# Time Series Analysis II

#### FORECASTING

##### Assumptions

The reason for isolating the trend within a time series is to be able to make a prediction of its future values and thus estimate the movement of the time series. Before looking at the various methods available to carry out this process, we must state two assumptions that must be made when forecasting:

That Conditions Remain Stable

Those conditions and factors which were apparent during the period over which the trend was calculated must be assumed to be unchanged over the period for which the forecast is made. If they do change, then the trend is likely to change with them, thus making any predictions inaccurate, e.g. forecasts of savings trends based on given interest rates will not be correct if there is a sudden change either up or down in these rates.

That Extra Factors Will Not Arise

It is sometimes the case that, when trends are predicted beyond the limits of the data from which they are calculated, extra factors will arise which influence the trend. For example, there is a limit to the number of washing machines that can be sold within a country. This capacity is a factor that must be considered when making projections of the future sales of washing machines. Therefore, in forecasting from a time series it must be assumed that such extra factors will not arise.

These assumptions are similar to those mentioned when we looked at the extrapolation of a regression line.

##### Methods of Forecasting

There are two main methods of forecasting, although both are primarily concerned with short-term forecasts because the assumptions mentioned previously will break down gradually for periods of longer than about a year.

Moving Averages Method

This method involves extending the moving average trend line drawn on the historigram of the time series. The trend line is extended by assuming that the gradient remains the same as that calculated from the data. The further forward you extend it, the more unreliable becomes the forecast.

#### THE Z-CHART

We will conclude this study unit with a short description of a particular type of chart which plots a time series, called a Z-Chart. It is basically a means of showing three sets of data relating to the performance of an organisation over time. The three sets of data are plotted on the same chart and should be kept up-to-date. The graphs are:

• The plot of the current data, be it monthly, quarterly or daily.
• The cumulative plot of the current data.
• The moving total plot of the data.

It is often used to keep senior management informed of business developments. As an example we will plot a Z-Chart for the sales of premium bonds in 19.5 using the data of the table below with the sales broken down into months. the table also shows the cumulative monthly sales and the moving annual totals. Note that the scale used for (a) is shown on the right of the chart and is twice that used for (b) and (c) so that the fluctuations in monthly sales show up more clearly. This is a device often used so that the chart is not too large.

##### SUMMARY

In this study unit and the previous one we discussed the main models used to analyse time series. We began by identifying the various factors into which a time series may be divided in order to use these models, and went on to show how to separate a time series into these constituent factors. This is an important subject and you should particularly note the following points:

− Set out all calculations systematically in tables.

− The layout of the table used for calculation of centred moving averages is very important for all models.

You must learn thoroughly the method of calculating and adjusting seasonal variations for all models.

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