# R in Time Series: Holt-Winters Smoothing and Forecast

This tutorial tells about how to do Holt-WInters smoothing and forecast in R.

### 1  Basics of Holt-Winters method

$\text{Level: }a_t=\alpha(x_t-s_{t-p})+(1-\alpha)(a_{t-1}+b_{t-1})$
$\text{Trend (or slope): }b_t=\beta(a_t-a_{t-1})+(1-\beta)b_{t-1}$
$\text{Seasonal effect: }s_t=\gamma(x_t-a_t)+(1-\gamma)s_{t-p}$
where $$a_t$$, $$b_t$$, and $$s_t\,$$ are the estimated level, slope, and seasonal effect at time t, and $$\alpha$$, $$\beta$$, and $$\gamma\,$$ are the smoothing parameters. Read more R in Time Series: Holt-Winters Smoothing and Forecast