R Arima Equation Question - Please help!

the three components (p, d, q) are the AR order, the degree of differencing, and the MA order. In your case, you have p=1, d=1, q=0, which means that you don’t consider a moving average (MA) term but an auto-regressive-1 (AR-1) structure conducted on one time integrated time series.

Thus, the general structure of your model is: Y[t] = a[1]Y[t-1] with the coefficient a[1] given in your R output. And furthermore, since d=1, you consider first-order differences Y[t] = X[t]-X[t-1], which you have to substitute accordingly in the equation above.

you final equation would be: X[t]-X[t-1] = 0.0099 * (X[t-1]-X[t-2]) which is equivalent to X[t] = X[t-1] + 0.0099 * (X[t-1]-X[t-2]).

Best regards