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Random Walk Forecasts of Stationary Processes Have Low Bias
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Researchers investigating the possibility of mean reversion in stock prices with statistics based on multiyear returns have noted difficulties in drawing inferences from these statistics because the approximating asymptotic distributions perform poorly. We develop an alternative asymptotic distribution theory for statistics involving multiyear returns. These distributions differ markedly from those implied by the conventional theory. The alternative theory provides substantially better approximations to the relevant finite-sample distributions. It also leads to empirical inferences much less at odds with the hypothesis of no mean reversion.
This chapter summarizes recent literature on asymptotic inference about forecasts. Both analytical and simulation based methods are discussed. The emphasis is on techniques applicable when the number of competing models is small. Techniques applicable when a large number of models is compared to a benchmark are also briefly discussed.
This paper carries out the task of evaluating inflation forecasts from the Livingston Survey and the Survey of Professional Forecasters, using the Real-Time Data Set for Macroeconomists as a source of real-time data. We examine the magnitude and patterns of revisions to the inflation rate based on the output price index. We then run tests on the forecasts from the surveys to see how good they are. We find that there are several episodes in which forecasters made persistent forecast errors, but the episodes are so short that by the time they can be identified, they have nearly disappeared. Thus, improving on the survey forecasts seems to be very difficult in real time, and the attempt to do so leads to increased forecast errors.