Getting bizarre coefficients in the ARX model identification

Hi, I'm struggling with the system identification with the ARX model. The input data is a decaying sine signal. The output data is the system response to this input data. The input and output data looks like this:

The upper is the output and the lower is the input.

The model orders are [100 100 0].

I used the the following code to build the arx model:

     na=100; nb=100; nd=0;
     trainingSys=arx(data, [na nb nd]);
     compare(trainingSys,data);

which give very nice fit, as is shown below.

I also validate this arx model with another set of data, the predicted results are also very nice.

The problem is, if I look at the model constants, i.e., by

     b=trainingSys.b;
     plot(b);

this gives the following b coefficients vs the order number figure:

You can see that these coefficients appears very large at some points!

My question is, since my input-output data are of the order 10e-2, why is the coefficients obtained by the arx model so large? Am I missing something?

Best, Kai