Final answer:
A stationary time series must have a constant mean, constant variance, and constant autocorrelation structure over time, meaning none of the given options completely describe the necessary properties. Option (a) partially describes these properties but does not include autocorrelation structure.
Step-by-step explanation:
Properties of a Stationary Time Series
To be classified as a stationary time series, certain properties must be fulfilled. These include:
A constant mean over time, indicating that the average value does not change as time progresses.
A constant variance, meaning that the spread or dispersion around the mean remains the same through time.
A constant autocorrelation structure, suggesting that the degree of correlation between time series observations at different times depends only on the time lag or interval between observations, not the actual time at which they were taken.
To answer the question, it is not sufficient for a time series to only have a constant mean and variance; it must also possess a constant autocorrelation structure. Therefore, option (a) Constant mean and variance is part of the correct answer, but not complete. The correct choice including all the properties in context is none of the above as the listed options in the question do not encompass the autocorrelation aspect.
For clarification, option (b) Time-dependent mean and variance are characteristics of non-stationary time series. Option (c) No autocorrelation is incorrect because stationary time series can have autocorrelation; however, it must not depend on time.