What Is Interpolation?
Let me explain interpolation directly: it's a statistical method where you use related known values to estimate an unknown value or set of values. In the world of investing, you apply it to estimate prices or potential yields of securities. You achieve this by drawing on established values that sit in sequence with the unknown one.
Understanding Interpolation
If you see a consistent trend across data points, you can reasonably estimate values at uncalculated points. As an investor or analyst, you often create line charts with interpolated points to visualize security price changes, which is key in technical analysis. Remember, this contrasts with extrapolation, which estimates values beyond the known data rather than in between.
You use interpolation to generate new data points between known ones on charts, like those showing a security's price action or volume. Computers handle this now, but the concept dates back to ancient astronomers filling gaps in planetary observations. Formal types include linear, polynomial, and piecewise constant interpolation. For instance, you might use an interpolated yield curve to graph U.S. Treasury bond yields and gauge future market and economic directions.
Example of Interpolation
Consider linear interpolation, the easiest type, useful when estimating a security's value or interest rate without direct data. Say you're tracking a stock price over time, plotting it as function f(x). You have data for August (x1), October (x3), and December (x5), but need September (x2). Using linear interpolation, you estimate f(x) at x2 within that range.
Criticism of Interpolation
One major criticism is its lack of precision, despite its long history. Ancient uses focused on predictable astronomical patterns, but stock markets are volatile and unpredictable. Still, with vast securities data, interpolations of price movements are inevitable. Most stock history charts are interpolated using linear regression to approximate curves, though you can't pinpoint exact values at specific moments with full confidence.
Interpolation FAQs
- What Type of Interpolation Is Used in Technical Analysis? In technical analysis, you mainly see linear and exponential interpolation; linear draws a straight line between points, while exponential uses weighted averages adjusting for factors like trading volume.
- How Is Interpolation Used in Trading? Traders use interpolation, often as smoothing, to represent high-low price ranges between closing prices, creating regression lines that approximate moving averages for predicting support levels.
- What Is Interpolation vs. Extrapolation? Interpolation estimates values between known points to fill blanks, while extrapolation extends known points outward, carrying higher inaccuracy risks.
The Bottom Line
Interpolation is your mathematical tool to estimate unknown data points between known ones, helping fill in gaps. As a technical trader, you use it to understand past price behaviors even with incomplete info, predicting trends from a fuller picture of price action.
Other articles for you
The 4% rule is a guideline for retirees to withdraw 4% of their savings annually, adjusted for inflation, to make funds last about 30 years.
Escrowed shares are stocks held by a third party in an escrow account until specific conditions are met in transactions like mergers, employee plans, or bankruptcies.
Joint supply occurs when a single product or process yields multiple outputs, like cows providing milk, beef, and hide.
Tax benefits are provisions in tax laws that reduce your tax liability through deductions, credits, exclusions, exemptions, and shelters.
Average Selling Price (ASP) is the typical price at which a class of goods or services is sold, serving as a benchmark influenced by product type and life cycle.
Accounting is the essential process of recording, summarizing, and analyzing financial transactions for businesses and organizations to inform decisions and ensure compliance.
This guide explains what a business plan is, its key components, benefits, and how to create one effectively for startups and established businesses.
Cyclical unemployment occurs due to economic downturns and is a key focus of economic policy to mitigate during recessions.
Level-premium insurance maintains fixed premiums while potentially increasing coverage over time in permanent policies.
The profitability index evaluates a project's attractiveness by comparing the present value of its future cash flows to the initial investment.