Time- Session 6

8/3/2019 Time- Session 6

1/20

Time Series Analysis

Prepared by:

Prof. Ekta Bajaj


2/20


3/20

Utility of time Series Analysis

It helps in the analysis of pastbehavior of a variable.

It helps in forecasting.

It helps in evaluation of currentachievement.

It helps in making comparativestudies.


4/20

Components of a Time Series

Secular Trend/ Long term movements(T)

Seasonal variations (S)

Cyclical variations (C)

Irregular variations (I)


5/20

Objectives of measuring trend

Knowledge of past behavior

Estimation

Comparison


6/20

Seasonal variation

Objectives of measuring SeasonalVariations:

To analyze the past seasonal

variations. To predict the value of seasonal

variation.

To eliminate the effect of seasonalvariations from the data.


7/20

Cyclical variation

Objectives of measuring CyclicalVariations:

To analyze the behavior of cyclicalvariation in the past.

To predict the effect of cyclicalvariations so as to provide guidelinesfor future business policies.


8/20

Irregular or Random Variations


9/20

Mathematical models for analyzingTime Series

Additive model

Y= T + S + C + I

Multiplicative model

Y= T * S * C * I


10/20

Measurement of Trend

Freehand or Graphic method

Method of Semi- averagesMethod of Moving Averages

Method of Least Squares


11/20

Method of Moving Average

Q1) Calculate 3 yearly & 5 yearly moving average of thedata given below to obtain trend values:

Year 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990Production

(000

tones)26 27 28 30 29 27 30 31 32 31

Year 1981 1982 1983 1984 1985 1986 1987 1988 1989 19903 year ---- 27 28.33 29 28.67 28.67 29.33 31 31.33 -----

Ans:


12/20

Q2) Assuming a 4-yearly cycle, find the trend values for thefollowing data

Year 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992Sales 74 100 97 87 90 115 126 108 100 125 118 113 122 126

Year 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 19924 ------- ---- 91.5 95.38 100.88 107.13 111 113.5 117.75 113.38 116.75 119.63 --- ---

Ans :


13/20

Method of Least Squares

Q3) The production (000 maunds) of a

sugar factory is given below:

Year 1971 1972 1973 1974 1975 1976 1977Production 40 45 46 42 47 50 46

Fit a straight line trend by the Least Squares Method & tabulate the trend.

Ans: Y= 1.036X + 45.143

Trend

values 42.035 43.071 44.107 45.143 46.179 47.215 48.210


14/20

Q4) The following are the annual profits(000) in a certain business.

Year 1971 1972 1973 1974 1975 1976 1977Profit (000) 60 72 75 65 80 85 95

By the method of least squares fit a straight line. Using that estimate profit for1981.

Ans: Y= 4.857X + 76, 109.99


15/20

Q5) Calculate the trend values by the method ofleast squares from the data given below:

Year 1980 1981 1982 1983Sales (000 Rs.) 10 13 15 20

Ans: Y=3.2X+ 14.5,

Trend values: 9.7, 12.9, 16.1, 19.3


16/20

Measurement of Seasonal Variations

Method of Simple averages

Ratio to Trend method

Ratio to Moving Average method

Link Relative method


17/20

Method of Simple Average

Q6) Calculate the seasonal index for thefollowing data by using average method:

Year 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter1974 72 68 80 701975 76 70 82 741976 74 66 84 801977 76 74 84 781978 78 74 86 82

Ans: Q1= 98.43, Q2=92.15,


18/20

Q7) Calculate the seasonal index for the following data byusing average method:

Year 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter1977 3.7 4.1 3.3 3.51978 3.7 3.9 3.6 3.61979 4.0 4.1 3.3 3.11980 3.3 4.4 4.0 4.0

Ans: Q1= 98.7, Q2= 110.8, Q3= 95.3, Q4= 95.3


19/20

Ratio to Moving Average Method

Q8) Calculate the seasonal indices by the ratio tothe moving average method from the followingdata:

Year 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter1 68 62 61 632 65 58 56 613 68 63 63 674 70 59 56 625 60 55 51 58

Ans: Q1= 107.02, Q2= 96.43, Q3= 94.43, Q4= 102.12


20/20

Q9) Given the following quarterly sale figures, (Rs.000)for the year1986- 1989, find the specific seasonal indices by the method of movingaverages.

Year 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter1986 34 33 34 371987 37 35 37 391988 39 37 38 401989 42 41 42 44

Time- Session 6

Documents