It is possible to install car audio system at home but it will compromise with some other things like distortion in sound, noise like hissing in music and etc. The very important thing to consider when you are hooking up car audio system into your home is the power supply which will power everything as you need DC power for the car audio. You have options which can work to power car audio which can be DC power supply and Car batteries. Car audio system cannot perform as great as they work in car because they are built for the car environment. You cannot run the car audio equipments directly from the home power supply. The power voltage of AC differs from country to country. Some countries uses 240 Volts AC current and some uses 110 Volts AC current. 

A car electrical system has batteries which are been charged by alternator which provides current to the whole electrical system of the car. In this case when we are installing car audio equipments to our home we need a power supply which can hold the voltage of at least 12 Volts. 

The main important thing to consider in car audio is it requires minimum of 12 Volts of DC voltage to work. The car stereo or the aftermarket amplifiers, they all work at minimum 12 Volts of continuous power voltage to work properly. The best option to install the car audio system at your home is to install car batteries with charger for the best performance. A DC power supply will work for the purpose but it will not be able to survive for long time and it will damage the car audio setup when you will extract power from it. You need to consider how many amplifiers and speakers are gonna be installed for your setup before you plan anything. This will decide the total number of amperes you need for you to run your car audio setup at home. If the amperes are less than they require, then the amplifiers will go into protect mode or may even shut down because of loss of voltage output. When installing a car audio setup at home, the main root of it is the power supply and the wiring. Remember a heavy large subwoofer will require that much amount of power only on which it is working in a car, and heavy bass requires big powerful supply as well. 

Starting from the car stereo, you need to wire the yellow and the red wire for the positive wire connection and black wire for the negative connection (Ground). Do not connect in opposite direction as it will short circuit the equipment. try to put a in-line fuse in between of every equipment which can help to prevent any kind of problems which can arise. Check if the source unit is starting up and working correctly, If yes you are good to go for the next step. 

Next step is to wire speakers to the car stereo, if you are installing amplifier for your audio system then use a good quality gauge wire for the amplifier as it extracts more power than a normal car stereo. The positive wire and the negative wire of the amplifiers will be hooked to the power source according to their polarity. The speaker connections will remain the same for amplifier and the stereo both, they do not need any kind of modification to install. The same RCA cables will work to send signal to amplifier to stereo. 

 IF YOU DO NOT HAVE REMOTE WIRE ON THE CAR STEREO, THEN YOU CONNECT A WIRE FROM THE POSITIVE TERMINAL OF THE AMPLIFIER AND ATTACH IT TO THE REMOTE WIRE TERMINAL WHICH WILL ALSO WORK SAME. IF YOU WANT TO CONTROL THE AMPLIFIER TO ON OFF AT YOUR CHOICE YOU WILL NEED TO INSTALL THE IN LINE SWITCH TO REMOTE WIRE.

Sound Quality Issues

If you are not getting good sound quality after installing into your home, you need to remember some major points which makes sound quality better.

Design of the subwoofer enclosure if you have one. For example: A sealed enclosure will not produce enough bass compared to ported enclosure.

The room in which you installed the audio system should be according to your equipment specs. For example: A small subwoofer cannot shake your home easily but it can shake a car to some extend.

Wrong polarity of speaker wires and subwoofer wires installed.

Tuning of the audio system. For example: Same car tuning will not work for the home as well. Re tune the audio system according to the home suitable environment.

Note: You cannot get that sound quality which you get in a car because the car is enclosed environment and the car audio equipments are also designed to satisfy the car audio needs not the home audio needs, that is why the home theatres are made.