Seasonal Adjustment of Multiple Series

R
time-series
Author

Christoph Sax

Published

March 9, 2021

seasonal is an easy-to-use and full-featured R-interface to X-13ARIMA-SEATS, the seasonal adjustment software developed by the United States Census Bureau. The latest CRAN version of seasonal makes it much easier to adjust multiple time series.

Illustration
Photo by Meriç Dağlı


seasonal depends on the x13binary package to access pre-built binaries of X-13ARIMA-SEATS on all platforms and does not require any manual installation. To install both packages:

install.packages("seasonal")

seas is the core function of the seasonal package. By default, seas calls the automatic procedures of X-13ARIMA-SEATS to perform a seasonal adjustment that works well in most circumstances:

seas(AirPassengers)

For a more detailed introduction, read our article in the Journal of Statistical Software.

Multiple Series Adjusmtent

In the latest CRAN version 1.8, it is now possible to seasonally adjust multiple series in a single call to seas(). This is done by using the built-in batch mode of X-13. It removes the need for loops or lapply() in such cases and finally brings one missing feature of X-13 to seasonal – the composite spec.

Multiple adjustments can be performed by supplying multiple time series as an "mts" object:

library(seasonal)
m <- seas(cbind(fdeaths, mdeaths), x11 = "")
final(m)
          fdeaths  mdeaths
Jan 1974 614.1235 1598.740
Feb 1974 542.3500 1492.127
Mar 1974 613.5029 1443.238
Apr 1974 591.5725 1694.643
May 1974 607.4970 1696.021
Jun 1974 543.8415 1558.886
Jul 1974 597.0745 1663.176
Aug 1974 587.0533 1623.498
Sep 1974 588.2693 1741.394
Oct 1974 735.6666 1735.516
Nov 1974 602.0218 1665.590
Dec 1974 496.3985 1394.097
Jan 1975 564.0055 1560.605
Feb 1975 591.0320 1708.763
Mar 1975 585.7739 1652.994
Apr 1975 581.5294 1671.265
May 1975 537.8055 1588.605
Jun 1975 584.3284 1600.979
Jul 1975 566.4872 1541.099
Aug 1975 617.1197 1623.445
Sep 1975 516.4781 1521.497
Oct 1975 559.0481 1577.200
Nov 1975 561.6315 1602.659
Dec 1975 580.9778 1569.692
Jan 1976 519.8106 1477.855
Feb 1976 882.3725 2180.616
Mar 1976 674.5057 1744.114
Apr 1976 467.4502 1366.628
May 1976 509.7854 1344.809
Jun 1976 553.5233 1434.662
Jul 1976 503.2795 1447.952
Aug 1976 494.2373 1383.932
Sep 1976 529.1840 1453.496
Oct 1976 570.4128 1435.912
Nov 1976 590.4285 1540.551
Dec 1976 587.0971 1572.631
Jan 1977 583.2427 1607.153
Feb 1977 498.9514 1287.403
Mar 1977 500.4632 1306.324
Apr 1977 569.2076 1685.581
May 1977 565.6470 1405.231
Jun 1977 509.3196 1432.968
Jul 1977 548.4062 1414.216
Aug 1977 523.6985 1444.945
Sep 1977 563.3014 1402.720
Oct 1977 495.6653 1427.458
Nov 1977 453.9859 1307.828
Dec 1977 502.3045 1268.618
Jan 1978 535.2658 1415.724
Feb 1978 633.7605 1790.002
Mar 1978 559.2936 1469.883
Apr 1978 485.5062 1343.715
May 1978 590.4080 1509.166
Jun 1978 574.4467 1464.288
Jul 1978 571.2263 1428.398
Aug 1978 542.3579 1424.622
Sep 1978 551.2099 1422.428
Oct 1978 557.6905 1399.404
Nov 1978 479.8979 1199.762
Dec 1978 550.4253 1397.023
Jan 1979 548.9834 1557.853
Feb 1979 576.9922 1425.717
Mar 1979 549.3468 1393.788
Apr 1979 546.4590 1449.784
May 1979 525.9881 1359.843
Jun 1979 550.2481 1330.113
Jul 1979 533.7558 1373.156
Aug 1979 566.6884 1381.653
Sep 1979 552.6500 1377.175
Oct 1979 533.9571 1337.640
Nov 1979 557.9707 1414.101
Dec 1979 475.5049 1038.506

This will perform two seasonal adjustments, one for fdeaths and one for mdeaths. X-13 spec-argument combinations can be applied in the usual way, such as x11 = "". Note that if entered that way, they will apply to both series. The vignette on multiple adjustments describes how to specify options for individual series.

Backend

X-13 ships with a batch mode that allows multiple adjustments in a single call to X-13. This is now the default in seasonal (multimode = "x13"). Alternatively, X-13 can be called for each series (multimode = "R"). The results should be usually the same, but switching to multimode = "R" may be useful for debugging:

seas(cbind(fdeaths, mdeaths), multimode = "x13")
$fdeaths

Call:
seas(x = cbind(fdeaths, mdeaths), multimode = "x13")

Coefficients:
      Constant      AO1976.Feb  MA-Seasonal-12  
      -0.01578         0.43345         0.63119  


$mdeaths

Call:
seas(x = cbind(fdeaths, mdeaths), multimode = "x13")

Coefficients:
       AO1976.Feb         LS1976.Apr         AO1977.Apr         AO1978.Feb  
           0.3319            -0.1330             0.1957             0.2305  
       AO1979.Dec  MA-Nonseasonal-01     MA-Seasonal-12  
          -0.3149            -0.3854             0.6120  


$call
seas(x = cbind(fdeaths, mdeaths), multimode = "x13")

attr(,"class")
[1] "seas_multi" "list"      
seas(cbind(fdeaths, mdeaths), multimode = "R")
$fdeaths

Call:
seas(x = cbind(fdeaths, mdeaths), multimode = "R")

Coefficients:
      Constant      AO1976.Feb  MA-Seasonal-12  
      -0.01578         0.43345         0.63119  


$mdeaths

Call:
seas(x = cbind(fdeaths, mdeaths), multimode = "R")

Coefficients:
       AO1976.Feb         LS1976.Apr         AO1977.Apr         AO1978.Feb  
           0.3319            -0.1330             0.1957             0.2305  
       AO1979.Dec  MA-Nonseasonal-01     MA-Seasonal-12  
          -0.3149            -0.3854             0.6120  


$call
seas(x = cbind(fdeaths, mdeaths), multimode = "R")

attr(,"class")
[1] "seas_multi" "list"

In general, multimode = "x13" is faster. The following comparison on a MacBook Pro shows a modest speed gain, but bigger differences have been observed on other systems:

many <- rep(list(fdeaths), 100)
system.time(seas(many, multimode = "x13"))
#   user  system elapsed
#  9.415   0.653  10.079
system.time(seas(many, multimode = "R"))
#   user  system elapsed
# 11.130   1.039  12.324

composite spec

Support for the X-13 batch mode makes it finally possible to use the composite spec – the one feature of X-13 that was missing in seasonal. Sometimes, one has to decide whether seasonal adjustment should be performed on a granular level or on an aggregated level. The composite spec helps you to analyze the problem and to compare the direct and the indirect adjustments.

The composite argument is a list with an X-13 specification that is applied on the aggregated series. Specification works identically for other series in seas(), including the application of the defaults. If you provide an empty list, the usual defaults of seas() are used. A minimal composite call looks like this:

seas(
  cbind(mdeaths, fdeaths),
  composite = list(),
  series.comptype = "add"
)
$mdeaths

Call:
seas(x = cbind(mdeaths, fdeaths), composite = list(), series.comptype = "add")

Coefficients:
       AO1976.Feb         LS1976.Apr         AO1977.Apr         AO1978.Feb  
           0.3319            -0.1330             0.1957             0.2305  
       AO1979.Dec  MA-Nonseasonal-01     MA-Seasonal-12  
          -0.3149            -0.3854             0.6120  


$fdeaths

Call:
seas(x = cbind(mdeaths, fdeaths), composite = list(), series.comptype = "add")

Coefficients:
      Constant      AO1976.Feb  MA-Seasonal-12  
      -0.01578         0.43345         0.63119  


$composite

Call:
seas(x = cbind(mdeaths, fdeaths), composite = list(), series.comptype = "add")

Coefficients:
         Constant         AO1976.Feb  MA-Nonseasonal-01     MA-Seasonal-12  
         -0.03133            0.31247           -0.43509            0.99937  


$call
seas(x = cbind(mdeaths, fdeaths), composite = list(), series.comptype = "add")

attr(,"class")
[1] "seas_multi" "list"

You can verify that the composite refers to the total of mdeaths and fdeaths by running:

seas(ldeaths)

Call:
seas(x = ldeaths)

Coefficients:
         Constant         AO1976.Feb  MA-Nonseasonal-01     MA-Seasonal-12  
         -0.03133            0.31247           -0.43509            0.99937

where ldeaths is the sum of mdeaths and fdeaths.

Acknowledgement

Many thanks to Severin Thöni and Matthias Bannert, for demonstrating the benefits of the X-13 batch mode. Also to the ETH KOF, for partially funding this development.