The novel Coronavirus Disease 2019 (COVID-19) remains a worldwide threat to community health, social stability, and economic development . Since the first case was recorded on December 29 , 2019, in Wuhan of China, the disease has rapidly extended to other nations of the world to claim many lives, especially in the USA, the United Kingdom, and Western Europe . To stay ahead of the curve consequent of the continued increase in case and mortality, predictive tools are needed to guide adequate response . Therefore, this study aims to determine the best predictive models and investigate the impact of lockdown policy on the USA' COVID-19 incidence and mortality . This study focuses on the statistical modelling of the USA daily COVID-19 incidence and mortality cases based on some intuitive properties of the data such as overdispersion and autoregressive conditional heteroscedasticity . The impact of the lockdown policy on cases and mortality was assessed by comparing the USA incidence case with that of Sweden where there is no strict lockdown . Stochastic models based on negative binomial autoregressive conditional heteroscedasticity [NB INGARCH (p, q) ], the negative binomial regression, the autoregressive integrated moving average model with exogenous variables (ARIMAX) and without exogenous variables (ARIMA) models of several orders are presented, to identify the best fitting model for the USA daily incidence cases . The performance of the optimal NB INGARCH model on daily incidence cases was compared with the optimal ARIMA model in terms of their Akaike Information Criteria (AIC). Also, the NB model, ARIMA model and without exogenous variables are formulated for USA daily COVID-19 death cases . It was observed that the incidence and mortality cases show statistically significant increasing trends over the study period . The USA daily COVID-19 incidence is autocorrelated, linear and contains a structural break but exhibits autoregressive conditional heteroscedasticity . Observed data are compared with the fitted data from the optimal models . The results further indicate that the NB INGARCH fits the observed incidence better than ARIMA while the NB models perform better than the optimal ARIMA and ARIMAX models for death counts in terms of AIC and root mean square error (RMSE). The results show a statistically significant relationship between the lockdown policy in the USA and incidence and death counts . This suggests the efficacy of the lockdown policy in the USA.