1. 1S. Sivananthan

2. What is time series analysis? A time series is when data is collected at REGULAR time intervals to analyse long term trends and patterns in the data. If there seems to be a TREND in the data, we can predict how the data will change if the current trend continues. Time series can be extremely useful in many areas and are used in many professions to make predictions about the future. 2S. Sivananthan

3. Some examples of uses Business- e.g. To predict future sales –a pub needs to know how many bottles of beer to order for example. Government –e.g. To predict future needs for government spending such as the number of school places required in future years. Economists –e.g. Econometrics involves tracking the performance of shares and projecting these trends into the future to predict how the shares will perform 3S. Sivananthan

4. E.g. Population Growth In 1798 Thomas Malthus predicted that the world’s population would outrun food supply by the mid 19 th century. In 1968 Paul Enrich predicted world famine in the 80s and 90s. So far both men seem to be wrong –improvements in agriculture have meant that food production has been sufficient but it is still a hotly debated topic. 4S. Sivananthan

5. It is clear that the world’s population cannot continue growing at this rate. The question is can human society bring about this change in a humane manner or will it be down to wars, famines and other horrific events? 5S. Sivananthan

6. FOUR COMPONENTS OF A TIME SERIES TREND SEASONAL VARIATION SHORT-TERM, NON-RANDOM VARIATION RANDOM VARIATION 6S. Sivananthan

7. TRENDS 7S. Sivananthan

8. Example 1: Marriages in the UK Clearly the greengrocer’s data is invented data. Real data would not show such a perfect pattern. a)Use the data on marriages in the UK to plot a graph of the annual number of marriages in the UK from 1987-1997. Describe the trend. b) Plot the number of marriages and describe the trend for: i. Males aged under 21, ii. Males aged 35-44. 8S. Sivananthan

9. a) Marriages in the UK 9S. Sivananthan

10. bi)Marriages in UK- males under 21 10S. Sivananthan

11. bii) Marriages UK-males age 35-44 11S. Sivananthan

12. Marriages in UK-males aged 35-44 12S. Sivananthan

13. Practice Questions Complete EX 1A on p5. 13S. Sivananthan

14. Answers Ex1A Q1 a)I General upward trend. Fairly linear. ii. General upward trend, fairly linear. b) Both trends are upwards and linear but admissions shows greater variability. 14S. Sivananthan

15. Answers Ex 1A Q2 a) Measles: downward, non-linear trend. Sharp fall in reported cases between 1988 and 1990. Plateau after 1990 but 1994 is exception, being far higher than expected. b) Quite a steady upward, approximately linear trend. 15S. Sivananthan

16. Downward but not linear trend from 1930. Seems to decrease from 1930 and seems to plateau after 1980. No clear trend overall. Population seems to decrease after 1930. Comparison: Trend in city much smoother. The population of Greater Manchester is variable but the city population shows a marked decrease from 1930. This suggests that people are moving out of the city and into the suburbs. 16S. Sivananthan

17. FOUR COMPONENTS OF A TIME SERIES TREND A trend is a long-term smooth movement –e.g. No. of marriages in UK SEASONAL VARIATION A seasonal effect is a regular predictable pattern –e.g. Market stall takings/ requests from government website. SHORT-TERM, NON-RANDOM VARIATION Variation about a long term trend which is NOT random. RANDOM VARIATION All time series will contain some variation which is random and impossible to forecast. 17S. Sivananthan