The White Noise Model

In life, it helps to learn what not to waste one’s time on. So is the case in data science. For example, it’s useful to know the long term sales trend of a newly launched product.

In life, it helps to learn what not to waste one’s time on. So is the case in data science.

For example, it’s useful to know the long term sales trend of a newly launched product. It’s not very useful to know the sales trend from one second to the next.

The variation in sales at this level of granularity may well be, indistinguishable from white noise.

And yet, there happens to be a statistical model to do just that — modeling of white noise. It is known as the white noise model, and it goes like this for time series data:

In this model, we are saying that the value observed at time step i is the summation of the current level of the time series at time step i and a random component Ni_ around the current level.

If the extent of random variation is proportional to the current level, then we have the following multiplicative version of the same model:

The multiplicative white noise model

If the current level Li_ is constant for all i, i.e. Li = L_ for all i, then the noise will be seen to fluctuate around a fixed level.

It’s easy to generate a white noise data set. Here’s how to do it in Excel:

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