1. What are the features of a quality seasonal adjustment?
The following are some of the features of a quality seasonal adjustment.
- There should not be any estimable seasonal effects in the seasonally adjusted series.
The presence of seasonal and calendar effects in either the seasonally adjusted series or irregular component is
referred to as residual seasonality.
- The level of the series should lack bias. A lack of bias in the level
means that the local level of the series is similar for both the original and the seasonality adjusted series.
Other features are desirable, though not mutually exclusive. Many people (and also many government agencies, in my experience)
prefer adjustments that are stable, meaning that
as new data are added and incorporated into the estimation procedure, the revisions to the past estimates
are small. Big revisions can indicate that the initial estimates are misleading or even meaningless.
Another useful feature may be smoothness, particularly if you are looking for turning points
in the series. Unfortunately, a smoother series often has larger revisions.
2. What diagnostics are available in
X-12-ARIMA to help us judge the quality of the adjustment?
One of X-12-ARIMA's main advantages over other seasonal adjustment
programs is the diagnostics.
Some important diagnostics are:
Spectral Graphs:
A prominent spectrum peak at any of the seasonal frequencies for the spectrum
usually indicates the presence of seasonal effects. X-12-ARIMA can estimate
four spectra: the spectrum of the differenced original series, the spectrum of
the differenced seasonally adjusted series, the spectrum of the modified final
irregular component, and the spectrum of the regARIMA model residuals.
The program warns of visually significant peaks at seasonal frequencies for
monthly series of k/12 cycles/month where 1 ≤ k ≤ 5
and trading day frequencies of 0.348 and 0.432 cycles/month. For quarterly series
the seasonal peaks are at 1/4 and 1/2.
We use spectral graphs of the original series to see if the series
is seasonal. (If the series isn't seasonal, then there is no need to seasonally
adjust the series.)
We use the spectral graphs of the irregular and the
seasonally adjusted series to determine whether there is residual
seasonality or residual calendar effects. We use the spectral graph
of the regARIMA model residuals to see if there may be some problem
with the regARIMA model.
Let's look at an example. Below is the spectrum of the original series
for Retail Sales of Shoe Stores. The seasonal frequencies are marked in green
and the trading day frequencies in blue. Note that the original series shows signs
of very strong seasonality with peaks at the seasonal frequencies
1/12, 2/12, 3/12, 4/12, and 5/12 cycles per month.
The Graphs below show the spectrum of the seasonally adjusted series and
the irregular. Notice that peaks at the seasonal frequencies are suppressed
completely. This means there is no estimable seasonal effect still present in
the seasonally adjusted series or in the irregular. There is a slight peak
at the second trading day frequency, but because the 0.348 frequency has been
suppressed, we can also conclude there is no estimable trading day effect still present in
the seasonally adjusted series or in the irregular.
Sliding Spans : Sliding spans detect instability in the seasonally adjusted series.
Sliding spans compare different estimates from the seasonal adjustment
from overlapping subspans of the time series data. Some of the available estimates:
- the seasonal factors,
- the seasonally adjusted series, and
- the month-to-month (or quarter-to-quarter) change in the seasonally adjusted series.
An adjustment is considered acceptable if
- the percentage of unstable seasonal factors is less then 15%,
- the percentage of unstable seasonal adjustment values is less than 15%, and
- the percentage of unstable month-to-month (quarter-to-quarter) changes is less then 35%.
Revision Histories : Revision histories give information about stability
in the seasonally adjusted series or the trend.
In history analysis, X-12-ARIMA performs a sequence of modeling and/or
seasonal adjustment runs
on a sequence of increasing data spans, adding one point at a time to the
end of the series.
Available options in history spec of X-12-ARIMA include:
- revisions for seasonal adjustment, seasonal factors, and trend,
- month-to-month (or quarter-to-quarter) revisions for seasonal adjustment and trend,
- revisions from projected factors to final factors, and
- out-of-sample forecast errors and AICs for the regARIMA model.
M and Q Diagnostics :
M and Q diagnostics were developed at Statistic Canada for X-11-ARIMA
and are also included in X-12-ARIMA. They indicate the properties of the
adjustment that are often associated with adjustments of good quality.
There are 11 M statistics (M1-M11) and two Q statistics (Q and Q2).
Q is the weighted average of the M statistics.
The values of Ms and Qs range from 0.0 to 3.0.
Any M greater than 1.0 indicates a source of potential problems for the adjustment
procedure. Keep in mind that some M diagnostics are more important than others,
and not every M has to be less than one for the adjustment to be acceptable.
Among all M statistics, M7 is the most important statistic.
M7 can show if there is too much moving seasonality relative to the
stable seasonality. Because of the moving average procedures
in X-11-ARIMA and X-12-ARIMA, too much moving seasonality may cause
problems in the estimation of the series components.
3. What do I do if the diagnostics fail?
The first thing to keep in mind is that for most series,
not all of the diagnostics will pass, so it is not unusual to have
some diagnostics failures. The best thing to do is to decide what is
important for your series and rely the most on those diagnostics.
For example, I personally believe that the most important quality
of a seasonally adjusted series is that there should be no seasonality.
So I rely the most on the spectral diagnostics, and next I watch the
history diagnostics to check on the stability of the adjustment.
If you aren't sure what a change in the diagnostics means for your series,
a course on the diagnostics can be very helpful.
4. How much data do I need to get diagnostics information from X-12-ARIMA?
You need five years of monthly data and 15 years of quarterly data (60 data points)
to get fairly good spectral estimates.
To be able to use the revision diagnostics, you may need as few as seven years, but as many as
12 years of data. For series with 3x9 filters, it may be useful to have 15 years of data for
the revision history and sliding spans diagnostics. Most series will probably use a
3x5 filter which uses seven years of data, so you will need about 10 years to get revision diagnostics
and useful sliding spans information.
