**Introduction**

The aim of seasonal adjustment is to estimate and remove the systematic calendar related component of a time series.

In practice, the original series that has been collected or derived will typically be comprised of at least three component parts:

- the seasonal component, e.g. calendar related
- the trend component, e.g. the short or long term underlying direction
- the irregular component, e.g. one-off effects

What a lot of users of time series outputs don't realise is that by definition the seasonally adjusted estimates still contain a degree of volatility which can be due to way the original data has been collected (e.g. the sampling characteristics used by the survey), the nature of the data that is being measured, or one-off events such as snow, earthquakes, strikes, riots which can distort the time series and also distort the analysis. Depending on the degree of volatility, these one-off events can make interpretation of the seasonally adjusted estimates difficult and sometimes impossible.

To help interpretation of the movements in the time series, the seasonally adjusted estimates can be filtered, or smoothed, to derive an estimate of the underlying component where the impact of the volatility has been reduced. This is commonly refered to as the trend. The trend is your friend as it helps interpretation of the underlying direction without the impact of the one-off volatility that can distort and give misleading month-on-month or quarter-on-quarter movements.

All time series components can then be considered separately:

- the original series shows the raw data
- the seasonally adjusted estimates show the trend and the irregular component
- the trend estimates show the underlying direction of the series
- the irregular component shows the impact of the one-off events

**Defining a trend**

There is no unique definition for the trend. This is probably the most contentious point about the use of trend estimates as it always leads to a debate about whose method is best and how trend estimates should be used. Economists can refer to business cycles as indicative of trend which may be in terms of years, whereas localised trends may be in terms of much shorter periods such as eight to twelve months. Each persons trend can be different and there is no right or wrong answer.

For producers and publishers of trend estimates there is a simple approach to get around this problem. Clearly define your trend and how you've calculated it and then let everyone know how you've done it. If you also publish seasonally adjusted estimates, then the more sophisticated users can just get on with their job and produce their own.

It is even much simpler in that as a by-product of seasonal adjustment, a trend estimate is produced. In fact, what a lot of users don't realise, is that one of the first steps in the X-12-ARIMA program is to calculate a trend. Trend estimates in the X-11 and X-12-ARIMA framework are central to the derivation of the seasonally adjusted estimates. The use of the trend estimates direct from the seasonally adjusted package would ensure a consistent set of component estimates.

However, in practice, there are other alternatives. For example, the Australian Bureau of Statistics define trend estimates by taking the published seasonally adjusted estimates and then directly applying a Henderson filter.

**Where can I find out more information on trend estimates?**

We believe trend estimates are an important analytical product that helps users understand the movements in a time series without having the impact of the one-off irregular events.

The references below are a useful starting point in finding out more information on trend estimates.