Chapter 05.06: Extrapolation is a Bad Idea

Lesson: Extrapolation is a Bad Idea

Learning Objectives

After successful completion of this lesson, you should be able to:

1) enumerate why using extrapolation can be a bad idea.

2) show through an example why extrapolation can be a bad idea.



This conversation illustrates the pitfall of using extrapolation.

(Due to certain reasons, this student wishes to remain anonymous.)

This takes place in Summer Session B – July 2001

Student: “Hey, Dr. Kaw! Look at this cool new cell phone I just got!”

Kaw: “That’s nice. It better not ring in my class or it’s mine.”

Student: “What would you think about getting stock in this company?”

Kaw: “What company is that?”

Student: “WorldCom! They’re the world’s leading global data and internet company.”

Kaw: “So?”

Student: “They’ve just closed the deal today to merge with Intermedia Communications, based right here in Tampa!”

Kaw: “Yeah, and …?”

Student: “The stock’s booming! It’s at $14.11 per share and promised to go only one way—up! We’ll be millionaires if we invest now!”

Kaw: “You might not want to assume their stock will keep rising … besides, I’m skeptical of their success. I don’t want you putting yourself in financial ‘jeopardy!’ over some silly extrapolation. Take a look at these NASDAQ composite numbers (Table 1).”

Student: “That’s only up to two years ago …”

Kaw: “That’s right. Looking at this data, don’t you think you should’ve invested back then?”

Student: “Well, didn’t the composite drop after that?”

Kaw: “Right again, but look what you would’ve hoped for if you had depended on that trend continuing (Figure 1).”

Student: “So you’re saying that …?”

Kaw: “You should seldom depend on extrapolation as a source of approximation! Just take a look at how wrong you would have been (Table 2).”


Table 1. End of year NASDAQ composite data

End of year NASDAQ
\(1\) \(751.96\)
\(2\) \(1052.13\)
\(3\) \(1291.03\)
\(4\) \(1570.35\)
\(5\) \(2192.69\)
\(6\) \(4069.31\)

Note: The range of years in Table 1 are actually between 1994 (Year 1) and 1999 (Year 9). Numbers start from 1 to avoid round-off errors and near singularities in matrix calculations.

Figure 1 Data from 1994 to 1999 extrapolated to yield results for 2000 and 2001 using polynomial extrapolation.


Table 2 Absolute relative true error of polynomial interpolation.

End of Year Actual

Fifth order

polynomial interpolation

Absolute relative

true error
\(2000\) \(2471\) \(9128\) \(269.47 \%\)
\(2001\) \(1950\) \(20720\) \(962.36 \%\)

Student: “Now wait a sec! I wouldn’t have been quite that wrong. What if I had used cubic splines instead of a fifth-order interpolant?”

Kaw: “Let’s find out.”

Figure 2 Data from 1994 to 1999 extrapolated to yield results for 2000 and 2001 using cubic spline interpolation.


Table 3 Absolute relative true error of cubic spline interpolation

End of Year Actual

Cubic spline


Absolute relative

true error
\(2000\) \(2471\) \(5945.9\) \(140.63 \%\)
\(2001\) \(1950\) \(5947.4\) \(204.99 \%\)

Student: “There you go. That didn’t take so long (Figure 2 and Table 3).”

Kaw: “Well, let’s think about what this data means. If you had gone ahead and invested, thinking your projected yield would follow the spline, you would have only been 205% (Table 3) wrong, as opposed to being 962% (Table 2) wrong by following the polynomial. That’s not so bad, is it?”

Student: “Okay, you’ve got a point. Maybe I’ll hold off on being an investor and just use the cell phone.”

Kaw: “You’ve got a point, too—you’re brighter than you look … that is if you turn off the phone before coming to class.”

* * * * *

<One year later … July 2002>

Student: “Hey, Dr. Kaw! Whatcha got for me today?”

Kaw: “The Computational Methods students just took their interpolation test today, so here you go. <hands stack of tests to student> Time to grade them!”

Student: <Grunt!> “That’s a lot of paper! Boy, interpolation … learned that a while ago.”

Kaw: “You haven’t forgotten my lesson to you about not extrapolating, have you?”

Student: “Of course not! Haven’t you seen the news? WorldCom just closed down 93% from 83¢ on June 25 to 6¢ per share! They’ve had to recalculate their earnings, so your skepticism really must’ve spread. Did you have an”in” on what was going on?”

Kaw: “Oh, of course not. I’m just an ignorant numerical methods professor.”