1. SADC Course in Statistics Forecasting and Review (Sessions 04&05)

2. To put your footer here go to View > Header and Footer 2 Learning Objectives By the end of this session, you will be able to explain how a time series may be decomposed to extract its trend and seasonal effects, adjusted for the other explain how the decomposition assists in forecasting future observations carry out forecasts depending on the type of model assumed.

3. To put your footer here go to View > Header and Footer 3 Possible uses & further treatment Knowing the structure of the series allows us to use the information for forecasting Such applications are useful in many fields such as business, industry, economics, etc We now discuss how a series may be examined generally for purposes of forecasting But we keep in mind that forecasting too far ahead may lead to poor predictions

4. To put your footer here go to View > Header and Footer 4 Forecasting Where a time series shows both trend and seasonal effects, the first step is to estimate the seasonal effects Next, deseasonalise the series and use this to estimate the trend, e.g. fit a line Use the trend line to predict the value for a future observation Note the season corresponding to that future observation, and add the seasonal effect to that value (see example, slide 5)

5. To put your footer here go to View > Header and Footer 5 Forecasting – using additive model QuarterLeavers Fitted Line (trend) Deseasonal ised series Prediction (no seasonal effects) Prediction (with seasonal effects) 12226.4745.7335.5611.83 21233.5449.1340.973.84 311040.6143.5346.38112.85 43147.6836.6051.7946.19 52154.7544.7357.2033.47 62661.8263.1362.6125.48 715068.8983.5368.02134.49 87075.9675.6073.4367.83 95083.0373.7378.8455.11 103690.1073.1384.2547.12 1114697.1779.5389.66156.13 12110104.24115.6095.0789.47

6. To put your footer here go to View > Header and Footer 6 Demonstration of computations Steps needed to determine predictions as above will be done interactively in class using Excel tools. Course participants will be expected to contribute to how the calculations should be done.

7. To put your footer here go to View > Header and Footer 7 Some general points Any time series plot should be carefully compared with the relevant “history” This is needed because sudden and sharp changes can occur due to external effects For example, health indicators may change because of a change in definition, economic trends may change because of a change in government policy, rainfall records may change because of a change in units of measurement (inches to mm)

8. To put your footer here go to View > Header and Footer 8 Some general points (continued) It is important to keep in mind that successive observations are not independent Hence standard methods of analysis (e.g. regression modelling in Module H8) may not be appropriate More advanced modelling procedures exist for taking account of correlations between successive observations, e.g. ARIMA modelling - beyond the scope of this course

9. To put your footer here go to View > Header and Footer 9 You will spend the remainder of this session working on a given time series so as to consolidate ideas of these four sessions. You will be required to write a short report of your findings and conclusions, and/or report this in plenary to the rest of the class. Further practical work