# What's the difference between a random walk, AR(1) or a white noise process?

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Mash Wednesday on 22 Oct 2021
Answered: Jaynik on 29 Jul 2024
Hi,
I have a file with four columns with time-series data. The first three columns are either a random walk, AR(1) or a white noise process. I'm new to this so I'm not exactly sure how to determine that using Matlab. Any help is appreciated.
Thank you.

Jaynik on 29 Jul 2024
Hi,
A random walk is a time series model where each current term is the sum of the previous term and a random error. An AR(1) process is a time series model where each current term is the product of a certain coefficient and the previous term plus a random error. A white noise process is a time series where all terms are independent and identically distributed with a mean of zero. This means that all variables (X_t) are not autocorrelated and the variance is constant over time.
In MATLAB, you can use the autocorr function to plot the autocorrelation of the time series data. This can give some idea of whether the data follows a random walk, AR(1), or white noise process. For example:
% Assuming you want to check the first column
first_column = data(:, 1);
autocorr(first_column);
This will give you a plot of the autocorrelation of the first column of the data. If the autocorrelation drops off sharply after lag 1, it is likely an AR(1) process. If it drops off slowly, it is likely a random walk. If there is no significant autocorrelation at any lag, it is likely a white noise process.
For more formal testing of the data, using the adftest or kpsstest functions can be considered. You can refer the following documentation to read more about these functions:
Hope this helps!