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Introduction to Time Series
Prepared by: Bhakti JoshiFebruary 13, 2012
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
Data (Contd)
Year Company Name Sales (In crore rupees)
FY09 Company B 200
FY10 Company B 2110
FY11 Company B 1987
FY09 Company C 288
FY10 Company C 1177
FY11 Company C 1179
PANEL DATA : CROSS- SECTION + TIME SERIES
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/timeseries.asp#ixzz1mCNG2jEZ
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
Secular Trend or Trend
1089
1106
1122
1138
1154
1170
1186
FY05 FY06 FY07 FY08 FY09 FY10 FY11
Population between FY05 and FY11 (In million)
Source: Reserve Bank of India (RBI)
Cyclical Fluctuation
FY05 FY06 FY07 FY08 FY09 FY10 FY11
GDP at Factor Cost FY05 and FY11 (Rupees crore)
0
200000
400000
600000
800000
1000000
1200000
1400000
Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4
Seasonal Variation
0
50000
100000
150000
200000
250000
Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1
FY05 FY06 FY07 FY08 FY09 FY10 FY11
Agriculture Income FY05 and FY11 (Rupees crore)
Forecasting with Linear trend
Yi = a + bt
a = Σ Yi n
b = Σ XiYi
Σ Xi2 where Xi equals a particular time period ‘t’ minus mid-level time period
Yi = a + bXi, Yi equals estimated values of Yi used for forecasting future Yi
^ ^
Forecasting with Linear trend
Year (t)Profit: Y(in Rs.
Million)X = t - 2008
2005 60 -32006 72 -22007 75 -12008 65 02009 80 12010 85 22011 95 3
Yi = a + bt
Calculate trend values? Can you calculate trend values for 2012?
Forecasting with Linear trend – Problem 2
Year (t)
Sales - Y(in Rs. crore)
d = t – 2008.5 X = 2d
2006 15 -2.52007 17 -1.52008 20 -0.52009 21 0.52010 23 1.52011 24 2.5
Calculate trend values? Can you calculate trend values for 2012?
Moving Averages (MA)Y/Q Sales 4-Qtr Moving Total 4-Qtr MA 4-Qtr Centered
MA%age of actual to
MA values
2009-Q1 34
2009-Q2 33
2009-Q3 34 138 34.50 34.88 97.492009-Q4 37 141 35.25 35.50 104.232010-Q1 37 143 35.75 36.13 102.422010-Q2 35 146 36.50 36.75 95.242010-Q3 37 148 37.00 37.25 99.332010-Q4 39 150 37.50 37.75 103.312011-Q1 39 152 38.00 38.13 102.302011-Q2 37 153 38.25 38.38 96.422011-Q3 38 154 38.50 38.88 97.752011-Q4 40 157 39.25 39.75 100.632012-Q1 42 161 40.25 40.75 103.072012-Q2 41 165 41.25 41.75 98.202012-Q3 42 169 42.252012-Q4 44
Moving Averages (MA)Year Q1 Q2 Q3 Q4
2009 97.49 104.23
2010 102.42 95.42 99.33 103.31
2011 102.3 96.42 97.75 100.63
2012 103.07 98.20
Total 307.79 290.04 294.57 308.17Averages 102.60 96.68 98.19 102.72
• 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
Calculate Deseasonalised DataY/Q Sales Seasonal Index/100 Deseasonalised Sales =
Sales/(Seasonal Index/100)
2009-Q1 34 102.6/100 33.142009-Q2 33 96.68/100 34.132009-Q3 34 98.19/100 34.632009-Q4 37 102.72/100 36.022010-Q1 37 102.6/100 36.062010-Q2 35 96.68/100 36.202010-Q3 37 98.19/100 37.682010-Q4 39 102.72/100 37.972011-Q1 39 102.6/100 38.012011-Q2 37 96.68/100 38.272011-Q3 38 98.19/100 38.702011-Q4 40 102.72/100 38.942012-Q1 42 102.6/100 40.942012-Q2 41 96.68/100 42.412012-Q3 42 98.19/100 42.772012-Q4 44 102.72/100 42.83
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