library(forecast)
library(tseries)

y_ts <- AirPassengers                       # built-in monthly series, frequency = 12
n    <- length(y_ts)

lambda <- NULL                    
#lambda <-  BoxCox.lambda(y_ts) #to apply box cox transformation

ts_test     <- na.interp(y_ts)
adf_result  <- adf.test(ts_test)
kpss_result <- kpss.test(ts_test)

# Seasonal unit root (Canova-Hansen)
seasonal_diffs <- nsdiffs(y_ts, test = "ch")

split_ratio <- 0.80                                     # "80%" training-set  
train <- window(y_ts, end   = time(y_ts)[floor(split_ratio * n)])
test  <- window(y_ts, start = time(y_ts)[floor(split_ratio * n) + 1])

fit_auto <- auto.arima(
  train,
  seasonal      = TRUE,          
  stepwise      = TRUE,          
  approximation = TRUE,
  lambda        = lambda,
  biasadj       = !is.null(lambda),
  max.p = 4, max.q = 4, max.P = 1, max.D = 1, max.Q = 1
)

fc_test <- forecast(fit_auto, h = length(test))
acc     <- accuracy(fc_test, test)
checkresiduals(fit_auto)                                #  Ljung-Box test

p <- 1; d <- 1; q <- 1                                   # default (p, d, q) shown in the app
P <- 1; D <- 1; Q <- 1; use_sarima <- FALSE              # seasonal orders, off by default
period_use <- if (frequency(train) == 365) 7 else frequency(train)

fit_manual <- Arima(
  train,
  order        = c(p, d, q),
  seasonal     = if (use_sarima) list(order = c(P, D, Q), period = period_use)
                 else list(order = c(0, 0, 0)),
  lambda       = lambda,
  biasadj      = !is.null(lambda),
  include.mean = (d == 0 && (!use_sarima || D == 0))
)

fc_test_manual <- forecast(fit_manual, h = length(test))
acc_manual     <- accuracy(fc_test_manual, test)

fitdf <- (p + q) + if (use_sarima) (P + Q) else 0
Box.test(residuals(fit_manual), lag = 10, type = "Ljung-Box", fitdf = fitdf)

forecast(fit_auto, h = 5)          # default forecast horizon = 5 steps