Dear R users,

I picked up ARIMA(2,3,0) model for my time series analysis using
auto.arima() function.

>From my understanding, the model should be in this shape:

[Y(hat)(t)-Y(t-1)]-2[Y(t-1)-Y(t-2)]+[Y(t-2)-Y(t-3)]=Theta(1){[(Y(t-1)-Y(t-2)]-2[(Y(t-2)-Y(t-3)]+[Y(t-3)-Y(t-4)]}+Theta(2){[Y(t-2)-Y(t-3)]-2[Y(t-3)-Y(t-4)]+[Y(t-4)-Y(t-5)]}+mu(e(t))

which in this case, mu(e(t))=0, cause the residuals' mean is assumed and
estimated as zero.

In R, when t is 2013, the estimation value of Y(hat) is 7.084688, which is
different from my own calculation 7.1882, according to the model above.

Do you think that I missed something?
And is there any way that I can simplify the model or the differential
equation above???

Many thanks,
Chintemur Batur


############################################################################

Here is the code
library(tseries)
library(forecast)
d=scan("D:/Data.txt")
d
D=ts(data=d, start=1981,end=2012, frequency=1)
D
##############################################################################
Time Series:
Start = 1981
End = 2012
Frequency = 1
 [1]  384  403  427  450  499  550  575  615  640  680  702  730  760  790
[15]  790  830  870  871  906  920  968 1010 1060 1111 1165 1191 1217 1221
[29] 1089 1089 1090 1103
#############################################################################

lnD=log(D)
lnD3=diff(lnD, differences=3)
adf.test(lnD3)

par(mfrow=c(3,1))
acf(lnD3, lag.max=20)
pacf(lnD3, lag.max=20)

autoarima=auto.arima(lnD,d=3)
summary(autoarima)
Box.test(autoarima$residuals,lag=20,type="Ljung-Box")
ForecastAutoArima=forecast.Arima(autoarima, h=5, c=(0.95))
plot.forecast(ForecastAutoArima)

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