Page 288 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 22: Time Series Analysis—Introduction and Components of Time Series

of the pattern. To identify the seasonal component, the data could be in quarters or months or any Notes
other time period less than a year.
Example 2 : Consider the data given in Table 3. Compute the seasonal index of quarterly sales of
the departmental store by the method of ratio-to-moving average.
The first step in computing the seasonal index is to calculate the four-quarter moving
totals for the series. This total is written in between quarters II and III in column 4 of
Table 3. However, it could be “dropped down” one line to avoid the problem of having
data between the lines.
Secondly, we compute the four-quarter moving average by dividing each of the four-
quarter totals by four. We then find the centred four-quarter moving average so as to
centre the moving averages against the periods. The seasonal and irregular components
have thus been smoothened out. Figure 8 demonstrates how the moving average has
smoothened the peaks and troughs of the original time series. The dotted line
represents the cyclical and trend components.
Table 3: Computation of Ratios to Moving Averages to Quarterly Sales of a
Departmental Store
(Rs. in lakhs)
Year Quarter Sales 4-quarter 4-quarter Centred Ratio-to-
moving moving 4-quarter moving
total average moving average
average in percentage
1974 I 6.83
II 6.26 25.53 6.38 6.35 96.2
III 6.11 25.24 6.31 6.25 101.3
IV 6.33 24.77 6.19 6.13 106.7
1975 I 6.54 24.30 6.08 6.05 95.7
II 5.79 24.12 6.08 6.06 93.1
III 5.64 24.39 6.10 6.16 99.8
IV 6.15 24.87 6.22 6.30 108.1
1976 I 6.81 25.51 6.38 6.45 97.2
II 6.27 26.06 6.52 6.54 96.0
III 6.28 26.26 6.57 6.52 102.8
IV 6.70 25.90 6.48 6.39 109.7
1977 I 7.01 25.25 6.31 6.25 94.6
II 5.91 24.71 6.18 6.04 93.2
III 5.63 23.65 5.91 5.86 105.1
IV 6.16 23.22 5.81 5.74 103.7
1978 I 5.95 23.70 5.74 6.00 91.3
II 5.48 24.34 6.08
III 6.11
IV 6.80

The next step is to calculate the percentage of the actual value to the moving average
value for each quarter in the time series having a four-quarter moving average entry.

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