Which is/are time-invariant for a weakly stationary time series?a. meanb. variancec. autocovarianced. both a and be. a, b and c

A weakly stationary time series, also known as covariance stationary, has three main properties:

1. The mean of the series should not be a function of time. Rather, it should be a constant. The image below depicts a stationary series. Notice how the mean does not change over time.

2. The variance of the series should not a be a function of time. This property is known as homoscedasticity. Following figure depicts what is and what is not a stationary series. (Notice the varying spread of distribution in the ‘Non-stationary Series’).

3. The covariance of the i th term and the (i + m) th term should not be a function of time. In the following plot, you will notice the spread becomes closer as the height increases. Hence, the covariance is not constant with time for the ‘Non-stationary Series’.

So, the answer is e. a, b and c. The mean, variance and autocovariance are all time-invariant for a weakly stationary time series.

A weakly stationary time series, also known as covariance stationary, has three main properties:

1. The mean of the series should be constant over time. This means that the average value remains the same no matter at what point in time you measure it. So, the mean is time-invariant.

2. The variance of the series should also be constant over time. This means that the spread of values around the mean remains the same across time. So, the variance is time-invariant.

3. The covariance or autocovariance of the series should only depend on the difference in time between two periods, not on the actual time at which the covariance is computed. This means that the relationship between values at different time periods remains the same across time. So, the autocovariance is time-invariant.

Therefore, the answer is e. a, b and c. All three - mean, variance, and autocovariance - are time-invariant for a weakly stationary time series.