 # some problem with ARIMA

I use arima(1,1,0) to fit prob1, the result shows as follows:

``````> fitprod1

Call:
arima(x = prod1, order = c(1, 1, 0))

Coefficients:
ar1
-0.0798
s.e.   0.0212

sigma^2 estimated as 1.468:  log likelihood = -3561.4,  aic = 7126.8
``````

However, I use ARIMA(1,0,0) to fit diff(prod1). The result shows as follows:

``````> fitprod1=arima(diff(prod1),order = c(1,0,0))
> summary(fitprod1)

Call:
arima(x = diff(prod1), order = c(1, 0, 0))

Coefficients:
ar1  intercept
-0.0806     0.0323
s.e.   0.0212     0.0238

sigma^2 estimated as 1.466:  log likelihood = -3560.48,  aic = 7126.96

Training set error measures:
ME     RMSE       MAE MPE MAPE      MASE          ACF1
Training set 3.60474e-05 1.210953 0.8383019 NaN  Inf 0.6345769 -0.0003768319
``````

I want to know:

1. why the AR coefficient of this two model are different?
2. why ARIMA(1,1,0) doesn't have the intercept? How to write the ARIMA(1,1,0) equation?

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