© 2021, The Author(s).This research investigates the appropriateness of the linear specification of the market model for modeling and forecasting the cryptocurrency prices during the pre-COVID-19 and COVID-19 periods. Two extensions are offered to compare the performance of the linear specification of the market model (LMM), which allows for the measurement of the cryptocurrency price beta risk. The first is the generalized additive model, which permits flexibility in the rigid shape of the linearity of the LMM. The second is the time-varying linearity specification of the LMM (Tv-LMM), which is based on the state space model form via the Kalman filter, allowing for the measurement of the time-varying beta risk of the cryptocurrency price. The analysis is performed using daily data from both time periods on the top 10 cryptocurrencies by adjusted market capitalization, using the Crypto Currency Index 30 (CCI30) as a market proxy and 1-day and 7-day forward predictions. Such a comparison of cryptocurrency prices has yet to be undertaken in the literature. The empirical findings favor the Tv-LMM, which outperforms the others in terms of modeling and forecasting performance. This result suggests that the relationship between each cryptocurrency price and the CCI30 index should be locally instead of globally linear, especially during the COVID-19 period.