3-5-official-decom.Rmd

---
title: "3. Time series decomposition"
author: "3.5 Methods used in official statistics"
date: "OTexts.org/fpp3/"
classoption: aspectratio=169
titlepage: fpp3title.png
titlecolor: fpp3red
toc: false
output:
  binb::monash:
    colortheme: monashwhite
    fig_width: 7.5
    fig_height: 3
    keep_tex: no
    includes:
      in_header: fpp3header.tex
---

```{r setup, include=FALSE}
source("setup.R")
us_retail_employment <- us_employment |>
  filter(year(Month) >= 1990, Title == "Retail Trade") |>
  select(-Series_ID)
```

## History of time series decomposition

\fontsize{13}{15}\sf

  *  Classical method originated in 1920s.
  *  Census II method introduced in 1957. Basis for X-11 method and variants (including X-12-ARIMA, X-13-ARIMA)
  *  STL method introduced in 1983
  *  TRAMO/SEATS introduced in 1990s.
\pause

### National Statistics Offices
 * ABS uses X-12-ARIMA
 * US Census Bureau uses X-13ARIMA-SEATS
 * Statistics Canada uses X-12-ARIMA
 * ONS (UK) uses X-12-ARIMA
 * EuroStat use X-13ARIMA-SEATS

## X-11 decomposition

```{r, fig.height=3.6, fig.width=9}
x11_dcmp <- us_retail_employment |>
  model(x11 = X_13ARIMA_SEATS(Employed ~ x11())) |>
  components()
autoplot(x11_dcmp)
```

## X-11 decomposition
**Advantages**

  *  Relatively robust to outliers
  *  Completely automated choices for trend and seasonal changes
  *  Very widely tested on economic data over a long period of time.

\pause

**Disadvantages**

  *  No prediction/confidence intervals
  *  Ad hoc method with no underlying model
  *  Only developed for quarterly and monthly data

## Extensions: X-12-ARIMA and X-13-ARIMA

  *  The X-11, X-12-ARIMA and X-13-ARIMA methods are based on Census II decomposition.
  *  These allow adjustments for trading days and other explanatory variables.
  *  Known outliers can be omitted.
  *  Level shifts and ramp effects can be modelled.
  *  Missing values estimated and replaced.
  *  Holiday factors (e.g., Easter, Labour Day) can be estimated.

## X-13ARIMA-SEATS

```{r, fig.height=3.6, fig.width=9}
seats_dcmp <- us_retail_employment |>
  model(seats = X_13ARIMA_SEATS(Employed ~ seats())) |>
  components()
autoplot(seats_dcmp)
```

## X-13ARIMA-SEATS

**Advantages**

  * Model-based
  * Smooth trend estimate
  * Allows estimates at end points
  * Allows changing seasonality
  * Developed for economic data

\pause

**Disadvantages**

  *  Only developed for quarterly and monthly data