R interface to X-13ARIMA-SEATS

seasonal is an easy-to-use and (almost) 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).

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 not supported. Read the Input and Output sections and have a look at the wiki, where the examples from the official X-13ARIMA-SEATS manual are reproduced in R.


To install the stable version directly from CRAN, type to the R console:


seasonal does not include the binary executables of X-13ARIMA-SEATS. They can be obtained precompiled from here (Windows: x13asall.zip) or here (Linux, with g77: x13asall.tar.gz). A guide to manual compilation for Ubuntu can be found here. My own compilation for Mac OS-X can be obtained .

Download the file, unzip it and copy the folder to the desired location in your file system. Next, you need to tell seasonal where to find the binary executables of X-13ARIMA-SEATS, by setting the specific environmental variable X13_PATH. This may be done during your active session in R:

Sys.setenv(X13_PATH = "YOUR_X13_DIRECTORY")

Exchange YOUR_X13_DIRECTORY with the path to your installation of X-13ARIMA-SEATS. Note that the Windows path C:\something\somemore has to be entered UNIX-like C:/something/somemore or C:\\something\\somemore. You can always check your installation with:


If you want to set the environmental variable permanently, you may do so by adding it tho the Renviron.site file, which is located in the etc subdirectory of your R home directory (use R.home() in R to reveal the home directory). Renviron.site does not exist by default; if not, you have to create a file named Renviron.site with your favorite text editor (on Windows, be careful with the 'show extensions for known file types' option, the extension .site may be hidden). Add the following line to the file:


Alternatively, use the system terminal (on Windows, it's called command prompt; also, the cd command requires \ instead of /):

echo X13_PATH = YOUR_PATH_TO_X13 >> Renviron.site

There are other ways to set an environmental variable permanently in R, see ?Startup.

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 = list())

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

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 above can be easily generated from the automatic model:

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

If you are using RStudio, the inspect command offers a 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-SEAT. 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 list(). Several defaults of seas are empty lists, such as the default seats = list(). See the help page (?seas) for more details on the defaults.

It is possible to manipulate almost all inputs to X-13ARIMA-SEATS in this way. 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 = list(),
     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. 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 in the wiki.

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:


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 forecast.save = "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, forecast.save = "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")

The out function shows the full content of the .out text file from X-13ARIMA-SEATS in a console viewer. It can also be searched:

out(m, search = "regARIMA model residuals")


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, outliers = FALSE)
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.


Inspect tool

The inspect function is a graphical tool for choosing a seasonal adjustment model. It uses the manipulate package and can only be used with the (free) RStudio IDE. 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 only argument:


The inspect function opens an interactive window that allows for the manipulation of a number of arguments. It offers several views to analyze the series graphically. With each change, the adjustment process and the visualizations are recalculated. Summary statistics are shown in the R console. The views in inspect are customizable, see the examples in ?inspect.

With the 'Show static call' option, a replicable static call is also shown in the console. Note that this option will double the time for recalculation, as the static function also performs a test of the static call.


seasonal is free and open source, licensed under GPL-3. It has been developed for the use at the Swiss State Secretariat of Economic Affairs. Its development is not connected to the development of X-13ARIMA-SEATS (licence).

Please report bugs and suggestions on Github or send me an . Thank you!