A statistical measure known as an index number estimates the relative changes in a set of connected variables across time. It offers a means of monitoring and contrasting changes in numerous social, economic, or other quantitative parameters. In order to assess trends, track economic indicators, and make educated decisions, index numbers are frequently employed in economics, finance, and other disciplines.

The choice of variables, the determination of weights, and the index computation are three crucial steps in the generation of index numbers. Various models or techniques are used to create index numbers, depending on the particular specifications and properties of the data. Here are some popular models for creating indexes:

The Laspeyres index is a fixed-base index that employs a set of weights that are predetermined depending on the base period. It gauges the variation in a basket's quantity in comparison to a predetermined base period. The Laspeyres index is calculated using the following formula:

((Pt * Q0)) / ((P0 * Q0)) is the Laspeyres Index.

where P0 is the item's base period price, Q0 is the item's quantity in the base period, and Pt is the item's price in the current period.

Paasche Index: The Paasche index employs weights based on the current period and has a fixed base index as well. It gauges how much a basket of products and services has changed in size since the present time frame. The Paasche index is calculated using the following formula:

The Paasche Index is equal to (Pt * Qt) / (P0 * Qt).

where P0 is the item's base period price, Qt is the item's current period quantity, and Pt is the item's current period price.

The Laspeyres and Paasche indices are geometrically averaged to get the Fisher index. It is a superlative index that seeks to eliminate some biases that are present in the Paasche and Laspeyres indices. The Fisher index is calculated using the following formula:

(Laspeyres Index + Paasche Index) = Fisher Index

When both the base period and current period data are available, the Fisher index is frequently employed because it offers a compromise between the Laspeyres and Paasche indices.

These are but a handful of illustrations of index construction models. Other models exist as well, including the Törnqvist, Marshall-Edgeworth, and Carli indices, each with unique properties and application based on the particular situation and data at hand.