Explanation

For a white noise process:

1. Option A is INCORRECT - White noise processes do NOT require normal distribution. A white noise process only requires:

   • Zero mean
   • Constant variance (homoscedasticity)
   • Zero autocorrelation at all lags
   • The observations can have any distribution, not necessarily normal

2. Option B is CORRECT - By definition, white noise has zero serial correlations (autocorrelations) at all non-zero lags.

3. Option C is CORRECT - For large samples, the sample autocorrelations follow approximately normal distribution with variance 1/n (where n is sample size), which can be expressed as $\sigma^2$.

4. Option D is CORRECT - For large samples, the distribution of sample autocorrelations has mean zero, consistent with the true autocorrelations being zero.

Key Distinction:

• Weak white noise: Requires only uncorrelatedness (not independence) and stationarity
• Strict white noise: Requires independence and identical distribution (i.i.d.)
• Gaussian white noise: Requires normal distribution in addition to white noise properties

Since the question asks for the statement that is NOT true, Option A is the correct answer because white noise does not require normally distributed observations.