Additive and Multiplicative Decomposition

From the Hyndman textbook, we know that we think of a time series as comprising of three components:
a trend-cycle component
a seasonal component
and a remainder component (containing anything else in the time series)

for additive decomposition, we can write: yt = St + Tt + Rt (this will be 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)

for multiplicative decomposition, we can write: yt = St x Tt x Rt (this will be most appropriate 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)

yt = the data
St = seasonal component
Tt = trend component
Rt = remainder component
all in period t

My Data

I will be working with the advance monthly sales for grocery stores in the United States. I found this data on the U.S Census Bureau website: https://www.census.gov/econ/currentdata/dbsearch?program=MARTS&startYear=1992&endYear=2020&categories%5B%5D=4451&dataType=SM&geoLevel=US&notAdjusted=1&submit=GET+DATA&releaseScheduleId=

mydata <- read.csv("C:/Users/andre/Documents/Boston College/2. Summer 2020/Forecasting/week 2/SeriesReport-202007081353.csv")

mydata_ts <- ts(mydata[,2], start = 1992, frequency = 12)

library(ggplot2)
library(forecast)
## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo
autoplot(mydata_ts) +
  ggtitle("U.S Census Bureau Advance Monthly Sales for Grocery Stores 1992-2020") + 
  xlab("Year") + 
  ylab("Monthly Millions of Dollars")

Classical Decomposition

mydata_ts %>% decompose(type="additive") %>%
  autoplot() + xlab("Year") +
  ggtitle("Classical additive decomposition
    of Advance Monthly Sales for Grocery Stores 1992 - 2020")

Classical Multiplicative Decomposition

mydata_ts %>% decompose(type="multiplicative") %>%
  autoplot() + xlab("Year") +
  ggtitle("Classical multiplicative decomposition
    of Advance Monthly Sales for Grocery Stores 1992 - 2020")

From what I can see, the remainders seem to increase more over time in the additive decomposition model, whereas the remainders seem to stay more constant in the multiplicative model. The Hyndman textbook also says that multiplicative time series are common with economic time series.

What I am struggling to understand is what is a good way to quantitatively determine whether this is correct or not? I would think that I would want to graph the remainders in a better way so as to oberserve and measure them, but I cannot seem to find code or explanations in the textbook that speak to that.

In terms of using these results for forecasting, I think that knowing whether or not to decompose additively or multiplicatively would be helpful to adjust the data properly. I think that this data would be okay to use for forecasting, since there is a very obvious positive trend as well as a constant seasonality to it as well.