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Permanent Income
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Optimal Properties of Exponentially Weighted Forecasts
Optimal Properties of Exponentially Weighted Forecasts,10.1080/01621459.1960.10482064,Journal of The American Statistical Association,John F. Muth
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Optimal Properties of Exponentially Weighted Forecasts
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Citations: 220
)
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John F. Muth
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.
Journal:
Journal of The American Statistical Association  J AMER STATIST ASSN
, vol. 55, no. 290, pp. 299306, 1960
DOI:
10.1080/01621459.1960.10482064
Cumulative
Annual
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Citation Context
(41)
...This model was for the first time considered by Muth (
1960
)...
Philippe Cogneau
,
et al.
Block bootstrap methods and the choice of stocks for the long run
...Muth [
45
], Goodman [46], and Graves [47] used MA process as the forecasting method...
...MA Sun and Ren [16], Chen et al. [42], Muth [
45
], Goodman [46], Graves [47],...
Ranjan Bhattacharya
,
et al.
A review of the causes of bullwhip effect in a supply chain
...In practice, there is a tradeoff to be made in choosing J and j . If the random walk Assumption (T1) was literally true, then the optimal choice would be to make the value of J large and use exponentiallydeclining weights, see
Muth (1960)
...
Andrew J. Patton
,
et al.
Optimal combinations of realised volatility estimators
...As originally shown by
Muth (1960)
, the subjective forecast rule (9) will coincide with rational expectations when the forecast variable follows a simple and intuitive law of motion...
Kevin J. Lansingy
.
Timevarying U.S. inflation dynamics and the New Keynesian Phillips cu...
...The second and third papers were published in the same volume of the Journal of the Royal Statistical Society, Series B. By the early 1960s, exponentially weighted moving averages (EWMAs) had become widely used for forecasting, particularly in industry and commerce, and
Muth (1960)
had recently shown that simple exponential smoothing, i.e., using the predictor ^t;h ¼ð 1 � hÞ X...
...
Muth (1960)
was the first to show that the ARIMA(0, 1, 1) process (2) (with the inclusion of a constant 0) was the reduced form representation of the random walk with drift plus noise model...
Terence C. Mills
.
Modelling trends and cycles in economic time series: historical perspe...
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Block bootstrap methods and the choice of stocks for the long run
Philippe Cogneau
,
Valeri Zakamouline
Journal:
Quantitative Finance  QUANT FINANC
, vol. aheadofp, no. aheadofp, pp. 115, 2012
A review of the causes of bullwhip effect in a supply chain
(
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, vol. 54, no. 9, pp. 12451261, 2011
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