Dear Vasantha,

Hope this will help you.

https://www.researchgate.net/post/How-to-transform-data-with-negative-values#view=59f199dc217e20ee9c3cc767

To be precise. I am reproducing following response.

Guido Bongi added an answer October 26, 2017

If it is a single and unique dataset you may apply first a translation by adding 1 and subtracting the minimum T= X+1-min(X) and then log, but if you want it to apply to any dataset the min() should be the absolute one. For scientific consensus please follow specific literature refs.

I see no problem in having negative values in time series. I would particularly avoid adding some value to make the negative values positive. You use log transformations if your series is multiplicative. A multiplicative series can not change signs. If it is positive it stays positive. If your series changes sign then it is not multiplicative and you do not log transform it. I agree that mechanically you can add some number to all the series and then log transform it but this will distort your data and give spurious results when you do an estimation. The fact that some people have done this does not make it correct.

If you are modeling something like a trade deficit which can be positive or negative consider modeling imports and exports separately. You can model imports and exports using log transformations as these do not change signs.

Perhaps of some interest for your query:

https://www.researchgate.net/post/How-to-enter-the-logarithm-of-negative-values-in-the-time-series-of-an-economic-variable