Which statement about white noise processes is false?

White noise processes are characterized by their lack of correlation and constant statistical properties over time. Understanding the characteristics of white noise helps identify which statements about them are true or false.

A fundamental property of white noise is that it is stationary, meaning its statistical features, such as mean and variance, don’t change over time. While there are different contexts in statistics that might lead to confusing terms, a standard white noise process is stationary, making the claim that all white noise processes are non-stationary incorrect.

White noise processes indeed have a constant variance, usually defined as the variance being equal to some fixed value, and often assumed to be constant over time. Additionally, they typically have a mean of zero, although other types of white noise processes (not standard white noise) might allow for non-zero means; the classical definition leans towards a mean of zero.

Differencing, commonly used to achieve stationarity in a time series, can generate a white noise series. When a non-stationary series is differenced, the residuals can often exhibit white noise characteristics if the original series contained a unit root or trends.

Thus, the assertion that all white noise processes are non-stationary stands out as false, as foundational definitions specify that white noise processes