Final answer:
To be considered a white noise process, a time series must exhibit a constant mean and variance along with no autocorrelation. Option 'b' does not describe a property of white noise. A standard deviation of zero in a data set indicates that all data values are identical.
Step-by-step explanation:
To determine the properties a time series must possess to be considered a white noise process, we can evaluate the given options:
- Constant mean and variance - A white noise process should indeed have a constant mean and variance over time. This implies that on average, the series does not tend to drift up or down, and the spread of values around the mean does not change.
- No autocorrelation - Another critical aspect of the white noise process is the lack of autocorrelation. This means that values within the time series are not correlated with one another; the value at one time point does not influence or provide information about any other value in the series.
Regarding the options presented, the correct answer would be a combination of 'a' Constant mean and variance, and 'c' No autocorrelation. Time-dependent mean and variance (option 'b') are not characteristics of white noise, as the properties of the series must be stable over time for it to be considered white noise.
Furthermore, when a data set has a standard deviation equal to zero, it means that all of the data have the same value (option 'C'). There is no variability or dispersion in the data set.