Percentage Changes

Procedure

Common in economic data where relative growth is more stable than absolute changes. The percentage change is defined as: $\frac{Z_t-Z_{t-1}}{Z_{t-1}}$ This is approximately equal to the first difference of the log-transformed data: $\nabla \ln (Z_t)=\ln (Z_t)-\ln (Z_{t-1})\approx \frac{Z_t-Z_{t-1}}{Z_{t-1}}$ Modeling $\nabla \ln (Z_t)$ as a stationary process handles both exponential growth and multiplicative variance.