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Which of the following statements best explains the main setback of the moving average representation of a first-order moving average process, MA(1)?
Explanation:
The moving average representation of a first-order moving average process, MA(1), does not incorporate observable shocks. This is a significant limitation because it attempts to estimate a variable in terms of random, unobservable white shocks. This makes the process less useful for estimation. The solution to this problem is to use an autoregressive representation. In an autoregressive representation, an observable item can be used, making it more useful for estimation. Therefore, the statement in choice A accurately describes the main setback of the moving average representation of an MA(1) process.
Choice B is incorrect. The moving average representation of an MA(1) process does show evidence of autocorrelation cutoff. This is because the autocorrelation function for an MA(1) process cuts off after lag 1, which means that there are no correlations for lags greater than 1.
Choice C is incorrect. The statement contradicts the nature of a moving average (MA) model. An MA model does incorporate observable shocks, but it's not a limitation; rather, it's one of its characteristics that differentiates it from autoregressive models.
Choice D is incorrect. While time series analysis can be complex and often requires computational tools, this isn't a specific limitation to the moving average representation of an MA(1) process. Both simple and complex statistical analyses can be performed manually or with computational assistance.