# Solved – How to interpret ARIMA(2,1,0) with drift

The code that Î used to generate ARIMA summary is

``arimafore = forecast(auto.arima(sales), h = 12) summary(arimafore) ``

For forecasting 12 months I got the summary below:

``Forecast method: ARIMA(2,1,0) with drift  Model Information: Series: sales  ARIMA(2,1,0) with drift   Coefficients:           ar1      ar2      drift       -0.8102  -0.4819  2774.6233 s.e.   0.1750   0.1688   682.3571  sigma^2 estimated as 62683829:  log likelihood=-248.34 AIC=504.67   AICc=506.78   BIC=509.39  Error measures:                    ME     RMSE      MAE        MPE     MAPE      MASE       ACF1 Training set 63.40175 7256.336 5466.688 -0.2247928 4.024713 0.1580417 -0.1562984  Forecasts:          Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95 Feb 2018       173223.9 163077.5 183370.4 157706.3 188741.6 Mar 2018       176272.6 165945.0 186600.2 160477.8 192067.3 Apr 2018       181744.1 170775.0 192713.2 164968.3 198519.9 May 2018       182201.7 169589.9 194813.4 162913.7 201489.6 Jun 2018       185553.8 172511.7 198595.9 165607.6 205500.0 Jul 2018       188977.2 175195.2 202759.2 167899.5 210054.9 Aug 2018       190947.9 176308.7 205587.0 168559.2 213336.5 Sep 2018       194061.2 178885.2 209237.1 170851.6 217270.8 Oct 2018       196948.9 181112.2 212785.5 172728.8 221168.9 Nov 2018       199468.7 182991.1 215946.3 174268.3 224669.0 Dec 2018       202395.3 185371.4 219419.1 176359.6 228430.9 Jan 2019       205169.6 187564.3 222774.9 178244.6 232094.6 ``

Can you help me to interpret ARIMA(2,1,0) with drift? Is it more of a trend model?

Contents

$$Delta x_{t} = b + sum_{i=1}^{m} phi(i) * Delta x_{t-i} + sum_{j=0}{m} theta(j) * epsilon(t-j)$$
"Integrating" this model gives you the original $$x_{t}$$ model. As you can see here by the integration you'll give $$a + b*t$$ member in you closed form for $$x(t)$$:
$$x(t) = a + b*t + sum_{i=1}{n+1} phi_{new}(i) x(t-i) + sum_{j=0}{m} theta_{new}(j) * epsilon(t-j)$$