CORRELATION

1

• Session 5
• Topic Time Series Analysis
• Faculty Ms Prathima Bhat K
• Department of Management Studies
• Acharya Institute of Technology
• Bangalore 90
• Contact prathimabhatk_at_gmail.com
• 9242187131

2
TIME SERIES

• A time series may be defined as a collection of
  readings belonging to different time periods, of
  some economic variable or composite of variables.

3
COMPONENTS OF TIME SERIES

• Secular Trend or Long term Movement. (T)
• Periodic Movement or Short term Fluctuations
• Seasonal Variations (S)
• Cyclical Variations (C)
• Random or Irregular Variations (R or I)

4
MEASUREMENT OF TREND

• Graphic (or Free-hand Curve fitting) Method
• Method of Semi-Averages
• Method of Curve Fitting by the Principle of Least
  Squares
• Method of Moving Averages

5
METHOD OF SEMI-AVERAGES

• Estimate value for 2000. If the actual
  sales figures is 35000 units, how do you account
  for the difference between the figures obtained?

• From the following series find the Trend by
  Semi Average method.
• Estimate the value for the year 1999.

6
(30-22) 8 8/3 2.667
7
The difference is because of the assumption that
there is a linear relationship between the given
time series values. Moreover, the effects of
seasonal, cyclical and irregular variations have
been completely neglected.
8
(310 232) 78 78 / 5. Estimate of the year
1999 310(5/2)(78/5) 349
9
METHOD OF CURVE FITTINGPRINCIPLE OF LEAST SQUARES
Fitting of Linear Trend y a bx To find a
b ?y na b?x ?xy a ?x b ?x2
Fitting of a Second Degree (Parabolic) Trend y
a bx cx2 To find a, b c ?y na b?x
c?x2 ?xy a?x b?x2 c?x3 ?x2y a
?x2 b?x3 c?x4
10

• Fit a linear trend from the following data.
  Estimate the production for the year 1999. Verify
  ?(y-ye)0 where ye is the corresponding trend
  value of y.

ANSWER Let us consider the year 1994 to be the
mid point (It would be nice to take this as the
mid point as there are odd number of years).
11
(No Transcript)
12
Fitting of Linear Trend y a b x To find a
b ?y n a b? x 105 a5 b0 a
21 ?xy a ?x b ?x2 4 a0
b40 b 0.1 Therefore the equation will be
given by y 21 0.1x Estimated production of
1999 y 21 0.15 y21.5 thousands of
units.
13

• Calculate the quarterly trend values by the
  method of least squares for the following
  quarterly data for the last 5 years given below

14
(No Transcript)
15
Fitting of Linear Trend y a b U To find a
b ?y n a b? U 560 a5 b0 a
112 ?Uy a ?U b ?U2 240 a0
b10 b 24 Therefore the equation will be
given by y 112 24x Therefore the quarterly
increment is (24/4)6
16
By the calculations we come to know that the
quarterly increment is 6. Therefore the values
for second third Quarters of 1994 are 64 -
(6/2) 64 (6/2) respectively.