Time Series Analysis

This is a very simple example of time series analysis, but it illustrates the concept well. However, this example doesn’t consider the fact that the trend might not continue, nor does it factor any erroneous elements that might need to be considered. For example, what if trends change or there is a public transport strike that prevents people from using the service?

To help identify trends or predict future patterns as accurately as possible, there are various different time series considerations used by statisticians.

Time Series Considerations

Statisticians use time series considerations to ensure that their data is meaningful and balanced. Here, we outline some of the more common ones:

Time Series Effects

There are three types of time series effects: age, period, and cohort. (A cohort is a group that shares similar circumstances or unique occurrences.) Disentangling these three types of effects for one set of time series data is a major challenge of time series analysis.

• Age effects relate to aging or the life cycle. For example, an individual’s health tends to worsen as they get older, which will have an effect on a fitness study.
• Period effects relate to those in a given historical period. For example, people who grew up during a period of high unemployment could allow this to influence their decision to favor a government that provides more income support.
• Cohort effects reflect the unique reaction of a cohort to a historical event or which were experienced uniquely by the cohort. For example, in a country where national service is still in place, a group of individuals might reach draft age at the point of war. This could have a bearing on their decision to be for or against their country going to war.

Dependence

In time series analysis, dependence refers to relating observations at one point in time with observations of the same variable (what is being observed) at prior time points. For example, noting that retail spending increases at certain points each year, such as Christmas. The purpose of this would be to take this correlation (relationship), identify the type of dependency that exists, and then create mathematical formulae that emulate the dependence. This formula then helps with forecasting and further analysis.

Differencing

Differencing is an effective way of removing or controlling autocorrelation (automatic relationships) from a series. Autocorrelation might indicate there is a trend when there is, in fact, only a relationship. To this end, differencing the data helps provide a truer picture of trends. Using the previous example of the council’s transport study, you might discover that a certain proportion of your study group takes the bus more often than the train. However, further investigation into this might reveal that this is not a trend because there is, in fact, no train service in their area. Differencing could be used to remove or control the autocorrelation.

Smoothing

In some time series, seasonal variation is so strong that it obscures any trends or cycles that are very important to understanding the observed process. For example, the costs of certain fruits can be higher or lower depending on the time of year, which can affect the trend being examined. Smoothing removes seasonality and makes long-term fluctuations in the series stand out more clearly. The most common type of smoothing is ‘moving average smoothing’, where the average is amended to take into consideration seasonal or cyclical components of a time series.

Time Series Designs

There are various different time series design frameworks that statisticians can adopt to identify patterns or forecasts. Some of the more common ones are:

• Simple Time Series Design is the standard time series design. It is the collection of quantitative (numerical or statistical) observations taken at regular intervals through repeated analysis or surveys. But the various considerations, as outlined above, are applied. Our measuring of public transport conversions would be a simple time series design if we apply considerations to it. Another could be the index collected by the Retail Prices Index.
• Cohort Analysis Design involves the study of a group that has experienced an identical major event, such as the same birth date. Individuals or circumstances in a cohort are presumed to have similarities due to shared experiences that differentiate them from other cohorts. Cohort analysis seeks to explain an outcome through the exploitation of differences between cohorts. For example, why did one cohort vote for something and another vote against it?
• Panel Studies Design is similar to cohort analyses, except the same individuals are interviewed in each period, whereas in cohort studies, only a random sample of the same group is interviewed. The various data collection points are often called ‘waves’. Where cohort designs measure net change (at population level), panel designs can measure both net and gross change (at individual level). Unlike cohort studies, panel studies have the possible problem of subjects reacting differently on a second survey simply because they have had the experience of the first one, and this could prejudice their answers. It can also be difficult to get people to commit to answering the same questions several times.