Time series analysis 12 S

To compare the variation in average lengths of closed intervals over time, a time series

analysis is carried out. All birth intervals from the second to the fourteenth are strung

together individually for the two data sets together with the year in which the

individual interval was closed. Analysis of variance techniques was used to determine

if there were significant variations in average interval length by the year of closure by

survey and by selected time periods.

Figure 6.2.1 shows the graphs of average interval lengths by year of closing the interval

for the GFS and the GDHS. The diagrams show evidence of an underlying linear

trend. As expected, the earlier years show evidence of greater levels of fluctuation than

the later years probably because events in the later years are likely to be recalled more

correctly. It can also be seen that the graphs fluctuate most between 1957 and 1961

probably because the GDHS respondents were recalling events from a more distant past

and also probably because of the relatively smaller sample sizes for these earlier years.

In the GFS, the average interval length appears to be fairly steady in the period

between 1964 and 1977 when it began to increase. The GDHS data also show a small

but fairly steady rise from about 1960. Also, intervals occurring near the survey date

appear to be lengthening. The graphs suggest some underlying trend towards longer

average intervals in both samples. The average birth-interval length appears to vary

between 17 months and 37 months for the GFS and 25 and 42 months for the GDHS.

The next question of interest is whether this trend is statistically significant.

Table 6.2.1 shows F statistics for the analysis of variance of interval length by period

of closing the interval for various segments of the data sets available. The only period

for which yearly averages do not appear to be significantly different is between 1946

and 1953; data for this period are available only in the GFS. From Table 6.2.2 the F-

statistics for linearity tests for all the periods examined are significant. Next to be

examined are intervals that were closed 5, 10 and 20 years before each survey. It is

important to compare data for various periods because it has been seen in Chapter 4

that the length of the period over which events are recalled influences the accuracy of

the data. The somewhat more pronounced fluctuations observed in the earlier periods

of the graphs in Figure 6.2.1 probably show evidence for this.

il v e il I c M U jl h

Fig 6.2.1 Tim e series g ra p h of m e a n birth in te rva ls fo r th e GF3 a n d GDHS

Table 6.2.1 F-statistics for differences for yearly change in average interval length

for all intervals by survey.

survey

F-statistics

p-val

GFS

7.97

0.00

GDHS

8.83

0.00

Table 6.2.2 F- statistics for the significance of linearity for data in Table 6.2.1

survey

F-statistics

p-val

GFS

227.7

0.00

GDHS

257.4

0.00

6.9.1 Five years before either survey

The average interval for all birth orders for successive five-year periods before the GFS

appears to have have declined slightly from 36.3 in 1974 to about 35.9 in 1977 after

which it appears to have increased. The average intervals five years before the GDHS

rise gradually from a little above 35 months in 1983 to just above 39 months in 1987, a

change of about four months; the change for this period in the GFS was about two

months, which unlike that in the GDHS is not statistically significant.

6.9.2 Ten years preceding survey

For the period of ten years preceding the GFS survey the average interval length

increased from about 34.5 months to a little above 36 months between 1969 and 1971.

It appears to have been generally steady between 1971 and 1977, when it increased as

noted above. Again the apparent linear increase for the GFS is not statistically

significant. For the GDHS, average yearly interval length ten years before the survey

increased slightly from just under 36 months in 1978 to just above 37 months in 1979,

whence it declined to just above 34 months in 1983; it rose steadily thereafter to above

39 months in 1987. Unlike the increasing trend in the GFS, the increases in the latter

survey are statistically significant.

6.9.3 Twenty years before survey

Average intervals for the period 20 years before the GFS survey fluctuates between 31

to 34 months between 1959 and 1963, and is fairly constant till 1977, after which it

appears to be rising. The yearly changes in average birth interval length for the 20

years preceding the survey appear to be significant. The mean interval length for the

successive 20 years before the GDHS rose steadily from just above 30 months in 1968

to under 39 months in 1987, a difference of about nine months. If birth intervals

increased significantly as observed, it is expected that the increase be reflected in

fertility decline but this does not appear to be the case. This situation may arise if, for

example, age at starting childbearing decreased and childbearing continues throughout

the reproductive period. In this case, it is possible for women to have longer birth

intervals but maintain the same level of fertility. However, for Ghana, the start of

family formation has been observed to be fairly constant over time. The observed trend

may also result if the intervals that are closed in the earlier years occurred to the

women when they were generally younger since they would be relatively more fecund

and thus have shorter birth intervals. It is also possible that much of the observed trend

is just a reflection of errors in the birth interval data.