The good news is your plant is not dying. It is stressed and when stressed a plant is more vulnerable to disease and insects. Without being able to look closely this guy looks like he's got a case of spider mite. Easy to fix.
Do you have a southern window with more light but not direct sunlight? Do you have a covered patio or porch?
When that plant is watered, feel the heft. Pick it up to feel the weight. I'll bet it is heavy right now and that means do not water until that pot is substantially lighter in weight. Your palm looks like it will be needing an upgrade to a slightly larger pot, soon.
Right now, lets get this guy happy again. Better light, no drafts, let the soil dry out before watering, in between watering. Cut off the yellowing leaves right at the trunk. Get down on your knees with the plant between you and a light source. You might be able to see fine webbing between leaves and leaflets. With a magnifying glass you could see the spider mite. If you find both of these on your plant; the webbing and being able to see the insect, then we can talk about treatment. Not hard to do. Ask another question?
Allow the soil to dry out and the next watering I would put this plant in my shower and turn on the cold water spray over this plant...it cleans off all the dust, spider mite hates moisture...allow to drain and drip then take back to this plant's spot. (find a south window)...I do this will all of my indoor plants once or twice per year. My indoor plants get to go outside under the roof of a covered porch or patio for the summer. No acclimating necessary. No direct sun allowed. Still far more light to do photosynthesis than indoors from a window. If you use artificial lighting, use a fan 24/7 to keep the air moving. 16 hours light and 8 hours darkness. Use a simple timer. Ask another question if artificial lighting interests you at all...or how to treat spider mite if you see sign.
You will be up potting this palm soon. Find a pot that is 2 to 3" larger in diameter than this pot. Is that a 10" pot? Clay is the healthiest and the least expensive and has weight to balance the bulk of a large plant.
Use ONLY sterilized potting soil. No water holding gimmicks such as sponges and gels. Absolutely no fertilizer should have been added to the potting soil. You want to be in charge of the fertilizer because "less is best, more is death and none is dumb"...grins.
No rocks or gravel or packing peanuts below the potting soil and above the drainage hole. Just soil. After firming the soil around the plant's root ball you should have 1" of space between rim and surface of soil for proper watering purposes.
If you don't have a more airy, sun lite space, I would purchase a REAL grow light for this plant. Another question you could ask. Artificial lighting is not just a bulb called grow light...a bit more expensive as well, but not a deal breaker.
Be careful when changing environments for plants. Like Jurp asked, just driving or walking this plant home from a warm moist environment and spending 10 minutes in dry cold air can kill a plant. Transporting plants is where most people ruin their brand new plant, upright in the back of a pickup? Killer of any plant.
Please look for the spider mite, shop for a new pot and saucer, check out 'pot feet' for potted plants. They raise the bottom of the pot off of the saucer, patio floor, a bench so that the surface tension in the water doesn't slow the drainage. As water drains air is allowed back into the root system, the pore spaces of the soil medium. Broken pieces of tiles 1/4 inch thick work well for this job, pot feet are cute. And cost a few bucks.
Never use garden soil in potted plants.
The best fertilizer for you would be Osmocote 14-14-14 all purpose extended release fertilizer. One maybe two applications per year will be more than enough. Use half the amount the directions recommend.