As JQ Veenstra has pointed out your method of evaluation depends a lot on the particular type of time series model that you are estimating. Have a look at the following points.
Usually you should have a set of residuals in your model that are uncorrelated. You can test that.
You can test the forecasting ability of your model by starting with a subset of the data recursively estimate the model and look at the errors when forecasting each re-estimated model.
For general guidance on forecasting I would recommend Granger, Clive W. J. and Paul Newbold (1986) -Forecasting Economic Time Series - Academic Press 1986 which is a bit dated but covers well many aspects of forecast evaluation. Elliott, G. and Timmermann, A (2016). Economic Forecasting, Princeton University Press is, perhaps a little mathematical but provides a comprehensive coverage of forecasting. The references to specific areas in this may give you more guidance on the evaluation of specific forecalting methods.