ARIMA loop in R - r

Question

I'm pretty new to R and I've run into a problem with finding the optimal ARIMA model. So far I've modeled the trend and a seasonal component, and now I want to model the cyclical component with an ARIMA model. I want the output in the end to include coefficients for the time variable, the seasonal variables and also the ARIMA variables. I've tried to use a loop to find the optimal ARIMA model and the coefficients, but I just get this message:
"Error in optim(init[mask], armaCSS, method = optim.method, hessian = FALSE, :
non-finite value supplied by optim"
I've tried looking for other answers in here, but I just can't seem to figure out what I'm doing wrong.
I've included the entire code in case it is necessary, but the error appears after running the loop in the end.
I appreciate any help I can get, thank you!
#clear workspace
rm(list=ls())
#load data
setwd("~/Desktop/CBS/HA almen year 3 /Forecasting /R koder ")
data <- scan("onlineretail.txt")
data <- data[2:69] #cut off first period + two last periods for whole years
T=length(data)
s=4
years=T/s
styear=2000
st=c(styear,1)
data = ts(data,start=st, frequency = s)
plot(data)
summary(data)
#plot shows increasing variance - log transform data
lndata <- log(data)
plot(lndata)
dataTSE = decompose(lndata, type="additive")
plot(dataTSE)
########### Trend ##########
t=(1:T)
t2=t^2
lny <- lndata
lmtrend.model <- lm(lny~t)
summary(lmtrend.model)
#linear trend T_t = 8,97 + 0,039533*TIME - both coefficeients significant
#Project 2, explanation why linear is better than quadratic
qtrend.model <- lm(lny~t+t2)
summary(qtrend.model)
lntrend = fitted(lmtrend.model)
lntrend = ts(lntrend, start=st, frequency = s)
#lntrend2 = fitted(qtrend.model)
#lntrend2 = ts(lntrend2, start=st, frequency = s)
residuals=lny-lntrend
par(mar=c(5,5,5,5))
plot(lny, ylim=c(5,12), main="Log e-commerce retail sales")
lines(lntrend, col="blue")
#lines(lntrend2, col="red")
par(new=T)
plot(residuals,ylim=c(-0.2,0.8),ylab="", axes=F)
axis(4, pretty(c(-0.2,0.4)))
abline(h=0, col="grey")
mtext("Residuals", side=4, line=2.5, at=0)
############# Season #################
#The ACF of the residuals confirms the neglected seasonality, because there
#is a clear pattern for every k+4 lags:
acf(residuals)
#Remove trend to observe seasonal factors without the trend:
detrended = residuals
plot(detrended, ylab="ln sales", main="Seasonality in ecommerce retail sales")
abline(h=0, col="grey")
#We can check out the average magnitude of seasonal factors
seasonal.matrix=matrix(detrended, ncol=s, byrow=years)
SeasonalFactor = apply(seasonal.matrix, 2, mean)
SeasonalFactor=ts(SeasonalFactor, frequency = s)
SeasonalFactor
plot(SeasonalFactor);abline(h=0, col="grey")
#We add seasonal dummies to our model of trend and omit the last quarter
library("forecast")
M <- seasonaldummy(lny)
ST.model <- lm(lny ~ t+M)
summary(ST.model)
#ST.model <- tslm(lny~t+season)
#summary(ST.model)
#Both the trend and seasonal dummies appears highly significant
#We will use a Durbin-Watson test to detect serial correlation
library("lmtest")
dwtest(ST.model)
#The DW value is 0.076396. This is quite small, as the value should be around
2
#and we should therefore try to improve the model with a cyclical component
#I will construct a plot that shows how the model fits the data and
#how the residuals look
lntrend=fitted(ST.model)
lntrend = ts(lntrend, start=st, frequency = s)
residuals=lny-lntrend
par(mar=c(5,5,5,5))
plot(lny, ylim=c(5,12), main="Log e-commerce retail sales")
lines(lntrend, col="blue")
#tell R to draw over the current plot with a new one
par(new=T)
plot(residuals,ylim=c(-0.2,0.8),ylab="", axes=F)
axis(4, pretty(c(-0.2,0.4)))
abline(h=0, col="grey")
mtext("Residuals", side=4, line=2.5, at=0)
############## Test for unit root ############
#We will check if the data is stationary, and to do so we will
#test for unit root.
#To do so, we will perform a Dickey-Fuller test. First, we have to remove
seasonal component.
#We can also perform an informal test with ACF and PACF
#the autocorrelation function shows that the data damps slowly
#while the PACF is close to 1 at lag 1 and then lags become insignificant
#this is informal evidence of unit root
acf(residuals)
pacf(residuals)
#Detrended and deseasonalized data
deseason = residuals
plot(deseason)
#level changes a lot over time, not stationary in mean
#Dickey-Fuller test
require(urca)
test <- ur.df(deseason, type = c("trend"), lags=3, selectlags = "AIC")
summary(test)
#We do not reject that there is a unit root if
# |test statistics| < |critical value|
# 1,97 < 4,04
#We can see from the output that the absolute value of the test statistics
#is smaller than the critical value. Therefore, there is no evidence against
the unit root.
#We check the ACF and PACF in first differences. There should be no
significant lags
#if the data is white noise in first differences.
acf(diff(deseason))
pacf(diff(deseason))
deseasondiff = diff(deseason, differences = 2)
plot(deseasondiff)
test2 <- ur.df(deseasondiff, type=c("trend"), lags = 3, selectlags = "AIC")
summary(test2)
#From the plot and the Dickey-Fuller test, it looks like we need to difference
twice
############# ARIMA model ############
S1 = rep(c(1,0,0,0), T/s)
S2 = rep(c(0,1,0,0), T/s)
S3 = rep(c(0,0,1,0), T/s)
TrSeas = model.matrix(~ t+S1+S2+S3)
#Double loop for finding the best fitting ARIMA model and since there was
#a drift, we include this in the model
best.order <- c(0, 2, 0)
best.aic <- Inf
for (q in 1:6) for (p in 1:6) {
fit.aic <- AIC(arima(lny,order = c(p,2, q),include.mean = TRUE,xreg=TrSeas))
print(c(p,q,fit.aic))
if (fit.aic < best.aic) {
best.order <- c(p, 0, q)
best.arma <- arima(lny,order = c(p, 2, q),include.mean = TRUE,xreg=TrSeas)
best.aic <- fit.aic
}
}
best.order

Answer 1

Please use the forecast package from Prof. Hyndman.
The call to:
auto.arima(data)
will return you the most optimal ARIMA model for your time series. You will find https://www.otexts.org/fpp/8/7 a great reference as well.