Predictive Analytics - Week 1

# Load packages
library(readr)

# Load dataset
df <- read_csv('/Users/laykhoonyu/Documents/MSAA_AE/predictive_analytics/week_1/USEPUINDXM.csv', show_col_types = FALSE)

head(df)

## # A tibble: 6 × 2
##   DATE       USEPUINDXM
##   <date>          <dbl>
## 1 1985-01-01      125. 
## 2 1985-02-01       99.0
## 3 1985-03-01      112. 
## 4 1985-04-01      103. 
## 5 1985-05-01      120. 
## 6 1985-06-01      133.

df$DATE <- as.Date(df$DATE)

uncertainty_ts <- ts(df$USEPUINDXM, start=c(1985, 01), frequency = 12)

Additive Time Series

a_decomposition <- decompose(uncertainty_ts, type = "additive")
plot(a_decomposition)

Multiplicative Time Series

m_decomposition <- decompose(uncertainty_ts, type = "multiplicative")
plot(m_decomposition)

Comments

Typically, the multiplicative model is more suited towards when the magnitude of the seasonal fluctuations or the variability around the trend tends to increase or decrease with the level of the time series. On the other hand, additive models are best used when the magnitude of the seasonal fluctuations or the variability around the trend does not depend on the level of the time series. However, the differences between the additive and multiplicative model are minimal. This could potentially mean that the seasonal variations and trends are relatively stable and consistent across different levels of the time series. There are also cases where the time series is overly complex that neither the additive nor the multiplicative model are capable of modeling its unusual or non-standard patterns.