Interpolation
Interpolation is a widely used technique in statistics that applies known variables in order to determine the unknown price or potential asset’s yield. The interpolation is carried out by using other set values that are in the same row with the unknown value.
At its core, interpolation is not a complex mathematical idea. The value of the set at points which have not been calculated can be rationally estimated if a consistent tendency across a set of data points exists. It is quite common for investors and stock market analysts to build a line chart using interpolated data points. These graphic images are an essential part of technical analysis, since their purpose is to visualize a price movement of a security in the process of time.
What is Interpolation
Interpolation is applied by investors for creating new estimated data points between known data points on a graph. Graphical representations showing a price action and volume of a security exemplify how interpolation can be used.
Although these data points are generated by computer algorithms these days, the idea of interpolation is far from new. Observing the movement of the planets and trying to fill in their gaps, early astronomers from Mesopotamia and Asia Minor began to use interpolation.
It is worth mentioning that there are several types of interpolation: linear, polynomial, and piecewise constant interpolation. The interpolated yield curve is used by analysts to plot a chart of the yield of recently issued U.S. T-Bonds or fixed-maturity notes. This kind of interpolation allows analysts to form the general direction of the bond markets and the economy in the future.
Interpolation should be distinguished from extrapolation, which is concerned with estimating a data point outside the observed range of the data. The risks associated with obtaining inaccurate results are lower in the case of interpolation.
Interpolation example
The most common and easy to use is a linear type of interpolation. In the case when an investor is estimating the security’s value or interest rate for a point where there is no data, the current kind of interpolation is quite useful.
For example, the price of a certain security is tracked over a certain period of time. The function f(x) is the line along which the movement of the price of this security is tracked.
To represent points in time, it is required to plot the current price of a stock on a series of points. Function f(x) will be recorded for August, October and December. Mathematically the points will be represented as xAug, xOct, and xDec, or x1, x3 and x5.
In September, the investor may need to know the security’s price, however, he does not have data for this month. In this case, to estimate the value of f(x), a linear interpolation algorithm at a point xSep, or x2 will be applied. It appears within the available data range.
Limitations of Interpolation
Despite the fact that the interpolation methodology that has existed for centuries is quite simple, it still lacks accuracy. In Ancient Greece and Babylon, astronomical forecasts generated through interpolation allowed farmers to increase crop yields using a smart planting strategy.
If for astronomical forecasts the existing imprecision of interpolation is not critical, for the volatility of traded stocks this is a real problem. However, large interpolations of price movements are inevitable as the analysis of securities uses a huge amount of data.
Many graphic images containing the price history of a stock are widely interpolated.
To create the curves showing price changes in securities, a linear regression is used. Nevertheless, it is not possible to accurately predict the value of a stock over a given period of time, even if a chart measuring stocks for a year included data points for each day of the year.
