Publication date: 08/13/2020

## Decomposition Reports

This section provides details about the reports obtained from the three decomposition options:

### Linear Trend Report

Contains the values of β0 and β1 from the linear regression model that is fit to the data:

The detrended series is equal to Dt = Ot - Trendt, where Ot is the original time series.

### Cycle Report

Contains the values of the cyclical component that is fit to the data:

The parameter values are defined as follows:

C is the (optional) Constant

A is the Amplitude of the cosine wave

U is the number of Units per Cycle

P is the Phase of the cosine wave

t is one less than the row number of a given observation

The decycled series is equal to Dt = Ot - Cyclet, where Ot is the original time series.

### X11 Report

Depending on your selection of Decomposition Type, the X11 option adds an X11 - Multiplicative report or an X11 - Additive report. The reports contain the same four plots:

Overlays the X11-adjusted time series on the original time series, Ot. The X11-adjusted values are Ot/St for the multiplicative adjustment and Ot - St for the additive adjustment.

D10 - Final Seasonal Factors

Plots the seasonal factor components, St, over time.

D12 - Final Trend Cycle

Plots the trend cycle components, Ct, over time.

D13 - Final Irregular Series

Plots the irregular components, It, over time.

#### X11 Report Options

The X11 reports have the following red triangle options:

Show Tables

Shows or hides the X11 summary tables, as described in Shiskin et. al. (1967). The tables are grouped into five categories (labeled B through F), described in Table 17.1.

Save Columns

Saves four columns to the data table: the seasonally adjusted time series, the seasonal components (St), the trend cycle components (Ct), and the irregular series components (It).

Save All Columns

Saves columns to the data table for all of the tables produced in the report by the Show Tables option.

Table 17.1 Descriptions of the Categories of X11 Output Tables

Letter Prefix

Category Description

B

preliminary estimates of seasonal, trend cycle, and irregular components

C

intermediate estimates of seasonal, trend cycle, and irregular components

D

final estimates of seasonal, trend cycle, and irregular components

E

analytical tables

F

summary measures

For more information about the contents of the X11 output tables, see Shisken et. al. (1967) or SAS/ETS 13.1 User’s Guide (search for “The output from PROC X11”).