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I have a time series data that looks as follows

Time series data

The data has the following frequency distribution

Distribution

Here is the Q-Q plot

Q-Q plot

It looks like the data is exponentially distributed. My assumption is that the noise or error component of the data will also be similarly distributed. So to make the data normally distributed I applied a log transformation, which resulted in the following frequency distribution and Q-Q plots.

Frequency distribution of log-transformed data

Q-Q plot of log-transformed data

It looks like that even after log transformation the transformed data did not look normally distributed. Is there any other transformation that should be done? More importantly, does the prophet really require transformation?

I would really appreciate your answers/comments.

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I am not convinced from that first time series plot that you have exponential data. What you do have is a lot of observations in a small graph space with some unaccounted for periodicity possibly. Before deciding to transform the data, it is meaningful and useful to decompose your series.

Decomposition breaks out a trend (upward or downward trajectories), Seasonality (repeated periodic patterns in the data) and the remainder (which you can think of as noise, temporally localized variability)

When you look at this tryptic of graphs you will be able to assess better if there is some kind of pattern worth transforming.

There is a fantastic book (open sourced) by Rob Hyndman and George Athanasopoulos called Forecasting Principals & Practice. It gives really clear suggestions on how to start working with time series data and provides meaningful ways for interpreting plots tests.

I would start with understanding your series more completely before rushing to transform it.

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  • $\begingroup$ Thanks for the link. will check it out. $\endgroup$
    – mars
    Oct 7, 2022 at 17:13

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