1. Lecture 7 Dr. Haider Shah

2.  Continue understanding the primary tools for forecasting  Understand time series analysis and when and how to apply it

3.  Complex and difficult  Need to consider various factors

4. Economic conditions anticipated Past sales patterns New product introductions Selling channels Results of market research Changes in product mix Competition Consumer tastes Legal environment

5.  Sales of product A over the past 7 years were as follows: Yr Sales (‘000 units) 1 22 2 25 3 24 4 26 5 29 6 28 7 30 Noting that X becomes the years, identify the sales in Year 8 using regression analysis

6. YrXYXYX sq 1122 1 2225504 3324729 442610416 552914525 662816836 773021049 sum28184771140

7. Y = a + bX b=((7 x 771) -(28 x 184)) ((7 x 140) - (28 x 28) b= 245 / 196= 1.25 a =(184 ) -(1.25 x 28) = 21.3 77 For Yr 8 Y = 21.3 + (1.25 x 8) = 31.3 Y=21.3 + 1.25X so Y = 31,300 units

8.  A time series is a collection of observations of well-defined data items obtained through repeated measurements over time.  e.g. retail sales each month of the year  Data collected irregularly or only once are not time series.

9.  Records a series of figures or values over time. Time Values e.g. sales (£)

10. A graph version is called a histogram

11. Mean Absolute Deviation (MAD) Mean Square Error (MSE) Mean Absolute Percentage Error (MAPE)

13. Data Type : Choice of method  If static data: Naive or Average method  If trended data – Holts’s method; Regression  If seasonal data – Decomposition You must PLOT your data and then decide….

14.  A time series can be decomposed into four components:  Trend (long term direction),  Seasonal variations (time related movements)  Cyclical variations  Random variations (unsystematic, short term fluctuations).

15.  The underlying long-term movement over time in values of data recorded  There are three types of trend: 1.Downward trend 2.Upward trend 3.Static trend

16.  Short-term fluctuations in recorded values, due to different circumstances which affect results at different times of a period.

17. 10 5 123412341234 Year 1 Year 2 Year 3 Customers (‘000s) TREND

18.  Cyclical – ◦ medium-term changes in results caused by circumstances which repeat in cycles  Random ◦ non-recurring caused by unforeseen circumstances e.g. a war, stock market crash

19.  Y = T + S + C + R Where Y = the actual time series T = the trend series S = the seasonal component C = the cyclical component R = the random component

20. Expresses a time series as Y = T + S + R Y = T x S x R

21. AugSepOctNovDec Sales (£000 0.020.04 3.2014.50 How is the trend? Promising? What if it’s a Christmas card company? Post December slump in sales?

22. 1. Use moving averages to eliminate the seasonal effect ◦ Odd numbered (mid point is easy) ◦ If it is even numbered (4, 12) we must use centred moving averages 2. Use this series to extrapolate the trend into the future 3. Difference between trend and actual data = seasonality 4. Average this for similar seasonal periods (like for like quarters) 5. Project these averages (seasonal factors) into the future 6. Add the projected trend and seasonal factors together Adequacy of forecasts can be measured with MSE etc

23.  Can be hard to distinguish between a trend and seasonal fluctuations.  One way of doing this is using ‘moving averages’ which attempts to remove seasonal and cyclical variations  The average of the results of a fixed number of periods

24. Year Sales units 1 390 2 380 3 460 4 450 5 470 6 440 7 500 Required: What is the moving average using a period of 3 years

25. yearSalesMoving total of 3 yr sales Moving average of 3 yr sales 1390 2380 3460 4450 5470 6440 7500 1230 1290 1380 1360 1410 410 430 460 453 470 Moving Averages (MA3): Solution

26. Find the moving average over a period of 4 qtrs Yr Qtr Actual sales (units) 2008 1 1,350 2 1,210 3 1,080 4 1,250 2009 1 1,400 2 1,260 3 1,110 4 1,320

27. STEP 1STEP 2TREND YearQTRSalesMoving TOTALAverage of(mid point) of 4yr sales4 year sales 31 1,350 2 1,210 4,8901222.50 3 1,0801228.75 4,9401235.00 4 1,2501241.25 4,9901247.50 41 1,4001251.25 5,0201255.00 2 1,2601263.75 5,0901272.50 3 1,110 4 1,320 The trend

28.  Additive model was Y = T + S + R  Can be Y – T = S + R  If we assume random variations as negligible:  S = Y –T  So if we deduct trend from actual data we get seasonal variations

29. Find the trend and seasonal variations of the following sales data: Year Quarter Actual(£k) 2008 1 600 2 840 3 420 4 720 2009 1 640 2 860 3 420 4 740 Moving average = 4 quarters

30. YearQuarActualMoving TrendSeasonal total ofAverageVariation 4 Qtrs 20081600 2840 2580645 3420650-230 2620655 472065863 2640660 20091640660-20 2640660 2860663198 2660665 3420 4740

31. How decomposition of Time Series can be used for forecasting future estimates