Compute initial values used in the exponential smoothing recursions


The initial value used for the level component

initial_slope{float, None}

The initial value used for the trend component


The initial values used for the seasonal components


Convenience function the exposes the values used to initialize the recursions. When optimizing parameters these are used as starting values.

Method used to compute the initial value depends on when components are included in the model. In a simple exponential smoothing model without trend or a seasonal components, the initial value is set to the first observation. When a trend is added, the trend is initialized either using y[1]/y[0], if multiplicative, or y[1]-y[0]. When the seasonal component is added the initialization adapts to account for the modified structure.