Additive or multiplicative time series?

mora.R

if(!require("ggseas")) install.packages("ggseas")
if(!require("forecast")) install.packages("forecast")
if(!require("data.table")) install.packages("data.table")
if(!require("knitr")) install.packages("knitr")

library(ggseas)
library(forecast)
library(data.table)

# Get data
nzdata<-data.table(nzbop)
nzdata<-nzdata[!((Account=="Capital account"&
                               Category=="Balance")|
                              (Account=="Financial account"&
                                 Category=="Foreign inv. in NZ; Financial derivative liabilities")|
                   (Category=="Secondary income balance")),]
sample_ts<-nzdata[Account == "Current account" & Category=="Services; Exports total",
                  .(TimePeriod, Value)]
knitr::kable(head(sample_ts))

# Add trend
sample_ts[,trend := zoo::rollmean(Value, 8, fill=NA, align = "right")]
knitr::kable(tail(sample_ts))

# De-trend data
sample_ts[,`:=`( detrended_a = Value - trend,  detrended_m = Value / trend )]
knitr::kable(tail(sample_ts))

# Make seasonals
sample_ts[,`:=`(seasonal_a = mean(detrended_a, na.rm = TRUE),
             seasonal_m = mean(detrended_m, na.rm = TRUE)), 
          by=.(quarter(TimePeriod)) ]
knitr::kable(tail(sample_ts))

# Make residuals
sample_ts[,`:=`( residual_a = detrended_a - seasonal_a, 
                 residual_m = detrended_m / seasonal_m )]
knitr::kable(tail(sample_ts))

# Visuals
ggsdc(sample_ts, aes(x = TimePeriod, y = Value), method = "decompose", 
      frequency = 4, s.window = 8, type = "additive")+ geom_line()+
  ggtitle("Additive")+ theme_minimal()

ggsdc(sample_ts, aes(x=TimePeriod, y=Value), method = "decompose", 
      frequency=4, s.window=8, type = "multiplicative")+ geom_line()+
  ggtitle("Multiplicative")+ theme_minimal()

# Auto-correlated factor
ssacf<- function(x) sum(acf(x, na.action = na.omit)$acf^2)
compare_ssacf<-function(add,mult) ifelse(ssacf(add)< ssacf(mult), 
                                         "Additive", "Multiplicative") 
knitr::kable(sample_ts[,.(compare_ssacf(residual_a, residual_m ))])

# Combined function
ssacf<- function(x) sum(acf(x, na.action = na.omit, plot = FALSE)$acf^2)
compare_ssacf<-function(add,mult) ifelse(ssacf(add)< ssacf(mult), 
                                         "Additive", "Multiplicative") 
additive_or_multiplicative <- function(dt){
  m<-copy(dt)
  m[,trend := zoo::rollmean(Value, 8, fill="extend", align = "right")]
  m[,`:=`( detrended_a = Value - trend,  detrended_m = Value / trend )]
  m[Value==0,detrended_m:= 0]
  m[,`:=`(seasonal_a = mean(detrended_a, na.rm = TRUE),
                  seasonal_m = mean(detrended_m, na.rm = TRUE)), 
            by=.(quarter(TimePeriod)) ]
  m[is.infinite(seasonal_m),seasonal_m:= 1]
  m[,`:=`( residual_a = detrended_a - seasonal_a, 
                   residual_m = detrended_m / seasonal_m)]
  compare_ssacf(m$residual_a, m$residual_m )
}

# Applying it to all time series in table
results<-nzdata[,.(Type=additive_or_multiplicative(.SD)), 
                   .(Account, Category)]

knitr::kable(results)

Hello,

In # Visuals part, frequency has been set to 4, but in additive_or_multiplicative function, rollmean used a frequency of 8.

As nzdata are a set of quarter data, a frequency of 4 seems more adequate.

Can you explain the differences in frequency ? Thanks a lot.

@TuAnhPho My guess would be that you need at least 2 years of data to get the cycle of the data, and confirm that the seasonality is 4 per year.

Thanks for this information