# R/crost.ma.R In tsintermittent: Intermittent Time Series Forecasting

#### Documented in crost.ma

```crost.ma <- function(data,h=10,w=NULL,nop=c(2,1),type=c("croston","sba","sbj"),
cost=c("mar","msr","mae","mse"),outplot=c(FALSE,TRUE),
na.rm=c(FALSE,TRUE)){
# Croston style moving averages and variants
#
# Inputs:
#   data        Intermittent demand time series.
#   h           Forecast horizon.
#   w           Moving average order. If w == NULL then moving average orders are optimised.
#               If w is a single value then the same order is used for smoothing both the
#               demand and the intervals. If two values are provided then the second
#               is used to smooth the intervals.
#   nop         Specifies the number of model parameters. Used only if they are optimised.
#               1 - Demand and interval moving average order are the same
#               2 - Different demand and interval orders
#   type        Croston's method variant:
#                 1 - "croston" Croston's method;
#                 2 - "sba" Syntetos-Boylan approximation;
#                 3 - "sbj" Shale-Boylan-Johnston.
#   cost        Cost function used for optimisation
#                 "mar" - Mean absolute rate
#                 "msr" - Mean squared rate
#                 "mae" - Mean absolute error
#                 "mse" - Mean squared error
#   outplot     If TRUE a plot of the forecast is provided.
#   na.rm       A logical value indicating whether NA values should be remove using the method.
#
# Outputs:
#   model       Type of model fitted.
#   frc.in      In-sample demand rate.
#   frc.out     Out-of-sample demand rate.
#   order       Moving averages orders for demand and interval.
#   component   List of c.in and c.out containing the non-zero demand and interval vectors for
#               in- and out-of-sample respectively. Third element is the coefficient used to scale
#               demand rate for sba and sbj.
#
# Example:
#   crost.ma(ts.data1,outplot=TRUE)
#
# Notes:
# Optimisation cost functions and properties described in:
# N. Kourentzes, 2014, On intermittent demand model optimisation and selection,
# International Journal of Production Economics, 156: 180-190.
# http://dx.doi.org/10.1016/j.ijpe.2014.06.007
# http://kourentzes.com/forecasting/2014/06/11/on-intermittent-demand-model-optimisation-and-selection/
#
# Nikolaos Kourentzes, 2014 <nikolaos@kourentzes.com>

# Defaults
type <- tolower(type[1])
cost <- cost[1]
nop <- nop[1]
outplot <- outplot[1]
na.rm <- na.rm[1]
nop <- nop[1]

# Prepare data
if (isa(data,"data.frame")){
if (ncol(data)>1){
warning("Data frame with more than one columns. Using only first one.")
}
data <- data[[1]]
}
if (na.rm == TRUE){
data <- data[!is.na(data)]
}
n <- length(data)

# Croston decomposition
nzd <- which(data != 0)               # Find location on non-zero demand
k <- length(nzd)
z <- data[nzd]                        # Demand
x <- c(nzd[1],nzd[2:k]-nzd[1:(k-1)])  # Intervals

# Optimise parameters if requested
if (is.null(w)){
w <- crost.ma.opt(data,type,cost,nop,k-1)
}

# Assign parameters
if (length(w)==1){
k.demand <- w[1]
k.interval <- w[1]
} else {
k.demand <- w[1]
k.interval <- w[2]
}

# Set coefficient
if(type == "sba"){
coeff <- k.interval/(k.interval+1)
} else if(type == "sbj"){
coeff <- (k.interval-1)/k.interval
} else {
coeff <- 1
}

# Calculate MA using filter
zfit <- filter(z,rep(1/k.demand,k.demand),sides=2)
zfit <- c(rep(NA,k.demand-1),zfit[!is.na(zfit)])
xfit <- filter(x,rep(1/k.interval,k.interval),sides=2)
xfit <- c(rep(NA,k.interval-1),xfit[!is.na(xfit)])
cc <- coeff * zfit/xfit

# Calculate in-sample demand rate
frc.in <- x.in <- z.in <- rep(NA,n)
tv <- c(nzd+1,n)  # Time vector used to create frc.in forecasts
for (i in 1:k){
if (tv[i]<=n){
frc.in[tv[i]:min(c(tv[i+1],n))] <- cc[i]
x.in[tv[i]:min(c(tv[i+1],n))] <- xfit[i]
z.in[tv[i]:min(c(tv[i+1],n))] <- zfit[i]
}
}

# Forecast out-of-sample demand rate
if (h>0){
frc.out <- rep(cc[k],h)
x.out <- rep(xfit[k],h)
z.out <- rep(zfit[k],h)
} else {
frc.out <- x.out <- z.out <- NULL
}

# Plot
if (outplot==TRUE){
plot(1:n,data,type="l",xlim=c(1,(n+h)),xlab="Period",ylab="",
xaxs="i",yaxs="i",ylim=c(0,max(data)*1.1))
lines(which(data>0),data[data>0],type="p",pch=20)
lines(1:n,frc.in,col="red")
lines((n+1):(n+h),frc.out,col="red",lwd=2)
}

# Prepare demand and interval vectors for output
c.in <- array(cbind(z.in,x.in),c(n,2),dimnames=list(NULL,c("Demand","Interval")))
if (h>0){
c.out <- array(cbind(z.out,x.out),c(h,2),dimnames=list(NULL,c("Demand","Interval")))
} else {
c.out <- NULL
}
c.coeff <- coeff
comp <- list(c.in=c.in,c.out=c.out,coeff=coeff)

return(list(model=paste("ma.",type,sep=""),frc.in=as.numeric(frc.in),
frc.out=frc.out,order=c(k.demand,k.interval),components=comp))

}

#-------------------------------------------------
crost.ma.opt <- function(data,type=c("croston","sba","sbj"),
cost=c("mar","msr","mae","mse"),nop=c(2,1),k){

# Optimisation function for Croston and variants

type <- type[1]
cost <- cost[1]
nop <- nop[1]

if (nop==1){
jmax=1
} else {
jmax=k
}

err <- array(NA,c(k,jmax))

# Grid search to avoid integer optimisation
for (i in 1:k){
for (j in 1:jmax){
if (nop==2){
err[i,j] <- crost.ma.cost(c(i,j),data,cost,type)
} else {
err[i,j] <- crost.ma.cost(c(i,i),data,cost,type)
}
}
}

wopt <- as.numeric(which(err==min(err,na.rm=TRUE),arr.ind=TRUE))

if (nop==1){
wopt <- wopt[1]
}

return(wopt)

}

#-------------------------------------------------
crost.ma.cost <- function(w,data,cost,type){
# Cost functions for Croston and variants
frc.in <- crost.ma(data=data,w=w,h=0,type=type)\$frc.in

if (cost == "mse"){
E <- data - frc.in
E <- E[!is.na(E)]
E <- mean(E^2)
} else if(cost == "mae"){
E <- data - frc.in
E <- E[!is.na(E)]
E <- mean(abs(E))
} else if(cost == "mar"){
n <- length(data)
temp <- cumsum(data)/(1:n)
n <- ceiling(0.3*n)
temp[1:n] <- temp[n]
E <- abs(frc.in - temp)
E <- E[!is.na(E)]
E <- sum(E)
} else if(cost == "msr"){
n <- length(data)
temp <- cumsum(data)/(1:n)
n <- ceiling(0.3*n)
temp[1:n] <- temp[n]
E <- (frc.in - temp)^2
E <- E[!is.na(E)]
E <- sum(E)
}

return(E)

}
```

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tsintermittent documentation built on July 18, 2022, 9:06 a.m.