Does MATLAB have any toolboxes or commands for predicting the next number in a series?

I have a data series x as a function of time y:

x=[14,14,3,4,8,3,2,5,11,2,1,5,10,2,4,1,8,11,5,1,3,1,2;]
y=1:1:23

How do I predict the next number (x,y=24)? Does MATLAB have any toolboxes for that type of problem or will I need to code something like a neural network solution from scratch?

Cheers

[Greg Heath]

Why in the world are you using x(y) instead of the worldwide timetested standard y(x)?

Dizzily,

Greg

Answer 1

[Jan]

19.

Carl E. Linderholm showed, that any sequence of numbers can be continued by 19. It is easy to construct a corresponding Lagrange polynomial p(x) such that p(1), p(2), ... p(n) yields the given numbers and p(n+1) is 19. This rule is much easier than all other rules and is applies in general.

Of course you could use your favorite number also. But then this gives psychologists the chance to interpret your subconsciousness. So better choose 19 (and do not tell anybody if this is your favorite number).

See http://www.whydomath.org/Reading_Room_Material/ian_stewart/9505.html (they claim it was a Laplace interpolation - fortunately the law is such universal, that this detail does not matter.)

[Image Analyst]

I totally agree with Jan. In fact there was a controversy some years ago about using such "predict the next number" questions on college entrance exams because virtually any number (any one of their choices) could be an answer using some formula. You can't really say any of the numbers is right and all the rest are wrong.

Answer 2

[John D'Errico]

There is no reason to suppose that the next INTEGER in that series will be easily predicted. Neural nets are not a magical tool that will do here. For example, consider this vector?

[3  5  4  5  6  8  9  8 12 11 10 12  9 11 11 11 10  9 11 11 13 12 12 11]

What is the next term in that series?

Will any neural net be able to predict intelligently that the next term is 12? You might guess what the number is. But KNOWING with any confidence what the next number is will never be something a statistical tool can do, merely by looking at the numbers.

Worse, any numerical tool that would try to extrapolate a series would not understand that the result would be an integer. Any simple extrapolant would probably predict some floating point number.

Ok, I'll even be nice and tell you the next 5 numbers in that sequence. They are [12 15 17 17 16]. What is the next number? Feel free to postulate what is the mechanism behind that sequence. A little creative thinking should suffice. Statistics won't help though.

Unless you actually see the pattern, you will not be able to predict this sequence easily. In fact, I was wondering if oeis would be able to solve it.

https://oeis.org

oeis is a great source to solve such problem sequences. But I'm not at all surprised that it did not find a match for either the sequence you gave, or the one I posed.

[Alex]

The next term in this series is 16. You are certainly correct that this is not a well-posed mathematics problem. I do not assume the next integer in the series will be easily predicted. I don't need to necessarily predict the exact value (a floating point number would be OK).

Perhaps I should set a tolerance or threshold and either try to predict when the next value will be above/below the threshold. Using a tolerance, I would be happy if I could have predicted plus/minus 1 (maybe even within 2).

Thank you for sharing the link to https://oeis.org. this will be very useful in the future to quickly see if a pattern is recognizable in new data.

[Greg Heath]

The first thing you should do is to use the autocorrelation function to determine the statistically significant delays.

Hope this helps

Greg

[John D'Errico]

Actually, in the series I posed, the next term would have been 20. And the one after that? 24.

[Alex]

Great idea, I will look into the auto-correlation function more: https://www.mathworks.com/help/signal/ref/finddelay.html

16, then 1 are the next number for my series. I wasn't taking a guess at the new one you posed. I am not sure whether to treat the vector X as my signal or to pad it up to the value of the largest integer to treat each integer as a separate sensor to compute the time delay between when the same number is repeated.

Answer 3

[the cyclist]

The Statistics and Machine Learning Toolbox has many, many tools for making inferences from data.

You could also try the Neural Network Toolbox, but I don't think you need that.

But if you just plot your data

x=[14,14,3,4,8,3,2,5,11,2,1,5,10,2,4,1,8,11,5,1,3,1,2;]
y=1:1:23
figure; plot(y,x,'o')

you'll see that y is certainly not very predictive of x. (But maybe even a little predictive power is OK for your application.)

[Alex]

Thank you, but please try:

figure; plot(y,x)

There is definitely a pattern.

[the cyclist]

Ah, fair enough!

Do you have some underlying theoretical model? nlinfit from the Stats toolbox is one possible tool.

Also, I don't have much experience in this area, but this might be more of a signal processing problem. There is a separate toolbox for that, too. Or maybe you could use the fft function in base MATLAB.

[Alex]

Thank you, I am interpreting the data as voltages from a sensor so tried using FFT (I tried using all three examples in the FFT documentation: 'noisy signal', 'gaussian pulse' and 'cosine') to see if I could compute the amplitude and frequency spectrum(s), but do not see to have a central frequency. I believe I need more data.

I do not have a model to use nlinfit, but have noted this as something to try in the future. Thank you for your helpful suggestions!

Cheers,

Alex