Introduction to Seasonal R-interface to X-13ARIMA-SEATS

seasonal is an easy-to-use and full-featured R-interface to X-13ARIMA-SEATS, the newest seasonal adjustment software developed by the United States Census Bureau. X-13ARIMA-SEATS combines and extends the capabilities of the older X-12ARIMA (developed by the Census Bureau) and TRAMO-SEATS (developed by the Bank of Spain).

Seasonalview: An extended graphical user interface to X-13

While not yet on CRAN, the new seasonalview package offers an extended local graphical user interface to seasonal and X-13 — with the same look and feel as this website.

Try it out!

If you are new to seasonal adjustment or X-13ARIMA-SEATS, the automated procedures of seasonal allow you to quickly produce good seasonal adjustments of time series. Start with the Installation and Getting started section and skip the rest. Alternatively, demo(seas) gives an overview of the package functionality.

If you are familiar with X-13ARIMA-SEATS, you may benefit from the flexible input and output structure of seasonal. The package allows you to use (almost) all commands of X-13ARIMA-SEATS, and it can import (almost) all output generated by X-13ARIMA-SEATS. The only exception is the ‘composite’ spec, which is easy to replicate in basic R. Read the Input and Output sections and have a look at the website of seasonal, where the examples from the official X-13ARIMA-SEATS manual are reproduced in R.

seasonal includes a graphical user interface that facitlitates the use of X-13 both for beginners and advanced users. The final sections of this vignette cover additional topics: User defined holidays, such as Chinese New Year, the use of seasonal for production, and the import of existing X-13 model specs to R.


No separate binary download required anymore!

seasonal now depends on the x13binary package (by Dirk Eddelbuettel and myself) to access pre-built binaries of X-13ARIMA-SEATS for all platforms. Installing seasonal and the binaries is now as easy as installing any other CRAN package.

Since version 1.2, seasonal relies on the x13binary package to access prebuilt binaries of X-13ARIMA-SEATS. To install both packages, type to the R console:


This automatically installs x13binary. If you are using an older version of R (< 3.2) on Windows, you have to install seasonal from source:

install.packages("seasonal", type = "source") 

See the documentation of ?seasonal if you want to set the path to X-13 manually.

Getting started

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:

m <- seas(AirPassengers)

The first argument of seas has to be a time series of class "ts". The function returns an object of class "seas" that contains all necessary information on the adjustment.

There are several functions and methods for "seas" objects: The final function returns the adjusted series, the plot method shows a plot with the unadjusted and the adjusted series. The summary method allows you to display an overview of the model:


By default, seas calls the SEATS adjustment procedure. If you prefer the X11 adjustment procedure, use the following option (see the Input section for details on how to use arbitrary options with X-13):

seas(AirPassengers, x11 = "")

A default call to seas also invokes the following automatic procedures of X -13ARIMA-SEATS:

  • Transformation selection (log / no log)
  • Detection of trading day and Easter effects
  • Outlier detection
  • ARIMA model search

Alternatively, all inputs may be entered manually, as in the following example:

seas(x = AirPassengers, 
     regression.variables = c("td1coef", "easter[1]", "ao1951.May"), 
     arima.model = "(0 1 1)(0 1 1)", 
     regression.aictest = NULL,
     outlier = NULL, 
     transform.function = "log")

The static command returns the manual call of a model. The call above can be easily generated from the automatic model:

static(m, coef = TRUE)  # also fixes the coefficients

If you have Shiny installed, the inspect command offers an easy way to analyze and modify a seasonal adjustment procedure (see the section below for details):



In seasonal, it is possible to use almost the complete syntax of X-13ARIMA- SEATS. This is done via the ... argument in the seas function. The X -13ARIMA-SEATS syntax uses specs and arguments, with each spec optionally containing some arguments. These spec-argument combinations can be added to seas by separating the spec and the argument by a dot (.). For example, in order to set the ‘variables’ argument of the ‘regression’ spec equal to td and ao1999.jan, the input to seas looks like this:

m <- seas(AirPassengers, regression.variables = c("td", "ao1955.jan"))

Note that R vectors may be used as an input. If a spec is added without any arguments, the spec should be set equal to an empty string (or, alternatively, to an empty list, as in early versions). Several defaults of seas are empty strings, such as the default seats = "". See the help page (?seas) for more details on the defaults. Note the difference between "" (meaning the spec is enabled but has no arguments) and NULL (meaning the spec is disabled).

It is possible to manipulate almost all inputs to X-13ARIMA-SEATS in this way. The best way to learn about the relationship between the syntax of X-13ARIMA- SEATS and seasonal is to study the comprehensive list of examples. For instance, example 1 in section 7.1 from the manual,

series { title  =  "Quarterly Grape Harvest" start = 1950.1
       period =  4
       data  = (8997 9401 ... 11346) }
arima { model = (0 1 1) }
estimate { }

translates to R in the following way:

     x11 = ""),
     arima.model = "(0 1 1)"

seas takes care of the ‘series’ spec, and no input beside the time series has to be provided. As seas uses the SEATS procedure by default, the use of X11 has to be specified manually. When the ‘x11’ spec is added as an input (like above), the mutually exclusive and default ‘seats’ spec is automatically disabled. With arima.model, an additional spec-argument is added to the input of X-13ARIMA-SEATS. As the spec cannot be used in the same call as the ‘automdl’ spec, the latter is automatically disabled.

There are some mutually exclusive specs in X-13ARIMA-SEATS. If more than one mutually exclusive spec is included in seas, specs are overwritten according the following priority rules:

  • Model selection
    1. arima
    2. pickmdl
    3. automdl (default)
  • Adjustment procedure
    1. x11
    2. seats (default)

As an alternative to the ... argument, spec-arguments can also be supplied as a named list. This is useful for programming:

seas(list = list(x = AirPassengers, x11 = ""))


seasonal has a flexible mechanism to read data from X-13ARIMA-SEATS. With the series function, it is possible to import almost all output that can be generated by X-13ARIMA-SEATS. For example, the following command returns the forecasts of the ARIMA model as a "ts" time series:

m <- seas(AirPassengers)
series(m, "forecast.forecasts")

Because the = "forecasts" argument has not been specified in the model call, series re-evaluates the call with the ‘forecast’ spec enabled. It is also possible to return more than one output table at the same time:

series(m, c("forecast.forecasts", "d1"))

You can use either the unique short names of X-13 (such as d1), or the the long names (such as forecasts). Because the long table names are not unique, they need to be combined with the spec name (forecast). See ?series for a complete list of options.

Note that re-evaluation doubles the overall computation time. If you want to speed it up, you have to be explicit about the output in the model call:

m <- seas(AirPassengers, = "forecasts")
series(m, "forecast.forecasts")

Some specs, like ‘slidingspans’ and ‘history’, are time consuming. Re-evaluation allows you to separate these specs from the basic model call:

m <- seas(AirPassengers)
series(m, "history.saestimates")
series(m, "slidingspans.sfspans")

If you are using the HTML version of X-13, the out function shows the content of the main output in the browser:



There are several graphical tools to analyze a seas model. The main plot function draws the seasonally adjusted and unadjusted series, as well as the outliers. Optionally, it also draws the trend of the seasonal decomposition:

m <- seas(AirPassengers, regression.aictest = c("td", "easter"))
plot(m, trend = TRUE)

The monthplot function allows for a monthwise plot (or quarterwise, with the same function name) of the seasonal and the SI component:

monthplot(m, choice = "irregular")

Also, many standard R function can be used to analyze a "seas" model:


The identify method can be used to select or deselect outliers by point and click. Click several times to loop through different outlier types.



The inspect function is a graphical tool for choosing a seasonal adjustment model, using Shiny, with the same structure as the demo website of seasonal. To install the latest version of Shiny, type:


The goal of inspect is to summarize all relevant options, plots and statistics that should be usually considered. inspect uses a "seas" object as its main argument:


Frequently used options can be modified using the drop down selectors in the upper left panel. Each change will result in a re-estimation of the seasonal adjustment model. The R-call, the output and the summary are updated accordingly.

Alternatively, the R-Call can be modified manually in the lower left panel. Press ‘Run Call’ to re-estimate the model and to adjust the option selectors, the output, and the summary. With the ‘Close and Import’ button, inspect is closed and the call is imported to R. The ‘static’ button substitutes automatic procedures by the automatically chosen spec-argument options, in the same way as static.

The views in the upper right panel can be selected from the drop down menu. The views can also be customized (see ?inspect for details)

The lower right panel shows the summary, as descibed in the help page of ?summary.seas. The ‘Full X-13 output’ button opens the complete output of X-13 in a separate tab or window.

While not yet on CRAN, the new seasonalview package offers an extended GUI with the same look and feel as this website. It is planned to replace the inspect function in a future version.

Chinese New Year, Indian Diwali and other customized holidays

seasonal includes genhol, a function that makes it easy to model user-defined holiday regression effects. genhol is an R replacement for the equally named software by the Census Office; no additional installation is required. The function uses an object of class "Date" as its first argument, which specifies the occurrence of the holiday.

In order to adjust Indian industrial production for Diwali effects, use, e.g.,:

# variables included in seasonal
# iip: Indian industrial production
# cny, diwali, easter: dates of Chinese New Year, Indian Diwali and Easter

x11 = "",
xreg = genhol(diwali, start = 0, end = 0, center = "calendar"), 
regression.usertype = "holiday"

For more examples, including Chinese New Year and complex pre- and post-holiday adjustments, see ?genhol.

Production use

While seasonal offers a quick way to adjust a time series in R, it is equally suited for the recurring processing of potentially large numbers of time series. There are two kind of seasonal adjustments in production use:

  1. a periodic application of an adjustment model to a time series
  2. an automated adjustment to a large number of time series

This section shows how both tasks can be accomplished with seasonal and basic R.

Storing calls and batch processing

seas calls are R objects of the standard class "call". Like any R object, calls can be stored in a list. In order to extract the call of a "seas" object, you can access the $call element or extract the static call with static(). For example,

# two different models for two different time series
m1 <- seas(fdeaths, x11 = "")
m2 <- seas(mdeaths, x11 = "")

l <- list()
l$c1 <- static(m1)  # static call (with automated procedures substituted)
l$c2 <- m2$call     # original call

The list can be stored and re-evaluated if new data becomes available:

ll <- lapply(l, eval)

which returns another list containing the re-evaluated "seas" objects. If you want to extract the final series, use:, lapply(ll, final))

Of course, you also can extract any other series, e.g.:

# seasonal component of an X11 adjustment, see ?series, lapply(ll, series, "d10"))

Automated adjustment of multiple series

X-13 can also be applied to a large number of series, using automated adjustment methods. This can be accomplished with a loop or an apply function. It is useful to wrap the call to seas in a try statement; that way, an error will not break the execution. You need to develop an error handling strategy for these cases: You can either drop them, use them without adjustment or switch to a different automated routine.

# collect data 
dta <- list(fdeaths = fdeaths, mdeaths = mdeaths)

# loop over dta
ll <- lapply(dta, function(e) try(seas(e, x11 = "")))

# list failing models
is.err <- sapply(ll, class) == "try-error"

# return final series of successful evaluations, lapply(ll[!is.err], final))

If you have several cores and want to speed things up, the process is well suited for parallelization:

# a list with 100 time series
largedta <- rep(list(AirPassengers), 100)

library(parallel)  # this is part of a standard R installation

If you are on Windows or want to use cluster parallelization, use parLapply:

# set up cluster
cl <- makeCluster(detectCores())

# load 'seasonal' for each node
clusterEvalQ(cl, library(seasonal))

# export data to each node
clusterExport(cl, varlist = "largedta")

# run in parallel (2.2s on a 8-core Macbook, vs 9.6s with standard lapply)
parLapply(cl, largedta, function(e) try(seas(e, x11 = "")))

# finally, stop the cluster

On Linux or OS-X, ‘forking’ parallelization allows you to do the same in a single line:

mclapply(cl, largedta, function(e) try(seas(e, x11 = "")))

Import X-13 models and series

Two experimental utility functions allow you to import .spc files and X-13 data files from any X-13 set-up. Simply locate the path of your X-13 .spc file, and the import.spc function will construct the corresponding call to seas as well as the calls for importing the data.

# importing the orginal X-13 example file
import.spc(system.file("tests", "Testairline.spc", package="seasonal"))

If data is stored outside the .spc file (as it usually will be), the calls will make use of the import.ts function, which imports arbitrary X-13 data files as R time series. See ?import.ts for examples.

License and Credits

seasonal is free and open source, licensed under GPL-3. It requires the X -13ARIMA-SEATS software by the U.S. Census Bureau, which is open source and freely available under the terms of its own license.

seasonal has been originally developed for the use at the Swiss State Secretariat of Economic Affairs. It has been greatly improved over time thanks to suggestions and support from Matthias Bannert, Freya Beamish, Vidur Dhanda, Alain Galli, Ronald Indergand, Preetha Kalambaden, Stefan Leist, James Livsey, Brian Monsell, Pinaki Mukherjee, Bruno Parnisari, and many others. I am especially grateful to Dirk Eddelbuettel for the fantastic work on the x13binary package.

Please report bugs and suggestions on Github. Thank you!