EXP Command

The EXP command applies the exponential function to each observation in a time series. It is most commonly used to reverse a previous LOG transformation and return a logged series to its original scale.

Main idea: The EXP function is the inverse of the LOG function. If a series has been transformed using LOG, applying EXP restores the original values.

Example


EXP(LOG(GDP))

This example takes the logarithm of GDP and then applies the exponential function, reproducing the original GDP series.

Syntax


EXP(series)

Mathematical Definition

For a time series X, the EXP function raises Euler's constant e ≈ 2.71828 to the value of each observation:


EXP(Xt) = e^(Xt)

Why Use EXP?

Many statistical and econometric models are estimated using logarithmic transformations. After performing analysis in log space, it is often necessary to convert the results back to their original scale for interpretation.

The EXP function provides this conversion. It is commonly used when working with GDP, prices, earnings, money supply, and other economic series that are frequently analyzed in logarithmic form.

Common Applications

Reversing a LOG transformation
Converting forecasts from log space back to original units
Economic and financial modeling
Visualizing logged data on its original scale

Example: Recovering Original GDP


LOG_GDP = LOG(GDP)
GDP_RESTORED = EXP(LOG_GDP)

The resulting series will closely match the original GDP data, demonstrating that EXP is the mathematical inverse of LOG.