Year over Year Monthly Indices

For each month m=1,2,…,12, let S(m) denote the set of products that are available for purchase in each year t=0,1,…,T. For t = 0,1,…,T and m = 1,2,…,12, let p_n^t,m and q_n^t,m denote the price and quantity of product n that is available in month m of year t for n belongs to S(m). Then the year over year monthly Laspeyres, Paasche and Fisher indices going from month m of year t to month m of year t+1, in price relative and monthly revenue share form, can be defined as follows:

; m=1,2,…,12;

; m=1,2,…,12;

.
where the monthly revenue share for product nÎS(m) for month m in year t is defined as:

; m=1,2,…,12; nÎS(m); t = 0,1,…,T

Approximate year over year monthly Laspeyres and Paasche indices are defined as follows:

; m=1,2,…,12;

; m=1,2,…,12;

Where s_n^0,m is the base period monthly revenue share.