Final answer:
MMSE forecasts in stationary ARMA models are correct in being unbiased, which means they do not systematically overestimate or underestimate. These forecasts are designed for stationary time series and may not be optimal for non-stationary data. While autocorrelation can influence forecast performance, it is not the sole determinant of optimality.
Step-by-step explanation:
The statement about MMSE (Minimum Mean Square Error) forecasts in stationary ARMA (AutoRegressive Moving Average) models that is correct is:
A) MMSE forecasts are unbiased.
When dealing with ARMA models for time series analysis, the MMSE forecasts are designed to minimize the expected value of the square of the forecast errors, which implies they are unbiased. Forecast performance in these models is predicated on the notion of stationarity—which requires that statistical properties like mean and variance remain constant over time.
However, statement B is incorrect because MMSE forecasts are not always optimal for non-stationary time series, which may require differencing or other transformations to achieve stationarity. Statement C is also incorrect because there is no inherent tendency for MMSE forecasts to overestimate—unbiased forecasts should neither systematically overestimate nor underestimate. Lastly, regarding statement D, while higher autocorrelation may improve the performance of forecasts, it's not accurate to say MMSE forecasts perform best only with high autocorrelation, as the optimality also depends on other factors such as model specification and the nature of the data.