ARIMA, what is the interpretation for the sum of AR coefficients? I have used auto.arima, results are:
Regression with ARIMA(1,1,0)(2,0,0)[4] errors 

Coefficients:
         ar1       sar1       sar2          xreg1      xreg2       xreg3       xreg4     xreg5
      0.4787349  0.1285586  0.3230805    -0.0007353  0.0000041  0.0000006  -0.0001028  0.000029
s.e.  0.0166596  0.0144297  0.0892615         NaN        NaN        NaN     0.0000485     NaN

sigma^2 estimated as 0.0000000003864757:  log likelihood=982.56
AIC=-1947.12   AICc=-1945.56   BIC=-1921.67

I have read somewhere that:

If there is a unit root in the AR part of the model--i.e., if the sum
  of the AR coefficients is almost exactly 1--you should reduce the
  number of AR terms by one and increase the order of differencing by
  one.

Should I be worried about my AR coefficients? I use the model for forecasting, I do not need s.e., but are NaN related to the AR coefficients? The signs are as I expected.
 A: Just rearrange your $\text{AR}(p)$ polynomial $\phi(z) = 1 - \phi_1 z - \cdots - \phi_p z^p$. If $z'$ is a root, then $1 - \phi_1 z' - \cdots - \phi_p (z')^p = 0$. If $z'$ is a unit root, then you can rearrange that to get
$$
\sum_i \phi_i = 1.
$$
This suggests you can write your $\text{AR}(p)$ polynomial as $\phi(z) = (1 - z)\phi^*(z) = \phi^*(z)(1 - z)$, where $\phi^*(z)$ is an $\text{AR}(p-1)$ polynomial. Differencing your data and then estimating an $\text{AR}(p-1)$ model $\phi^*(z)$ is the same as estimating the initial $\text{AR}(p)$ polynomial $\phi(z)$ but under the assumption that it has one unit root.
A: Differencing like any other transformations like power transformations should only  be done when deemed necessary. Assuming ( which I would never do ! ) that the exogenous predictors only have a contemporaneous effect , compute a regression , study the error processs's acf/pacf and cautiously/iteratively construct/identify an AR/MA model perhaps ultimately incorporating differences. Note well that pulses/level shifts/seasonal pulses and time trends may also be necessary to render a white noise error process and if untreated will create confusion in your modelling process. If you wish post your data in a column oriented csv file and I will try and help you further.
EDITED AFTER RECEIPT OF DATA: Note as @Taylor suggested a smaller model is more appropriate . I scaled his dependent variable by 10**6 . The user wished to retain all input series thus no stepdown was implemented thus the final model contains a few non-significant (non-intrusive) coefficients.


106 quarterly values and 5 predictor series were automatically analyzed by AUTOBOX using transfer function modelling procedures yielded the following model 

Automatic Transfer Function model identification was accomplished essentially following TSAY http://www.math.cts.nthu.edu.tw/download.php?filename=569_fe0ff1a2.pdf&dir=publish&title=Ruey+S.+Tsay-Lec1 BUT definitely avoiding the Corner Method as it is not robust (i.e. doesn't work ) when you have Gaussian Violations.
In more detail  and     here] suggesting 9 deterministic input series anomalies. A significant change in error variance at period 69 was detected leading to WLS .   and    . The residuals from this transfer function are here   . The ACF of the residuals is here  . Finally the model is (1,1,0)(0,0,0) 4 with an error variance change at period 46 and 9 unusual values including a seasonal pulse and a level shift. Your model had an unnecessary sar coefficient and did not treat the anomalies OR the evidented non-constancy of the error variance over time thus the answer to your question is "YES". Finally the seasonality in your data is deterministic NOT autoregressive thus the need for a seasonal dummy starting at period 14 ( 1994 qtr 2 ) . The sum of the ar coefficients has to be interpreted based upon/given  the order of the ar polynomial.
