Time-series filters
The new tsfilter command separates a time series into trend and
cyclical components. The trend component may contain a deterministic or a
stochastic trend. The stationary cyclical component is driven by stochastic
cycles at the specified periods.
Many time series contain trends and are thus nonstationary. Fitting
nonstationary time series to statistical models can be difficult. Some
researchers use filters to remove the trends and analyze the stationary
components that the filters leave behind.
tsfilter implements the Baxter–King, Butterworth,
Christiano–Fitzgerald, and Hodrick–Prescott filters
commonly used for this purpose.
For example, we have quarterly data on GDP from 1952 through 2010.
. webuse gdp2
(Federal Reserve Economic Data, St. Louis Fed)
The data are strongly trended. Here is a graph of gdp_ln, the log of
GDP over time, variable :
We will use a Baxter–King band-pass filter for this series. Band-pass
filters remove components below the minimum frequency or above the
maximum frequency. Below we specify we want to remove frequencies with
periods shorter than 6 months or longer than 32 months.
. tsfilter bk gdp_bk = gdp_ln, minperiod(6) maxperiod(32)
We have now created new variable gdp_bk containing the filtered
series. To evaluate how the filter performed, we use Stata’s
pergram command to compute and plot the periodogram of the filtered
series. We put vertical lines at the minimum and maximum frequencies (1/32
and 1/6). If the filter did exactly want we want, the periodogram would be
a horizontal line below the minimum and above the maximum frequencies.
While the Baxter–King filter performed adequately, perhaps the
Butterworth filter could do better. The Butterworth filter is a high-pass
filter, meaning that it only removes the low-frequency components.
High-pass filters can be used to make band-pass filters, but here we will
just look at the high-pass results. The Butterworth filter has a tuning
parameter called the order of the filter. We set the order of the filter to
8 in the application below.
. tsfilter bw gdp_bw = gdp_ln, order(8) maxperiod(32)
The resulting periodogram for this filtered series is
The periodogram indicates that the Butterworth filter did a better job of
removing the low-frequency components than the Baxter–King filter did.
We could continue with this story. We would filter the series using the
Christiano–Fitzgerald band-pass filter and the Hodrick–Prescott
high-pass filter and compare the results. The Christiano–Fitzgerald
filter would produce results rivaling the Butterworth filter. The
Hodrick–Prescott filter would not perform as well with these data.
For a complete list of what’s new in time-series analysis,
click here.
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New in Stata 12
for more about what was added in Stata Release 12.
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