###########################
## Convenience functions ##
###########################

## EACF tables (Franses 1998, p. 99)
ctrafo <- function(x) residuals(lm(x ~ factor(cycle(x))))
ddiff <- function(x) diff(diff(x, frequency(x)), 1)
eacf <- function(y, lag = 12) {
  stopifnot(all(lag > 0))
  if(length(lag) < 2) lag <- 1:lag
  rval <- sapply(
    list(y = y, dy = diff(y), cdy = ctrafo(diff(y)),
         Dy = diff(y, frequency(y)), dDy = ddiff(y)),
    function(x) acf(x, plot = FALSE, lag.max = max(lag))$acf[lag + 1])
  rownames(rval) <- lag
  return(rval)
}

#######################################
## Index of US industrial production ##
#######################################

data("USProdIndex", package = "AER")
plot(USProdIndex, plot.type = "single", col = 1:2)

## Franses (1998), Table 5.1
round(eacf(log(USProdIndex[,1])), digits = 3)

## Franses (1998), Equation 5.6: Unrestricted airline model
## (Franses: ma1 = 0.388 (0.063), ma4 = -0.739 (0.060), ma5 = -0.452 (0.069))
arima(log(USProdIndex[,1]), c(0, 1, 5), c(0, 1, 0), fixed = c(NA, 0, 0, NA, NA))

###########################################
## Consumption of non-durables in the UK ##
###########################################

data("UKNonDurables", package = "AER")
plot(UKNonDurables)

## Franses (1998), Table 5.2
round(eacf(log(UKNonDurables)), digits = 3)

## Franses (1998), Equation 5.51
## (Franses: sma1 = -0.632 (0.069))
arima(log(UKNonDurables), c(0, 1, 0), c(0, 1, 1))

##############################
## Dutch retail sales index ##
##############################

data("DutchSales", package = "AER")
plot(DutchSales)

## Franses (1998), Table 5.3
round(eacf(log(DutchSales), lag = c(1:18, 24, 36)), digits = 3)

###########################################
## TV and radio advertising expenditures ##
###########################################

data("DutchAdvert", package = "AER")
plot(DutchAdvert)

## Franses (1998), Table 5.4
round(eacf(log(DutchAdvert[,"tv"]), lag = c(1:19, 26, 39)), digits = 3)