What is the reason why ARIMA(0,1,0) on $y_t$ and ARIMA(0,0,0) on diff($y_t$) are not identical time-series models? 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):

&gt; arima010a

Call:
arima(x = munrate, order = c(0, 1, 0))


sigma^2 estimated as 19.23:  log likelihood = -2126.56,  aic = 4255.11
&gt; 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.
I don't know R code but are you estimating an intercept in the ARIMA(0,1,0) model? Because if not, this could be why there is a difference, since you are estimating an intercept in the ARIMA(0,0,0) model.