Hello and thanks for your question. My name is XXXXX XXXXX I will do all I can to help.
The reason you have this "Anti Skid Service" message, is because there is a fault code stored in the ABS control module.
You will need an advanced type scanner to read off the codes stored in the ABS control module to know where to begin fault tracing the system.
Most of the times, this anti-skid light comes from a defective SAS sensor. or Steering Angle Sensor behind the steering wheel.
The SAS sensor sends a signal to the ABS control module about which position the steering wheel is in and how sharp of a turn you are making.
Could it be related to the stability control system?
Yes, those systems are tied to the ABS control module. All your anti skid and stability control functions are related to the ABS. But you will need to check codes in the ABS system to know for sure if it is the Steering Angle Sensor. (or some call it a contact reel)
I have replaced many SAS sensors for Anti Skid service messages before. I have replaced a sensor called the YAW sensor as well under the seat, but more often is the SAS sensor that sets the light off.