X-13ARIMA-SEATS is a seasonal adjustment program developed and maintained by the U.S. Census Bureau.

X_13ARIMA_SEATS(
formula,
...,
na.action = seasonal::na.x13,
defaults = c("seasonal", "none")
)

## Arguments

formula Decomposition specification. Other arguments passed to seasonal::seas(). a function which indicates what should happen when the data contain NAs. na.omit (default), na.exclude or na.fail. If na.action = na.x13, NA handling is done by X-13, i.e. NA values are substituted by -99999. If defaults="seasonal", the default options of seasonal::seas() will be used, which should work well in most circumstances. Setting defaults="none" gives an empty model specification, which can be added to in the model formula.

## Details

The SEATS decomposition method stands for "Seasonal Extraction in ARIMA Time Series", and is the default method for seasonally adjusting the data. This decomposition method can extract seasonality from data with seasonal periods of 2 (biannual), 4 (quarterly), 6 (bimonthly), and 12 (monthly). This method is specified using the seats() function in the model formula.

Alternatively, the seasonal adjustment can be done using an enhanced X-11 decomposition method. The X-11 method uses weighted averages over a moving window of the time series. This is used in combination with the RegARIMA model to prepare the data for decomposition. To use the X-11 decomposition method, the x11() function can be used in the model formula.

## Specials

The specials of the X-13ARIMA-SEATS model closely follow the individual specification options of the original function. Refer to Chapter 7 of the X-13ARIMA-SEATS Reference Manual for full details of the arguments.

The available specials for this model are:

#'

### arima

The arima special is used to specify the ARIMA part of the regARIMA model. This defines a pure ARIMA model if the regression() special absent and if no exogenous regressors are specified. The lags of the ARIMA model can be specified in the model argument, potentially along with ar and ma coefficients.

arima(...)

 ... Arguments described in the reference manual linked below.

### automdl

The automdl special is used to specify the ARIMA part of the regARIMA model will be sought using an automatic model selection procedure derived from the one used by TRAMO (see Gomez and Maravall (2001a)). The maximum order of lags and differencing can be specified using maxorder and maxdiff arguments. Models containing mixtures of AR and MA components can be allowed or disallowed using the mixed argument.

automdl(...)

 ... Arguments described in the reference manual linked below.

### check

The check special is used to produce statistics for diagnostic checking of residuals from the estimated model. The computed statistics include ACF and PACF of residuals, along with some statistical tests. These calculations are included in the model object, but difficult to access. It is recommended that these checks are done in R after estimating the model, and that this special is not used.

check(...)

 ... Arguments described in the reference manual linked below.

### estimate

The estimate special is used to specify optimisation parameters and estimation options for the regARIMA model specified by the regression() and arima() specials. Among other options, the tolerance can be set with tol, and maximum iterations can be set with maxiter.

estimate(...)

 ... Arguments described in the reference manual linked below.

### force

The force is an optional special for invoking options that allow users to force yearly totals of the seasonally adjusted series to equal those of the original series for convenience.

force(...)

 ... Arguments described in the reference manual linked below.

### forecast

The forecast special is used to specify options for forecasting and/or backcasting the time series using the estimated model. This process is used to enhance the decomposition procedure, especially its performance at the start and end of the series. The number of forecasts to produce is specified in the maxlead argument, and the number of backcasts in the maxback argument.

forecast(...)

 ... Arguments described in the reference manual linked below.

### history

The history special is an optional special for requesting a sequence of runs from a sequence of truncated versions of the time series. Using this special can substantially slow down the program.

history(...)

 ... Arguments described in the reference manual linked below.

The metadata special is used to insert metadata into the diagnostic summary file. This is typically not needed when interacting with the program via R.

metadata(...)

 ... Arguments described in the reference manual linked below.

### identify

The identify special is used to produce tables and line printer plots of sample ACFs and PACFs for identifying the ARIMA part of a regARIMA model.

identify(...)

 ... Arguments described in the reference manual linked below.

### outlier

The outlier special is used to perform automatic detection of additive (point) outliers, temporary change outliers, level shifts, or any combination of the three using the specified model. The seasonal::seas() defaults used when defaults="seasonal" will include the default automatic detection of outliers.

outlier(...)

 ... Arguments described in the reference manual linked below.

### pickmdl

The pickmdl special is used to specify the ARIMA part of the regARIMA model will be sought using an automatic model selectionprocedure similar to the one used by X-11-ARIMA/88 (see Dagum 1988).

pickmdl(...)

 ... Arguments described in the reference manual linked below.

### regression

The regression special is used to specify including regression variables in a regARIMA model, or for specifying regression variables whose effects are to be removed by the identify() special to aid ARIMA model identification. Any exogenous regressors specified in the model formula will be passed into this specification via the user and data arguments. The seasonal::seas() defaults used when defaults="seasonal" will set aictest = c("td", "easter"), indicating that trading days and Easter effects will be included conditional on AIC-based selection methods.

regression(...)

 ... Arguments described in the reference manual linked below.

### seats

The seats special is optionally used to invoke the production of model based signal extraction using SEATS, a seasonal adjustment program developed by Victor Gomez and Agustin Maravall at the Bank of Spain.

seats(...)

 ... Arguments described in the reference manual linked below.

### slidingspans

The optional slidingspans special is to provide sliding spans stability analysis on the model. These compare different features of seasonal adjustment output from overlapping subspans of the time series data.

slidingspans(...)

 ... Arguments described in the reference manual linked below.

### spectrum

The optional spectrum special is used to provide a choice between two spectrum diagnostics to detect seasonality or trading day effects in monthly series.

spectrum(...)

 ... Arguments described in the reference manual linked below.

### transform

The transform special is used to transform or adjust the series prior to estimating a regARIMA model. This is comparable to transforming the response on the formula's left hand side, but offers X-13ARIMA-SEATS specific adjustment options.

transform(...)

 ... Arguments described in the reference manual linked below.

### x11

The optional x11 special is used to invoke seasonal adjustment by an enhanced version of the methodology of the Census Bureau X-11 and X-11Q programs. The user can control the type of seasonal adjustment decomposition calculated (mode), the seasonal and trend moving averages used (seasonalma and trendma), and the type of extreme value adjustment performed during seasonal adjustment (sigmalim).

x11(...)

 ... Arguments described in the reference manual linked below.

### x11regression

The x11regression special is used in conjunction with the x11() special for series without missing observations. This special estimates calendar effects by regression modeling of the irregular component with predefined or user-defined regressors. Any exogenous regressors specified in the model formula will be passed into this specification via the user and data arguments.

x11regression(...)

 ... Arguments described in the reference manual linked below.

## References

Gomez, Victor, and Agustin Maravall. "Automatic modeling methods for univariate series." A course in time series analysis (2001): 171-201.

Dagum, E.B. (1988), The X11 ARIMA/88 Seasonal Adjustment Method - Foundations And User’s Manual, Time Series Research and Analysis Division Statistics Canada, Ottawa.

Dagum, E. B., & Bianconcini, S. (2016) "Seasonal adjustment methods and real time trend-cycle estimation". Springer.

X-13ARIMA-SEATS Documentation from the seasonal package's website: http://www.seasonal.website/seasonal.html

Official X-13ARIMA-SEATS manual: https://www.census.gov/ts/x13as/docX13ASHTML.pdf

seasonal::seas()

## Examples


# \donttest{
fit <- tsibbledata::aus_production %>%
model(X_13ARIMA_SEATS(Beer))#> Model used in SEATS is different: (0 1 1)(0 1 1)
report(fit)#> Series: Beer
#> Model: X-13ARIMA-SEATS
#>
#> Coefficients:
#>                   Estimate Std. Error z value Pr(>|z|)
#> MA-Nonseasonal-01  0.96503    0.06307  15.301  < 2e-16 ***
#> MA-Nonseasonal-02 -0.34106    0.06362  -5.361 8.26e-08 ***
#> MA-Seasonal-04     0.77186    0.04380  17.621  < 2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> SEATS adj.  ARIMA: (0 1 2)(0 1 1)  Obs.: 218  Transform: log
#> AICc:  1748, BIC:  1761  QS (no seasonality in final):    0
#> Box-Ljung (no autocorr.): 16.09   Shapiro (normality): 0.994
#> Messages generated by X-13:
#> Notes:
#> - Model used for SEATS decomposition is different from the model
#>   estimated in the regARIMA modeling module of X-13ARIMA-SEATS.
#> components(fit)#> # A dable: 218 x 7 [1Q]
#> # Key:     .model [1]
#> # :        Beer = f(trend, seasonal, irregular)
#>    .model                Quarter  Beer trend seasonal irregular season_adjust
#>    <chr>                   <qtr> <dbl> <dbl>    <dbl>     <dbl>         <dbl>
#>  1 X_13ARIMA_SEATS(Beer) 1956 Q1   284  255.    1.05      1.06           271.
#>  2 X_13ARIMA_SEATS(Beer) 1956 Q2   213  255.    0.860     0.970          248.
#>  3 X_13ARIMA_SEATS(Beer) 1956 Q3   227  256.    0.912     0.973          249.
#>  4 X_13ARIMA_SEATS(Beer) 1956 Q4   308  257.    1.19      1.01           258.
#>  5 X_13ARIMA_SEATS(Beer) 1957 Q1   262  258.    1.04      0.976          251.
#>  6 X_13ARIMA_SEATS(Beer) 1957 Q2   228  259.    0.863     1.02           264.
#>  7 X_13ARIMA_SEATS(Beer) 1957 Q3   236  260.    0.915     0.992          258.
#>  8 X_13ARIMA_SEATS(Beer) 1957 Q4   320  261.    1.19      1.03           268.
#>  9 X_13ARIMA_SEATS(Beer) 1958 Q1   272  262.    1.04      1.00           262.
#> 10 X_13ARIMA_SEATS(Beer) 1958 Q2   233  262.    0.864     1.03           270.
#> # … with 208 more rows# }