What is bad, good and excellent metric score for time series model?
I do not think there is a silver bullet for metric value, because it is highly problem-specific, one way or another you need to compare your result to baseline in order to understand how viable it is.
For example, in time series common baseline for the next point predicted is a previous point or some moving average. You can get an error metric like MAPE (but be careful with it, since it has its downsides) and compare your models MAPE to Baseline MAPE (say moving average) and with this comparison, you can argue about how your approach is better.
Also, check this article regarding MAPE and other metrics.