# 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

# R in Time Series: Exponential Smoothing

This tutorial talks about the exponential smoothing and forecasts based on it.

### 1  Objective and Assumptions

Given a past history $$\{x_1,x_2,\cdots,x_n\}\Longrightarrow$$we want to predict some future value $$x_{n+k}$$.

We assume that:

1. We assume there is no systematic trend or seasonal effects in the process, or that these have been identified and removed.
2. The mean of the process can change from one time step to the next, but we have no information about the likely direction of these changes.