Optimal Properties of Exponentially Weighted Forecasts
ABSTRACT The exponentially weighted average can be interpreted as the expected value of a time series made up of two kinds of random components: one lasting a single time period (transitory) and the other lasting through all subsequent periods (permanent). Such a time series may, therefore, be regarded as a random walk with “noise” superimposed. It is also shown that, for this series, the best forecast for the time period immediately ahead is the best forecast for any future time period, because both give estimates of the permanent component. The estimate of the permanent component is imperfect, and so the estimate of a regression coefficient is inconsistent in a relation involving the permanent (e.g. consumption as a function of permanent income). Its bias is small, however.
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ABSTRACT: In this paper we examine the effects of model misspecification (robustness or RB) on international consumption correlations in an otherwise standard small open economy model with endogenous capital accumulation. We show that in the presence of capital mobility in financial markets, RB lowers the international consumption correlations by generating heterogeneous responses of consumption to productivity shocks across countries facing different macroeconomic uncertainty. In addition, we show that RB can also improve the model's predictions in three other moments of consumption dynamics: the relative volatility of consumption to income, the persistence of consumption, and the correlation between consumption and output. After calibrating the RB parameter using the detection error probabilities, we show that the model can explain the observed international consumption correlations as well as the other consumption moments quantitatively. Finally, we show that the main conclusions of our benchmark model do not change in an extension in which the agent cannot observe the state perfectly due to finite information-processing capacity.European Economic Revie. 04/2014; 67:1-27.
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ABSTRACT: In this paper, we consider an adaptive base-stock policy for a single-item inventory system, where the demand process is nonstationary. In particular, the demand process is an integrated moving average process of order (0, 1, 1), for which an exponential-weighted moving average provides the optimal forecast. For the assumed control policy we characterize the inventory random variable and use this to find the safety stock requirements for the system. From this characterization, we see that the required inventory, both in absolute terms and as it depends on the replenishment lead-time, behaves much differently for this case of nonstationary demand compared with stationary demand. We then show how the single-item model extends to a multi-stage, or supply-chain context; in particular we see that the demand process for the upstream stage is not only nonstationary but also more variable than that for the downstream stage. We also show that for this model there is no value from letting the upstream stages see the exogenous demand. The paper concludes with some observations about the practical implications of this work.Manufacturing & Service Operations Management 01/1999; 1(1):50-61. · 1.71 Impact Factor
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ABSTRACT: This paper studies the aggregate dynamics of durable and nondurable consumption under slow information diffusion (SID) due to noisy observations and learning within the permanent income framework. We show that SID can significantly improve the model’s predictions on the joint behavior of income, durable consumption, and nondurable consumption at the aggregate level. Specifically, we find that SID can significantly improve the model’s predictions for: (i) smoothness in durable and nondurable consumption, (ii) autocorrelation of durable consump- tion, and (iii) contemporaneous correlation between durable and nondurable consumption. Furthermore, we show that incorporating a fixed cost into our SID model does a better job of reproducing the infrequent adjustments of durable consumption at the individual level and the slow adjustments at the aggregate level.Journal of the European Economic Association 01/2015; · 1.36 Impact Factor