# Formulas for time series decomposition

```Formulas for Model-3 ( chapter 6)
Time series decomposition and exponential smoothing
Time series can be decomposed into four parts:
1.
2.
3.
4.
Trend
Seasonal component
Cyclical
Irregular
Step1: Smoothing the time series with Moving average
Moving average- 4 months
=Average(Average(Q1:Q4), Average(Q2:Q5))
It removes the seasonality from the data
Step -2 : Isolating the seasonality of a time series
1. Raw seasonal: ( it is used in the normalization for seasonality decomposition)
Formula= Sales/ moving average
2. Create a small table with three columns
Quarters
1
Raw factor
=Averageif (quarters range, quarters number
from this table, raw seasonal range)
2
3
4
3. Seasonal Index
Vllokup ( qtr no, above table range, col-indx-no)
4. Isolating the Irregularities:
=sales/ ( Moving average*seasonal index)
5. Reconstruction:
= Moving average*seasonal index* irregulaties
Normalisation
= Raw factor / average of Raw
factors
Exponential smoothing:
Exponential smoothing refers to a type of weighted average where largest weight is given to the most
recent observation, and the weights on the prior observations decline exponentially over time.
Steps:
1. Alpha = 0.25 ( initial value)
2. Exponential smoothing =
Initial cell = sales
Second cell= exponential smoothing previous +(alpha*(previous sales- previous exp smoothing))
1. MSE = SUMXMY2(Sales series: Exponential smoothing series)/ count( sales series)
2. MAPE =Average(Abs(sales series-exp smoothing series)/sales series)
Plot the line graph with three series
Re-estimate the alpha by using solver
1. set MSE is equal to zero
2. By changing Alpha value
3. Constrains alpha value should be &gt;= 0 and &lt;= 1
```