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

### 1 Basics of Holt-Winters method

#### 1.1 Additive model

\[\text{Level: }a_t=\alpha(x_t-s_{t-p})+(1-\alpha)(a_{t-1}+b_{t-1})\]

\[\text{Trend (or slope): }b_t=\beta(a_t-a_{t-1})+(1-\beta)b_{t-1}\]

\[\text{Seasonal effect: }s_t=\gamma(x_t-a_t)+(1-\gamma)s_{t-p}\]

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