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

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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