I studied at BA level, that ARIMA(0,1,0) on $y_t$ and ARIMA(0,0,0) on diff($y_t$) are the same models. I am doing the Box–Jenkins model estimation on the historic data of US unemployment rate.
My results (in R):
> arima010a Call: arima(x = munrate, order = c(0, 1, 0)) sigma^2 estimated as 19.23: log likelihood = -2126.56, aic = 4255.11 > arima010b Call: arima(x = diff(munrate), order = c(0, 0, 0)) Coefficients: intercept 0.0708 s.e. 0.1618 sigma^2 estimated as 19.23: log likelihood = -2126.46, aic = 4256.92
As you can see, the information criterion (AIC) differs and the $log(L)$, too. My question is, why do they differ in the two model?
I'm looking forward to any answer.
I tried the same later in gretl, and there wasn't any difference between the two models.