Interpolating Missing Data with Noise like Brownian Motion

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Hello folks,
I have a few questions regarding interpolating financial price data set.
I have a set of price points, but their frequency is not high, so I would like to interporlate between these between.
For instance, consider 24 by 2 double price data points where it spans over 24 hours.
Between each hour, I would like to interporlate 15, 30, 45, so total three interporlated points, that way I now have 72 points per day.
However, I would like to insert some noise that follows possibly a geometric brownian motion or random walk to give a flavor of randomness in the data and they are not all linear connected.
What might be the best way to do this?
I have the basic codes so far of importing the data and converting to 24 by 2 double format:
file= "pricedata.xlsx";
Tab =readtable(file);
T=table2array(Tab);
Any suggestions?
Thanks in advance!

Accepted Answer

Bruno Luong
Bruno Luong on 2 Sep 2022
"What might be the best way to do this?'"
Interpolation THEN
adding noise.
There is no reason to mix the noise generation with interpolation step.
  9 Comments
Tatte Berklee
Tatte Berklee on 8 Sep 2022
Excellent. No, you are correct. I wanted this, but your sample code had 3600, so now it is clear to me you put 3600 for demonstration. Thanks!

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More Answers (1)

Image Analyst
Image Analyst on 2 Sep 2022
Try this:
rows = 24;
prices = round(100*rand(rows, 2), 2) % [Beginning of day, end of day]
% Scan down getting prices.
% Allocate 72 points per day, including the start and end.
interpPrices = zeros(rows, 72);
for row = 1 : rows
% Add up to +/- 2 unit of noise.
noise = 2 * rand(1, 72);
interpPrices(row, :) = round(linspace(prices(row, 1), prices(row, 2), 72) + noise, 2);
end
  3 Comments
Tatte Berklee
Tatte Berklee on 6 Sep 2022
Thanks for the response and comments. I will try this method as well!

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