Time Series Analysis: Issues With Seasonal Adjustment
Figure 1: Daily weights for Australia total retail turnover
A time series will not exhibit a trading day effect if levels of activity are constant over each day of the week. However, different months have different lengths (28,29,30 and 31 days), hence monthly activity can vary purely because certain months are longer than others. This is known as the length of month effect. If a series has trading day corrections, then these adjustments will include the effect. If there is no trading day effect in a time series, then the length of month effect is accounted for in the seasonal component.
Stock series should not experience a trading day effect since they only measure the level of activity at a certain point in time and are therefore not affected by how many trading days there are in a given period of time.
Why are trading day adjustments rarely made to quarterly series?
Quarters can have 90, 91, or 92 days. Those with 91 days do not experience the trading day effect as this is a multiple of seven, hence they always contain the same number of each day. The others only lose or gain a day, and unless the activity on this day is significant, the effect is nearly impossible to quantify accurately. Trading day effects are rarely seen in ABS quarterly series.
EXTREMES or OUTLIERS
Extremes or outliers are values in a time series that are unusually large or small relative to the other data. They can distort the appearance of the underlying movement of the time series by altering the trend. For this reason, and to improve estimation of the three series components (trend, seasonal and irregular), it is necessary to detect and correct outliers.
For example, consider the Figure 2. The peak in the seasonally adjusted series in late 1994, corresponds to a significantly large irregular value. Because it has not been corrected, it is quite obviously distorting the trend around that time point.
Figure 2: Quarterly Imports of Industrial Transport Equipment
TREND AND SEASONAL BREAKS
Although a time series is a collection of consistently and rigorously defined data items, it is likely that a series will undergo structural breaks during its span. These can be the result of a change in the population they are measuring or in the way that the population is being measured.
An abrupt but sustained change in the level of a time series is known as a trend break. This is reflected in at least 6 months or 3 quarters of raised or lowered levels. If the span of anomalous values is shorter than this, they are classified as extreme values.
A trend break may be caused by:
Seasonal breaks are abrupt changes in the seasonality of a series, which do not affect the level of the series. They may be caused by changes in coverage of the survey, social traditions, administrative practices or technological innovations.
REVISIONS TO TIME SERIES
Estimates of time series components may be revised over time. This can occur for the original, seasonally adjusted and trend estimates. For example, the trend estimate for unemployment for a particular month will change from month to month as new original estimates become available. The revisions to seasonally adjusted and trend estimates will occur until there is enough original estimates available to use symmetric filters to calculate the seasonal and trend components for that month. Typically, such revisions will reduce over time and become negligible after a few months. However, this will depend on the nature of the time series.
FORWARD FACTORS VERSUS CONCURRENT ANALYSIS
There are two approaches to deriving seasonal and trading day factors:
Forward factors rely on an annual analysis of the latest available data to determine the seasonal and trading day factors that will applied to the data received during the forthcoming year.
Concurrent analysis involves re-estimating seasonal factors as each new data point becomes available. Obviously this method is more computationally intense than the forward factor method, but the seasonal factors will be more responsive to dynamic changes.
Currently, the ABS uses forward factor analysis for most time series. However, it has introduced concurrent adjustment into some series and is intending to implement this approach with the majority of ABS time series.
DIRECT (DISAGGREGATE) VERSUS INDIRECT (AGGREGATE) METHODS OF ADJUSTMENT
Sometimes we may deal with series which are related in an aggregative way. For example, we may have data relating to some activity for each individual state, but we would like to obtain a seasonally adjusted series for the Australian total. There are two ways in which we can do this.
Under an indirect (aggregate) method of adjustment, we seasonally adjust each of the lower component series individually, then sum all the values to obtain the seasonally adjusted series for the total.
Directly (disaggregatively) adjusting a series involves summing all the original series to form a total series and then seasonally adjusting the total series directly.
How do we decide which method of adjustment to use?
If the component series each have very different seasonal patterns, then indirect seasonal adjustment is preferable. However if seasonality is minor and difficult to identify in the individual series, then using direct seasonal adjustment may remove any residual seasonality from the aggregate series.