Consider the following two price index series:
Year 1995 = 100
2002 80
2003 86
2004 90
2005 94
Year 2000 = 100
2005 115
2006 121
2007 130
2008 133
Splice the two index series to form one continuous series with 1995 as the base year. The index for 2007 is:
100.82
102.64
104.28
106.26
To splice the two index series together, we need to convert the second series to be based on 1995 = 100. We can do this by multiplying all the values in the second series by 100/115 (the base for 2005 in the second series).
Year 2005 in the second series: 115 * (100/115) = 100
Year 2006 in the second series: 121 * (100/115) ≈ 105.22
Year 2007 in the second series: 130 * (100/115) ≈ 113.04
Year 2008 in the second series: 133 * (100/115) ≈ 115.65
Now, we can calculate the index for 2007 by finding the geometric mean of the two index series for that year:
(86 * 105.22)^0.5 ≈ 100.82
Therefore, the index for 2007 is 100.82.