Modelling in Time Series Object

Machine Learning and Modeling
,
#1

For discussions related to modeling, machine learning and deep learning. Related packages include caret, modelr, yardstick, rsample, parsnip, tensorflow, keras, cloudml, and tfestimators.

the time series model (which doesn't have periodic component) can be decomposed to
Y = T + S + R
Y = T.S.R
Y = T.S + R
Y = T + S.R (T = trend, S = Seasonal, R = Random)
But forecast package gives only additive and multiplicative models but not the combination
I want to try all 4 combinations and take the best fit. How can I do it and compare ?

#2

See Hydnman and Athanasopoulos

The additive decomposition is the most appropriate if the magnitude of the seasonal fluctuations, or the variation around the trend-cycle, does not vary with the level of the time series. When the variation in the seasonal pattern, or the variation around the trend-cycle, appears to be proportional to the level of the time series, then a multiplicative decomposition is more appropriate. Multiplicative decompositions are common with economic time series.

An alternative to using a multiplicative decomposition is to first transform the data until the variation in the series appears to be stable over time, then use an additive decomposition. When a log transformation has been used, this is equivalent to using a multiplicative decomposition on the original data \dots