Far East Journal of Theoretical Statistics
Volume 3, Issue 1, Pages 139 - 157
(July 1999)
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RESOLUTION OF THE DESTRUCTIVE EFFECT OF NOISE ON LINEAR
REGRESSION OF TWO TIME SERIES
Igor Zurbenko (U. S. A.) and Mycroft Sowizral (U. S. A.)
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Abstract: When noise is present in both the independent and dependent
variables, linear regression will be inaccurate. Noise in the regression
variable will lead to underestimation of the regression coefficient. Significant
underestimation will occur if the signal-to-noise ratio is low. If the data are
time series, we can use a filter to separate the signal from the noise.
Regression on the smoothed data will give an accurate estimation of the
regression coefficient. Several simulations are show that demonstrate these
results. |
Keywords and phrases: noise, linear regression, signal-to-noise ratio, time series,
KZ filter |
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