Interpolation

DEFINITION of 'Interpolation'

Interpolation is a statistical method by which related known values are used to estimate an unknown price or potential yield of a security.  

BREAKING DOWN 'Interpolation'

Interpolation is a method of estimating an unknown price or yield of a security. This is achieved by using other related known values that are located in sequence with the unknown value.

Interpolation is at root a simple mathematical concept. If there is a generally consistent trend across a set of data points, one can reasonably estimate the value of the set at points that hasn't been calculated. However, this is at best an estimate; interpolators can never offer complete confidence in their predictions.

Different Kinds of Interpolation

There are several formal kinds of interpolation, including linear interpolation, polynomial interpolation and piecewise constant interpolation.

The easiest and most prevalent kind is linear interpolation, which is useful if one is trying to estimate the value of a security or interest rate for a point at which there is no data. Let's assume that, for a security price being tracked over a period of time, we call the line on which the value of the security is tracked the function f(x). The current price of a stock is plotted over a series of points representing moments in time. So if f(x) is recorded for the months of August, October and December, those points would be mathematically represented as xAug, xOct, and xDec, or x1, x3 and x5.  

For a number of reasons, one might want to know the value of the security during the month of September. You can use a linear interpolation algorithms to determine the value of f(x) at plot point xSep, or x2 that appears within the existing data range.

Interpolation should not be confused with extrapolation, by which one could estimate a data point outside of the known range of data. Most charts representing a stock's history are in fact widely interpolated. Linear regression is used to make the curves which approximately represent the price variations of a security. Even if a chart measuring a stock over a year included data points for every day of the year, one could never say with complete confidence where a stock will have been valued at a specific moment in time.  

Interpolation is fairly simple, but it lacks precision. Interpolation has been used by human civilizations since antiquity, particularly by early astronomers in Mesopotamia and Asia Minor attempting to fill in gaps (the observation possibilities for astronomers being inherently limited). While the movement of planetary bodies is subject to many factors, they are still better suited to the imprecision of interpolation than the wildly variant, unpredictable fluctuations of publicly-traded stocks. Nevertheless, with the overwhelming mass of data involved in securities analysis, large interpolations of price movements are fairly unavoidable.

 

 

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