Parametric spectral density estimation
A stationary process can be decomposed into random components that occur at
different frequencies. The spectral density of a stationary process
describes the relative importance of these random components.
Stata’s new psdensity command estimates the spectral density of
a stationary process using the parameters of a previously estimated
Consider the changes in the number of manufacturing employees in the United
. webuse manemp2
(FRED data: Number of manufacturing employees in U.S.)
The horizontal line corresponds to the mean. There appear to be more runs
above the mean, and more runs below the mean, than we would expect from a
series without autocorrelation. These runs suggest positive
Fitting these data to a first-order autoregressive process confirms our
The statistically significant estimate of 0.518 for the autoregressive
coefficient indicates that there is an important amount of positive
autocorrelation in this series.
Next we can use psdensity to estimate the spectral density of the
process implied by the estimated parameters.
. psdensity density omega
. twoway line density omega
The above graph is typical of a spectral density of an AR(1) process with a
positive coefficient. The curve is highest at frequency 0, and it tapers off
toward zero or a positive asymptote. This estimated spectral density tells
us that the low-frequency random components are the most important random
components of an AR(1) process with a positive autoregressive coefficient.
For a complete list of what’s new in time-series analysis,
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New in Stata 12
for more about what was added in Stata Release 12.