1. Introduction to Time Series Prepared by: Bhakti Joshi February 13, 2012

2. Data Company Name Sales for FY11 (In crore rupees) Company A 1000 Company B 1763 Company C 1623 Company D 9876 Company E 172 Company F 1273 Company G 338 Company A Sales (In crore rupees) FY05 200 FY06 123 FY07 127 FY08 210 FY09 100 FY10 150 FY11 90 CROSS-SECTION DATA TIME SERIES

3. Data (Contd) Year Company Name Sales (In crore rupees) FY09Company B 200 FY10Company B 2110 FY11Company B 1987 FY09Company C 288 FY10Company C 1177 FY11Company C 1179 PANEL DATA : CROSS- SECTION + TIME SERIES

4. Time Series: Definition A sequence of numerical data points in successive order, usually occurring in uniform intervals.(daily, monthly, quarterly, semi- annually or annually). Time series analysis is a forecasting or predicting too for any decision making process Read more: http://www.investopedia.com/terms/t/ti meseries.asp#ixzz1mCNG2jEZhttp://www.investopedia.com/terms/t/ti meseries.asp#ixzz1mCNG2jEZ

5. Time Series: Identifying Variations Secular trend – the value of a variable tends to increase or decrease over a long period of time Cyclical fluctuation – business cycles that reach its peak above the trend line followed by a slump below the trend and so on Seasonal variation – involves pattern of change within a year that tend to be repeated from year to year Irregular variation – completely unpredictable and random movement

6. Secular Trend or Trend Population between FY05 and FY11 (In million) Source: Reserve Bank of India (RBI)

7. Cyclical Fluctuation FY05FY06FY07 FY08 FY09FY10FY11 GDP at Factor Cost FY05 and FY11 (Rupees crore)

8. Seasonal Variation FY05FY06FY07 FY08 FY09FY10FY11 Agriculture Income FY05 and FY11 (Rupees crore)

9. Forecasting with Linear trend Y i = a + bt a = Σ Yi n b = Σ XiYi Σ Xi 2 where Xi equals a particular time period ‘t’ minus mid-level time period Y i = a + bXi, Yi equals estimated values of Yi used for forecasting future Yi ^ ^

10. Forecasting with Linear trend Year (t) Profit: Y (in Rs. Million) X = t - 2008 200560-3 200672-2 200775 2008650 2009801 2010852 2011953 Y i = a + bt Calculate trend values? Can you calculate trend values for 2012?

11. Forecasting with Linear trend – Problem 2 Year (t) Sales - Y (in Rs. crore) d = t – 2008.5 X = 2d 200615-2.5 200717-1.5 200820-0.5 2009210.5 2010231.5 2011242.5 Calculate trend values? Can you calculate trend values for 2012?

12. Moving Averages (MA) Y/QSales4-Qtr Moving Total4-Qtr MA4-Qtr Centered MA %age of actual to MA values 2009-Q134 2009-Q233 2009-Q334 13834.5034.8897.49 2009-Q437 14135.2535.50104.23 2010-Q137 14335.7536.13102.42 2010-Q235 14636.5036.7595.24 2010-Q337 14837.0037.2599.33 2010-Q439 15037.5037.75103.31 2011-Q139 15238.0038.13102.30 2011-Q237 15338.2538.3896.42 2011-Q338 15438.5038.8897.75 2011-Q440 15739.2539.75100.63 2012-Q142 16140.2540.75103.07 2012-Q241 16541.2541.7598.20 2012-Q342 16942.25 2012-Q444

13. Moving Averages (MA) YearQ1Q2Q3Q4 200997.49104.23 2010102.4295.4299.33103.31 2011102.396.4297.75100.63 2012103.0798.20 Total 307.79290.04294.57308.17 Averages 102.6096.6898.19102.72 Sum of the average quarters should be equal to or close to 400 Grand average across 4 quarters must be close to or equal to 100 The above mentioned implies that there are no seasonal fluctuations

14. Calculate Deseasonalised Data Y/QSalesSeasonal Index/100Deseasonalised Sales = Sales/(Seasonal Index/100) 2009-Q134102.6/100 33.14 2009-Q23396.68/100 34.13 2009-Q334 98.19/10034.63 2009-Q437 102.72/10036.02 2010-Q137102.6/100 36.06 2010-Q23596.68/100 36.20 2010-Q337 98.19/10037.68 2010-Q439 102.72/10037.97 2011-Q139102.6/100 38.01 2011-Q23796.68/100 38.27 2011-Q338 98.19/10038.70 2011-Q440 102.72/10038.94 2012-Q142102.6/100 40.94 2012-Q24196.68/100 42.41 2012-Q342 98.19/10042.77 2012-Q444 102.72/10042.83

15. Email: bhaktij@gmail.com Website: www.headscratchingnotes.netbhaktij@gmail.comwww.headscratchingnotes.net