此数据是否适合 ARIMA 建模？

Question

I used below data to develop Auto ARIMA model. But after looking at the results, I dont understand if this data is fit to run ARIMA model. Differencing the variable Count at 3rd lag gave the significant p-value and auto.arima suggested the order (3,0,0). But the predicted values turned out to be not something expected, which are mostly negative values. The actual data didn't consist of any negative values. I dont understand what is the issue. The model looks statistically correct but the predicted values are not looking good. Any help much appreciated.

Data:

dput(Enrollment_Data)
structure(list(COUNT = c(17L, 1L, 5L, 8L, 45L, 21L, 18L, 43L, 
82L, 116L, 192L, 289L, 242L, 254L, 335L, 138L, 71L, 98L, 91L, 
138L, 175L, 232L, 155L, 376L, 197L, 271L, 421L), Enrolment_date = structure(c(25L, 
20L, 5L, 10L, 8L, 16L, 1L, 18L, 14L, 12L, 3L, 26L, 23L, 21L, 
6L, 11L, 9L, 17L, 2L, 19L, 15L, 13L, 4L, 27L, 24L, 22L, 7L), .Label = c("APR2018", 
"APR2019", "AUG2018", "AUG2019", "DEC2017", "DEC2018", "DEC2019", 
"FEB2018", "FEB2019", "JAN2018", "JAN2019", "JUL2018", "JUL2019", 
"JUN2018", "JUN2019", "MAR2018", "MAR2019", "MAY2018", "MAY2019", 
"NOV2017", "NOV2018", "NOV2019", "OCT2018", "OCT2019", "SEP2017", 
"SEP2018", "SEP2019"), class = "factor")), class = "data.frame", row.names = c(NA, 
-27L))

Code:

Enrollment_Data <- read.csv('EnrollmentRateT0.csv')

print(Enrollment_Data)
dput(Enrollment_Data)
#load packages
library("tseries")
library("ggplot2")
library("forecast")
library(FitAR)
library("fUnitRoots")
library(lmtest)
library(fpp2)


attach(Enrollment_Data)
#Step-1 : Model Identification
#Stationarity Check - Dicky-Fuller test

#P-value > 0.5 Heance the data is non - stationary

d.COUNT <- diff(COUNT, differences = 3)
summary(COUNT)
summary(d.COUNT)

plot(d.COUNT)

adf.test(d.COUNT, alternative="stationary")

acf(d.COUNT)
pacf(d.COUNT)

#Step 2: Model Estimation


#Step 4: Diagnosis
auto.arima(d.COUNT)
auto.arima(d.COUNT, stepwise = FALSE, approximation = FALSE)

arima.final <-auto.arima(d.COUNT, stepwise = FALSE, approximation = FALSE, D=1)

tsdiag(arima.final)

arima.final

'Choose the one that has least AIC and significant co-efficients'

#arima.final <-arima(COUNT, c(3,3,1))

forecast1 <- forecast(arima.final,h = 12)

forecast1

plot.forecast(futurVal)
plot(forecast1)
class(forecast1)
print(forecast1)
summary(forecast1)
accuracy(forecast1)
plot(d.COUNT)

p <- predict(arima.final,n.ahead = 12); 
f <- forecast(arima.final, h = 12); 
all.equal(f$mean, p$pred)

accuracy(f)
p
f

results:

Point    Forecast      Lo 80    Hi 80     Lo 95     Hi 95
25  -234.78798559 -376.20497 -93.3710 -451.0666 -18.50937
26   248.28301149  -21.68036 518.2464 -164.5903 661.15636
27    38.07516814 -281.53132 357.6817 -450.7208 526.87112
28  -278.77782716 -600.00425  42.4486 -770.0513 212.49560
29   251.40378400  -74.76879 577.5764 -247.4341 750.24168
30   -31.49668698 -359.73170 296.7383 -533.4888 470.49545
31  -144.02466378 -474.75484 186.7055 -649.8328 361.78350
32   130.22859430 -211.26598 471.7232 -392.0423 652.49947
33    13.52166802 -332.92417 359.9675 -516.3215 543.36485
34  -123.35180366 -469.81119 223.1076 -653.2157 406.51210
35   103.92492852 -244.63788 452.4877 -429.1559 637.00574
36    -0.06911659 -349.40010 349.2619 -534.3247 534.18651

Answer 1

You're running auto.arima() on d.COUNT which are the 3rd lag differences of original Enrollment_Data$COUNT . That d.COUNT do contain lots of negative values. I believe you want to run auto.arima on Enrollment_Data$COUNT instead.