title: ARIMA(1,1,1) throws value error: The model specification cannot be estimated
body: <p>I'm forecasting website visits using ARIMA model in time-series forecast with Python. Here is main details to get the picture of the process:
  <a href="https://i.stack.imgur.com/FMFyn.png" rel="nofollow noreferrer">imported modules</a></p>
  <p><a href="https://i.stack.imgur.com/wwMI4.png" rel="nofollow noreferrer">Data and actual plot</a>
  Figures represent the number of visits. Dates used as index, but as string (formatted date)</p>
  <p><a href="https://i.stack.imgur.com/l9etQ.png" rel="nofollow noreferrer">Differences (1 and 2)</a></p>
  <p><a href="https://i.stack.imgur.com/FrZA1.png" rel="nofollow noreferrer">Correlations (auto &amp; Partial)</a></p>
  <p><a href="https://i.stack.imgur.com/GE6tm.png" rel="nofollow noreferrer">ARIMA model with (1,1,1) order</a></p>
  <p><a href="https://i.stack.imgur.com/ToAYS.png" rel="nofollow noreferrer">ARIMA error</a></p>
  <p>So, as you see, for p and q, 1 is the best choice, and differencing 1 is more stationary (and even doesn't work with 2). So, I chose order = (1,1,1) which must best fit, but I get value error result that says:
  The model specification cannot be estimated. The model contains 7 regressors (0 trend, 0 seasonal, 7 lags) but after adjustment for hold_back and creation of the lags, there are only 2 data points available to estimate parameters.
  It doesn't work for (1,2,1) too, and the same error. However, it works for (0,1,1) which gives not bad q (MA) value (0.01), and with AIC 147.596. But the plot doesn't seem good when comparing with actuals:
  <a href="https://i.stack.imgur.com/AXRoU.png" rel="nofollow noreferrer">Actual with Forecast (plot_predict())</a></p>
  <p>Please, help to identify the reason why ARIMA gives error for (1,1,1) which must be the best order. How can I solve this?
  Thanks in advance!</p>