Federal Reserve Bank of New York

The Empire State Manufacturing Survey seasonally adjusted data based on the Census X-12 additive procedure utilizing a logistic transformation. Logistic transformation procedure as follows: The not-seasonally adjusted series, expressed in decimal form (referred to as "p"), is transformed using the following equation: X = log(p/(1-p)) The seasonal factor is then subtracted from X: adjX = X - seasonal factor The result is then transformed using the following equation: Seasonally Adjusted Series = exponential(adjX)/(1+exponential(adjX)) The "increase" and "decrease" percentage components of the diffusion indexes are each tested for seasonality separately and adjusted accordingly if such patterns exist. If no seasonality is detected, the component is left unadjusted. The "no change" component contains the residual, computed by subtracting the (adjusted) increase and decrease from 100.