How do you interpret the variance of time series data using the average growth rates? I have been recently given a piece of time series data for analysis. I have calculated the average growth rate for infant mortality per 1000 births and have achieved a variance of 60449.1376 and thus a standard deviation of 245.864, how would I interpret this?
The data are annual infant mortality rates per thousand from 1951 through 1981 inclusive:
82  78  71  72  71  67  68  64  58  57  52
53  56  55  53  54  48  50  53  47  45  
46  46  51  45  44  42  37  38  34  29.5

 A: It is not clear what you exactly calculated.  The time series is clearly trending down.  Logging the data and then taking the differences gives a good approximation to the percentage changes.  We would find from your numbers that the average rate of change in infant mortality is -3.41%.  Variance of these rate numbers is not close to what you report.  It doesn't seem that the 60449.1376 number is the variance of the original series.  If it was, then it would be a meaningless number.  Any descriptive statistic (mean or variance) is fairly meaningless in the presence of a nonstationary process in the sense the statistics have no predictive value.
A: The statistics you quoted are meaningless since the series has autoprojective structure. The series  can be characterized as having a few local trends and some unusual values. The unusual values only become clear have the series has been detrended.  The trend variables are 0 prior to the point the trend begins and the counting numbers thereafter. For example x3 would have 16 0's and then the numbers 1,2,3,....15.  There were 5 unusual values at 11,24,19,7 and 3.     . Tests of significance are shown in                       . A plot of the ACTUAL FIT AND FORECAST is  with residuals suggesting independence  . In summary your series is relatively highly predictable with 4 local trends ... all down. 
A: It appears that you are computing descriptive statistics on the observed data which is probably ( nearly definitely ! ) non-stationary. The overall mean of a time series is not descriptive in the classical sense as being the expected value. What comes to mind is the Phd orals question that goes like this .... "When is the mean of a series equal to it's expected value ?" . Please post your data and perhaps we can provide some inferential statistics.
