The characters do not have names. This way they are more representative of an ideal, than an identity.
The old man: This character represents hope for imagination, belief in the good, he is the wise elder of the story. He knows that nothing is ever permanent and you can change your circumstances if you can just imagine it.
The young boy: This character represents regret, enlightenment, and transformation after change. He lost touch of what it was like to be young, even while he was young, and now he has received a chance to forever claim his vitality.
The father: This character represents the inner child. The vitality that children forget while they go through life from one progression to the next. He is with the young boy on every adventure.
The jack-o-lantern: This is the contract and port key to time travel. It has obligations and strings attached. This character represents the delicate balance between childhood and adulthood.