# Seasonal adjustment Census X-13 analysis

This document refers to Macrobond 1.14 and later.

#### Introduction

This analysis uses the X-13-ARIMA-SEATS program from the US Census Bureau to seasonally adjust series. The program is a superset of the X12-ARIMA, X-11-ARIMA and X-11 programs.

You can find comprehensive documentation of this program and method at the Census Bureau web site. This documentation explains how the settings in Macrobond corresponds to the settings in the X-13-ARIMA-SEATS program. The US Census Basic Glossary explains some commonly used expressions.

The output will include the seasonally adjusted series, but also a report that is based on the output from the X-13-ARIMA-SEATS program.

#### Settings

###### Method

You can select to use the methodology of the Census Bureau X-11 program, or the SEATS program developed by the Bank of Spain. The SEATS method will implicitly use an ARIMA model.

###### Type

If the type is set to `Stock`, the instruction
`type=stock` will be added to the series element of
the configuration passed to the X-13ARIMA-SEATS program.

If `Auto` is selected, the `Class` property
of the time series is used to determine if the series is of type
Stock.

###### ARIMA

If this option is selected, the instruction `automdl`
is added to the configuration passed to the X-13-ARIMA-SEATS
program. This will instruct the program to use an automatic ARIMA
model based on the model used by TRAMO.

The ARIMA modelling often improves estimation of the different time series components. ARIMA cannot be used on all time series. There are conditions like at least three years of history and only positive values. In case there is an error, the report will contain a description of the problem.

Note that ARIMA is always needed for the SEATS method and this option is always set in that case.

###### Try trading day effect

The instruction `aictest=td` will be added to the
regression element of the configuration passed to the
X-13-ARIMA-SEATS program.

This instructs the program to do an AIC-based test to see if there is a trading day effect, based on Monday-Friday weeks. If there is, this factor will be included in the ARIMA model.

###### Try Easter effect

The instruction `aictest=easter` will be added to the
regression element of the configuration passed to the
X-13-ARIMA-SEATS program.

This instructs the program to do an AIC-based test to see if there is an effect of the Easter holiday. If there is, this factor will be included in the ARIMA model.

###### Conditional

When this option is set, the seasonal adjustment will only be applied if the series is not already seasonally adjusted by the source or by using one of the seasonal adjustment analyses.

###### Calculate trend

Produce a series of the final trend-cycle, which is the long-term and medium-to-long term movements of the series.

#### Outliers

The instruction `outlier` will be added to the
configuration passed to the X-13-ARIMA-SEATS program.

This instructs the program to check for single point outliers and level shifts.

#### Multiplicative/additive

The instruction `transform function=auto` instructs
the program to automatically consider log-additive adjustment if
all numbers are positive and an AICC test shows that this is a
better method. In most cases the multiplicative method will be
used.

#### Limitations

There are some requirements on the time series:

- Seasonal adjustment cannot be done on series that are daily, weekly or annual.
- There must be no missing values in the series. Missing values can be filled in by using one of the methods configured at the Conversion settings tab of the Series list analysis.
- There must not be any skipped dates in the series. You can make sure that all dates are included in the series by selecting All points for the Observations setting in the Series list.
- There are limitations in the X-13-ARIMA-SEATS program when it comes to the maximum number of observations, maximum number of years etc. The report will contain any errors reported by the program.