Causal Modelling and Forecasting of Covid Time Series
The Covid pandemic has been devastating, causing many deaths in the USA. The government has to manage the pandemic in the best way possible, by introducing new policies, which will be based on certain data. One of the data sources used will be the daily measured Covid cases. However there is a measurement error associated with the day of the week, because at times during the pandemic some states closed all or some test centres over the weekends. This created a ’weekend effect’, where there were zero or reduced measured cases on the weekend, but more than expected measured cases on the adjacent days - Friday and Monday. One of the goals of this thesis was to correct the measurement error caused by the weekend effect. Three different models were developed in order to correct the measurement error in the data. The measurement error is treated as latent variables, and the parameter of the AR(1) process is also treated as a latent variable. Each of the models was based on the Expectation Maximization (EM) algorithm. The best performing model was the most complicated model. A Granger Causality analysis was also conducted on the daily Covid cases between each of the US states. It was found that there is a very slight positive relationship between a state’s population and the number of states it Granger causes. It was also discovered that there is a slight positive relationship between the number of neighboring states a state has and the number of states it Granger causes. The first lag is the most common Granger causing lag. A map of the Granger causing states was created, visualizing which states Granger cause which other states. It shows that most Granger causing occurs in the East side of the USA.
K.M. Toner, "Defense against Gradient Inversion Attacks using Kurtosis Regularization", M.S. Thesis, Machine Learning, MBZUAI, Abu Dhabi, UAE, 2022.