What is the problem? Is it that you want to use log transformations of negative series? This is clearly not possible. If for example, you have a trade balance that is negative sometimes and positive other times try using imports and exports separately in your model. A sensible economic model is an absolute prerequisite for econometric modeling. Perhaps you might elaborate on your difficulties.

Ram Prasad Gajurel

Hello

I did not understand you. Can you explain?

In economic models, it often happens that some data are positive and some are negative, and this does not cause a problem.

Unless you want to take log transformations

One way to deal with both negative and positive time series in a single econometric model is to use the absolute value of the time series. Another way is to use logarithmic transformation. The logarithmic transformation can be used when the data contains both positive and negative values. The log transformation can be applied to the absolute value of the data plus one.

Ram sir, I strongly support to Chuck A Arize sir's response. Log transfotmation of negative time-series is possible, though it is a hectic process.

Thank you Aditya Pokhrel , John C Frain Zeinab Shabani Koshalshahi and thank you Chuck A Arize

Chuck A Arize

Ram Prasad Gajurel

Aditya Pokhrel

The log of a negative number is not defined. Perhaps I do not understand what you mean but one can not take the logarithms of a series that has negative values.

There is no reason why you can not smooth economic data or deal with both negative and positive numbers in a single econometric model.

Have a look at the Census Bureau X13-ARIMA-SEATS program. The free statistical packages gretl and R have an interface to these routines as do many other statistical software packages. You may find these routines useful.

One way to deal with both negative and positive time series in a single econometric model is to use the Box-Cox transformation. The Box-Cox transformation is a family of power transformations that can be used to normalize data. It is used to transform non-normal data into normal data by raising the data to a power. The power parameter is estimated from the data using maximum likelihood estimation. Another way is to use the difference between the logarithms of two time series. This method is called the log difference method. It involves taking the logarithm of each time series and then taking the difference between them. This method can be used when one time series is positive and the other is negative.

Chuck A Arize

Ram Prasad Gajurel

I don't understand how a Box-Cox transformation can help here. My problem is as follows

The Box-Cox transformation is

B(y,\lambda) = (y^(\lambda)-1)/(\lambda) if \lambda not equal to 0

B(y,\lambda) = log(y) if \lambda =0

When \lambda = 1 this corresponds to the identity transformation

When \lambda =1/2 this corresponds to a square root transformation

etc.

For many values of \lambda y must be positive.

If you use Box-Cox transformations in "regressions" the \lambda(s) used in the regression is/are estimated jointly with the coefficients. See

Baltagi (2011), Econometrics, 5th Edition, Springer. page 213 et seq. or

Green(2018), Econometric Analysis, Pearson, page 214.

I don't see any problem in using positive and negative values in a series in any econometric analysis except where one tries to carry out an inappropriate transformation of the data (like taking logs or square roots of negative numbers). If you think that you need to do this either your data or your model are wrong. Perhaps Ram could explain in more detail what he is trying to do.