Question

If a variable is exponentially increasing, then the logarithm of that variable would have a linear trend. You are not convinced that fitting a trend line would bring a good forecast. Why would you think so? Why fitting a trend line on logarithm may not generate good forecasts in this case?

Answer 1

If a variable is exponentially increasing it means that the rate of change in data increases swiftly with time. This is the original character of data being captured for the variable.

The moment we apply a logarithm to the data we are transforming the variable to its log value. The data post the log transform becomes more linear.

Forecasting requires that the data be more symmetric or normally distributed for a better outcome. In the process of transformation, we try to normalise the data to make it more symmetric or normally distributed.

To apply a linear regression, one of the assumptions is to have a linear relationship between the dependent and the independent variable. With the log transformed data, we can easily apply linear regression to the "transformed" data and forecast the figure.

The weights generated for the variable will have a linear relationship with respect to past data. i.e. the slope of the line is the same across all data points. Therefore, the forecast is applicable ONLY to the transformed data that has lost its original character (i.e exponential nature).

The original data would need to have weights that would have a relationship that changes with time as against the linear transformed data. Here, unlike slope of the linear data, the slope of the curve changes with reference to time. More importance will need to be given to more recent data points.

So, the forecasted value of such log transformed linear data will NOT be applicable to the original exponential data.