There are speculative explanations for red shift such as the tired light theory, but I am not referring to those. There are three mainstream explanations
Red shift due the expansion of the universe giving rise to a Doppler effect.
Cosmological red shift. The red shift is due to the stretching of light as the universe expands. Numerically, this seems to explain all of red shift, leaving no room for the other explanations.
Gravitational time dilation. Time runs slower as the force of gravity, or the gravitational field, gets stronger. Slower time equates to a reduced frequency, which is a red shift. There is definitely gravitational red shift at the local scale but I think there is at the cosmological scale. As the universe gets younger, the density increases, as will the force of gravity, or at least the gravitational field.
It is interesting that Doppler red shift can be termed temporary red shift. When the velocity stops the red shift stops. On the other hand, gravitational red shift due to the expansion of the universe could be termed permanent red shift. If the expansion stops, the red shift will remain. I think cosmological red shift must be permanent red shift.
How do all of these different red shifts relate to each other?