Answer: Observations in the time series are normally distributed

## 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.

Author: Nikitesh Somanthe