# Exponential smoothing models backcasting and determining initial values python

I have made python code for exponential smoothing (ES) that takes in about 15 different cases including:

• Simple Exponential Smoothing (SES)
• Simple Seasonal models (both multiplicative and additive)
• Brown's Linear Exponential Smoothing
• Holt's Double Exponential Smoothing
• Exponential trend method
• Damped-Trend Linear Exponential Smoothing
• Multiplicative damped trend (Taylor, 2003)
• Holt-Winters Exponential Smoothing: multiplicative trend, additive trend, multiplicative season, additive season, and damped models for all four variations

14 of these cases can be found in page 8 of Exponential smoothing: The state of the art Part II.

What values are commonly used for the initial values for the different ES models? What methods are used to determine points at time 0 and 1? (I am using Nan (not a number) to substitute in the code right now).