Epidemiology SIR with Regression, Arima, and Prophet in Forecasting Covid-19

Epidemiology maths resorts to Susceptible-Infected-Recovered (SIR)-like models to describe contagion evolution curves for diseases such as Covid-19. Other time series estimation approaches can be used to fit and forecast curves. We use data from the Covid-19 pandemic infection curves of 20 countries to compare forecasting using SEIR (a variant of SIR), polynomial regression, ARIMA and Prophet. Polynomial regression deg2 (POLY d(2)) on differentiated curves had lowest 15 day forecast errors (6% average error over 20 countries), SEIR (errors 25–68%) and ARIMA (errors 15–85%) were better for spans larger than 30 days. We highlight the importance of SEIR for longer terms, and POLY d(2) in 15-days forecasting.

Uniform nonparametric inference for time series using Stata

In this article, we introduce a command, tssreg, that conducts nonparametric series estimation and uniform inference for time-series data, including the case with independent data as a special case. This command can be used to nonparametrically estimate the conditional expectation function and the uniform confidence band at a user-specified confidence level, based on an econometric theory that accommodates general time-series dependence. The uniform inference tool can also be used to perform nonparametric specification tests for conditional moment restrictions commonly seen in dynamic equilibrium models.

A semiparametric model for matrix regression

We focus on regression problems in which the predictors are naturally in the form of matrices. Reduced rank regression and related regularized method have been adapted to matrix regression. However, linear methods are restrictive in their expressive power. In this work, we consider a class of semiparametric additive models based on series estimation of nonlinear functions which interestingly induces a problem of 3rd order tensor regression with transformed predictors. Risk bounds for the estimator are derived and some simulation results are presented to illustrate the performances of the proposed method.