I've been reading up on different models used to forecast the equity risk premium, and I've seen a couple of papers that had questionable methods. For example, this paper by Javier Estrada goes into detail on how to use the Shiller PE ratio to forecast 10-year equity returns.
And this paper, which looks to be a draft, also uses a similar methodology to Estrada. The only paper I have seen where they specifically address the issue of independent observations and model misspecification is the one by Klement on using the Shiller PE in emerging markets.
The problem I have with the first two papers is that they look at the data available today and make a prediction about the next ten years. They then roll everything forward one month and make another prediction about the next ten years. Clearly, there are overlapping data between the two time periods. Should the authors only be evaluating model usability by looking at non-overlapping time periods? What is the most appropriate way to evaluate their models?