1. INTERNAL ACHIEVEMENT STANDARD 3 CREDITS Time Series 1

2. I Can Do… 2

3. Unit Overview Introduction Plotting Time Series Analysing Time Series  Cycles and Trends  Forecasting  Smoothing  Adjusting for Seasonal Effects  Index Numbers  Linear and Non-linear Trends 3

4. Week One: Just in Time By the end of this week you should be able to: Explain what a time series is, what the main features are and why time series are used. Plot on the same axes raw time series data and the calculated smoothed mean. Explain what an Individual seasonal effect is and calculate it from the raw and smoothed data. Make key observations from a set of plotted data. Use a spreadsheet to calculate smoothed means and seasonal effects. 4

5. Time Series Data that is collected over time and at regular intervals is often referred to as time series data. This data is usually presented on a line graph with time intervals on the horizontal axis and the data being measured on the vertical axis. A time series is used to identify trends and patterns. 5

6. Time Series The following graph shows the number of tourists at a Farmstay over a five year period from 1996 to 2000 recorded at 3 month intervals. 6

7. Time Series Trends Trends fall into three main types:  short term variations where the graph changes over a short time span  long term variations such as seasonal fluctuations  overall trends where the general shape of the graph may be increasing, decreasing or staying approximately the same over the whole time span. 7

8. Your Turn Heta’s school bus was supposed to arrive at 7:30 am each day to take him to school. It was always late so Heta decided to record the minutes it was late over a month to see if he could spot any patterns and predict if he could sleep in on some days and get away with it! 8

9. Your Turn Here are his results: Draw a line graph of this data. Identify any patterns that you see. On which days do you think Heta could sleep in and for how long? Conduct Seasonal Analysis/Adjustments and predict the times for the next 5 days. 9

10. Group Task Over the next few periods, you are going to use the resources provided to complete a group assignment on Time Series. 10

11. Smoothing Techniques Moving Means/Medians Seasonally Adjusted Data Predicted Value 11

12. Moving Means/Medians We know how to calculate a moving mean/median from an odd number of data values. (3pt, 5pt moving mean…) However, when we have data involving the seasons of the year (Summer, Autumn, Winter, Spring) or Quarterly Sales (1 st, 2 nd, 3 rd, 4 th ) it would be more logical to use an even numbered moving average. (In this case a 4pt moving mean.) But how… 12

13. Even Numbered Moving Average YearQuarterSales ($Mill.) Moving Mean Centered Mean 1999127 245 334 421 128 247 332 424 13

14. Even Numbered Moving Average YearQuarterSales ($Mill.) Moving Mean Centered Mean 1999127 245 31.75 33431.875 32 42132.25 32.5 200012832.25 32 24732.375 32.75 332 424 14

15. Seasonally Adjusted Data When the data has been smoothed and trends analysed, each value can be looked at for seasonal effects. This is to see if the values are significantly different from what might be expected and to help make predictions. Individual Seasonal Effect = Value – Moving Average 15

16. Seasonally Adjusted Data The seasonal effect is the average of the individual seasonal effects for a particular day. Seasonally Adjusted Value = Value – Seasonal Effect 16

17. Predicting and Forecasting Future Years To predict values in the future from existing time series data requires the calculation: Predicted Value = Estimated Moving Mean + Seasonal Effect 17