The Multiplicative Model of Time Series Analysis
Essay by Khánh Vân Bùi • June 4, 2019 • Course Note • 661 Words (3 Pages) • 728 Views
The multiplicative model of time series analysis can be expressed as Y = T x S x R
In this model, only T is expressed in the original units, S and R are stated in terms of percentages.
If the random component R is negligible, which means R = 1 in this case, the seasonal percentage is calculated by S = Y/ T
For multiplicative model, the sum of average seasonal factor is the number of values, so 5 in this case. If not, make adjustment.
Forecasting by extrapolation
Extrapolation is the process of estimating, beyond the original observation range, the value of a variable on the basis of its relationship with another variable.
Use the trend T and seasonal factor S to forecast the unknown Y values in a near future.
In this examples, we can predict the output in each day of the forth week.
To have the Y values for each day of week 4, we need both trend values T and seasonal values S. For S: use adjusted average S for each day.
For T: we need to estimate it from known T-values. Then for additive model Y = T+S
multiplicative model Y = T x S
Trend T in this example is in an increasing trend. Then we calculate the average increase of T over each time period. Min value = 103.2, max value = 110.2. 11 boundary points => 10 periods.
Average increase of T = (110.2 – 103.2) / 10 = 0.7
Hence, for he unknown T-values, we add 0.7 to the previous value to get the next value.
We make time period Mon-Fri to week 4
Now, to forecast the Y-values for additive model: Y=T+S
Multiplicative Y = TxS
For additive Multiplicative
Mon: 100 99
Tue: 129 130
Wed: 114 114
Thu: 142 144
Fri: 84 81
There is a slight difference between two models. Which model is more reliable?
- Both models are reliable
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