Answer to Question #226087 in Statistics and Probability for Carrie

Question

Use the exponential smoothing with w D 0:1 to detect the components of the following time series.

Period: 1 2 3 4 5

Time series: 63 72 86 71 60

The exponential smoothed value at period 3 is

1. 86

2. 66:11

3. 66:60

4. 65:94

5. 54:5

Answer 1

The given time series data is shown below

The problem objective is to apply exponential smoothing with $w = 0.1 \space w = 0.8$ to help detect the components. 

The exponentially smoothed values are calculated from the formula

$S_t=wy_t+(1-w)S_{t-1}$

Where S_t= Exponentially smoothed time series at time period t

y_t= Time series at time period t

w= Smoothing constant, where 0 ≤ w ≤1

S_t-1= Exponentially smoothed time series at time period t-1

 

The below figure shows the graph of the original time series and the exponentially smoothed series when w=0.1