2. Moving average method A quantitative method of forecasting or smoothing a time series by averaging each successive group (no. of observations) of data values. term MOVING is used because it is obtained by summing and averaging the values from a given no of periods, each time deleting the oldest value and adding a new value.

3. For applying the method of moving averages the period of moving averages has to be selected This period can be 3- yearly moving averages 5yr moving averages 4yr moving averages etc. For ex:- 3-yearly moving averages can be calculated from the data : a, b, c, d, e, f can be computed as :

4. If the moving average is an odd no of values e.g., 3 years, there is no problem of centring it. Because the moving total for 3 years average will be centred besides the 2nd year and for 5 years average be centred besides 3rd year. But if the moving average is an even no, e.g., 4 years moving average, then the average of 1st 4 figures will be placed between 2nd and 3rd year. This process is called centering of the averages. In case of even period of moving averages, the trend values are obtained after centering the averages a second time.

5. Goals : – Smooth out the short-term fluctuations. Identify the long-term trend.

6. MERITS Of Moving average method simple method. flexible method. OBJECTIVE :- If the period of moving averages coincides with the period of cyclic fluctuations in the data, such fluctuations are automatically eliminated This method is used for determining seasonal, cyclic and irregular variations beside the trend values.

7. LIMITATIONS Of Moving average method No trend values for some year. M.A is not represented by mathematical function - not helpful in forecasting and predicting. The selection of the period of moving average is a difficult task. In case of non-linear trend the values obtained by this method are biased in one or the other direction.

8. Moving Average Example Year Units Moving 1994 2 1995 5 3 1996 2 3 1997 2 3.67 1998 7 5 1999 6 John is a building contractor with a record of a total of 24 single family homes constructed over a 6-year period. Provide John with a 3-year moving average graph. Avg.

9. Moving Average Example Solution Year Response Moving Avg. 1994 2 1995 5 3 1996 2 3 1997 2 3.67 1998 7 5 1999 6 94 95 96 97 98 99 8 6 4 2 0 Sales L = 3 No MA for 2 years

10. Calculation of moving average based on period When period is odd- example:- Calculate the 3-yearly moving averages of the data given below: yrs1980198119821983198419851986198719881989 Sales (million of rupees) 3 4 8 6 7 11 9 10 14 12

11. yearSales,(millions of rupees) 3-yearly totals3-yearly moving averages(trends) 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 3 4 8 6 7 1 1 9 1 0 1 4 1 2 1 5 1 8 2 1 2 4 2 7 3 0 3 3 3 6 5=(1 5/3) 6=(1 8/3) 7=(2 1/3) 8=(2 4/3) 9=(2 7/3) 1 0=(3 0/3) 1 1=(3 3/3) 1 2=(3 6/3)

12. In Figure, 3-yrs MA plotted on graph fall on a straight line, and the cyclic f luctuation have been smoothed out. The straight Line is the required trend line. 1980198119821983198419851986198719881989 1 2 3 years sales 4 6 8 10 12 Actual line Trend line (1981,5) (1983,7) (1984,8) (1988,12) (1988,14) (1985,11)

13. Calculation of moving average based on period When period is even:- Example :- Compute 4-yearly moving averages from the following data: year 19911992199319941995199619971998 Annual sale(Rs in crores ) 3643 3444543424

14. Year (1) Annual sales (Rs in crores) (2) 4-yearly moving total (T) (3) 4-yearly moving averages (A) (3)/4 {4} 4-yearly centred moving averages OR (trend values) (5) 1991 36 1992 43 156 39 1993 43 ( 39+41)/2=80/2=40 164 41 1994 34(41+43.75)/2=84.75/2= 42.375 175 43.75 1995 44(43.75+41.50)/2=42.625 166 41.50 1996 54(41.50+39)/2=40.25 156 39 1997 34 1998 24

15. sales year Actual line Trend line