ARRES is a method of automatically choosing the alpha value based on the errors of previous time periods. The smoothing constant adapts to the data.

The equation of ARRES has the same form as SES:

SES:
F_t = α * A_t-1 + (1 - α) * F_t-1 or rewritten as:
F_t = F_t-1 + α * (A_t-1 - F_t-1)

ARRES:
α is the replaced by a tracking signal.
F_t = F_t-1 + TST_t-1 * (A_t-1 - F_t-1)

The adaptive response rate (TST_t), tracking signal, is the ratio of the absolute value of two averages, average forecast error and average absolute forecast error.

TST_t = absolute( SAD_t / MAD_t )
SAD_t = β * (A_t - F_t) + (1 - β) * SAD_t-1
MAD_t = β * absolute( A_t - F_t ) + (1 - β) * SAD_t-1

TST_t-1 = Tracking signal in period t used for α in period t + 1
β = Beta, a smoothing constant for SAD and MAD Typically choosen to be 0.2
SAD_t = An exponentially weigthed average deviation (mean forecast error) in period t
MAD_t = An exponentially weigthed mean absolute deviation (mean absolute forecast error) in