I'm new to forecasting and playing with some forecasting techniques. I used the ets function from te forecast package to automatically select the model. I want to do a check to see if the model has adequately captured the information in the data.
I used the checkresiduals() function and the Ljung-Box test with Box.test() as described in https://otexts.com/fpp2/residuals.html.
checkresiduals gives me a p-value lower than 0.05 where the Ljung-Box test gives me a p-value greater than 0.05.
I was suspecting a p-value greater than 0.05 by both methods. I'm really confused now.
Question
Is my model correct? Or is it incorrect and can it be optimized with for example ARIMA?
Data
month_year n
1 2017-12-01 75
2 2018-01-01 253
3 2018-02-01 99
4 2018-03-01 155
5 2018-04-01 186
6 2018-05-01 290
7 2018-06-01 400
8 2018-07-01 248
9 2018-08-01 148
10 2018-09-01 167
11 2018-10-01 181
12 2018-11-01 136
13 2018-12-01 94
14 2019-01-01 135
15 2019-02-01 134
16 2019-03-01 168
17 2019-04-01 172
18 2019-05-01 206
19 2019-06-01 896
20 2019-07-01 270
21 2019-08-01 183
22 2019-09-01 174
23 2019-10-01 164
24 2019-11-01 100
25 2019-12-01 123
26 2020-01-01 182
27 2020-02-01 155
28 2020-03-01 178
Code
# define time serie #
timeserie.ts <- ts(data$n, start=c(2017, 12), end=c(2020, 03), freq=12)
time <- time(timeserie.ts)
# split data in train & test #
n.valid <- 2
n.train <- length(tijdserie.ts) - n.valid
train.ts <- window(tijdserie.ts, start=time[1], end=time[n.train])
valid.ts <- window(tijdserie.ts, start=time[n.train+1], end=time[n.train+n.valid])
# use ETS to find the 'best' model #
modelfit <- ets(train.ts, model = "ZZZ")
# write away residuals #
res <- residuals(modelfit)
# ACF plot #
acf(res)
#checkresiduals test#
checkresiduals(modelfit)
data: Residuals from ETS(M,N,M)
Q* = 19.517, df = 3, p-value = 0.0002137
# Ljung-Box test #
Box.test(res, type = "Ljung-Box")
data: res
X-squared = 3.1101, df = 1, p-value = 0.07781
# forecast 6 months #
plot(forecast(modelfit, 6))
