its statistical properties do not change over time, which is the essence of stationarity.

In contrast, a random walk is an example of a non-stationary process, where the variance increases over time as it accumulates the effect of random shocks. The first-order differencing of a random walk, which essentially subtracts the previous observation from the current one, results in a white noise series. This means that the increments of a random walk are independent and identically distributed, fulfilling the criteria for white noise.

As time increases in a random walk, the variance indeed increases, further underscoring the difference between non-stationary and stationary processes. Thus, the statement about white noise being non-stationary is the one that is false.