Seasonal adjustment Census X-13

Overview

The Seasonal adjustment Census X-13 (SA )analysis removes seasonal patterns, such as weather fluctuations or holiday effects, from time series. It’s useful when you want to analyze any data affected by seasonality.

Method

This analysis uses the X-13-ARIMA-SEATS program from the US Census Bureau, which is the most common method used around the world. The program is a superset of the X-12-ARIMA program and it implements the X-11 algorithm. A documentation regarding the X-13 ARIMA-SEATS Seasonal Adjustment Program can be found here.

Limitations

The input series must meet the following requirements:

  • The series cannot be daily, weekly or annual
  • There must be no missing values in the series (you can fill in missing values by using one of the methods in the conversion settings tab of the series list analysis)
  • There must be no skipped dates in the series (you can make sure that all dates are included in the series by selecting all points from the observations drop down menu in the series list)
  • There are also limitations in the X-13-ARIMA-SEATS program when it comes to the maximum number of observations, maximum number of years etc.

Settings

Method

You can select from the following methods:

  • the X-11 method from the Census Bureau program
  • the SEATS program developed by the Bank of Spain

Type

Select whether your input series is a stock or flow series.

If Auto is selected, the class property of the time series is used to determine if it is a stock or a flow.

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

Holiday regressor

An option for selecting “Chinese New Year” as a regression variable in the X-13 Seasonal adjustment analysis. This works only for monthly data.

The Chinese New Year Holiday regressor utilizes a standard approach to account for the moving holiday effects from the Lunar holiday observed in some high-frequency time series data. While no universally agreed method exists, the literature thus far suggests an approach similar to what is being used in the application. Three regressors (in the form of dummy variables) are assigned to each of three sub-period windows of 20 days before, 7 days during, and 20 days after the holiday, capturing the differential effects on data from the lunar holiday.

For further insights into the theoretical and practical considerations on seasonal adjustment and moving holiday adjustments, please click here.

ARIMA

Selecting this option instructs the program to use an automatic ARIMA model to calculate short term forecasts based on the model used by TRAMO. Using the ARIMA model often improves estimation of the different time series components.

You may get an error if you try using ARIMA on a series that doesn’t meet the necessary conditions, such as having at least three years of history and only positive values. In this case, the report will include a description of the problem.

Note that ARIMA is always needed for the SEATS method, so this option will be automatically selected.

Trading day

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

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

Easter

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

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

Constant

You can add a trend constant regression variable by checking box in the constant column.

Conditional

When this option is selected, the seasonal adjustment will only be applied if the series is not already seasonally adjusted by the source or by using another seasonal adjustment analysis.

Output trend

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

Outliers

Included in X-13 ARIMA SEATS program, automatically checks for single point outliers and level shifts. The results can be found in Report.

Multiplicative/additive

The instruction transform function=auto automatically considers 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.

The information about outliers and transform function can be found in Report.

Report

A Report is available as standard output for this analysis, it includes relevant statistics and information. It is generated by Census X-13 ARIMA-SEATS program and automatically added once you select the analysis. The report will contain any errors reported by the program.

To open the report, first click on the series you're interested in.

In the same window, whole report will be available:

Example

Seasonal adjustment

In this example we applied Seasonal adjustment Census X-13 to Russian retail trade and added the calculated trend.