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The rate of spread of an emerging epidemic is frequently characterized via the doubling time, which is the time it takes for the number of cases to double. This paper explores different ways to estimate doubling time, and investigates the estimation of doubling time in relationship to parameters in the HawkesN model and the SQUIDER (Susceptible, Quarantine, Undetected Infected, Infected, Dead, Exposed, Recovered) model. We observe an approximately exponential relationship between the productivity parameter κ in the HawkesN model and doubling time. We also evaluate the performance of the models in forecasting doubling times and compare to empirical doubling times using daily reported statewide totals for SARS-CoV-2 infections in California, and find that the HawkesN model forecasts doubling times more accurately, with 3.6% smaller root mean squared errors in Spring 2020, 79.4% smaller root mean squared errors in Autumn 2020, and 5.4% smaller root mean squared errors in Summer 2021. The HawkesN and SQUIDER models appear to forecast daily rate doubling times accurately at most times, though the SQUIDER forecasts of daily rate doubling times are far more volatile and thus occasionally have much larger errors, particularly in Fall 2020.