Statistical Data-Driven Modelling and Forecasting: An Application to COVID-19 Pandemic

One of the key objectives of statistics is to provide a model compatible with the data generated by an unknown random process. Often, it happens that the unknown process is intractable, and no prior data or information associated with the unknown process is available. Under such circumstances, well-known techniques like regression modelling techniques may not work. As a result, an alternative approach may be to observe the general features of the process from the available data. Afterward, a suitable statistical distribution, like a mixture of certain distributions, can be fitted to the existing available data, and future observations can be predicted using this fitting. For example, one may consider the prediction related to the COVID-19 pandemic. As it occurred for the first time, no prior data was available to apprehend the behaviour and progression of the COVID-19 pandemic. For such cases, a data-based statistical modelling procedure can be adopted to predict future occurrences based on a small data set. This article presents such an application-oriented, data-based statistical modelling procedure with an implementation on the COVID-19 data. The proposed procedure can be used for a wide range of modelling and forecasting of future events.