To capture location shifts in the context of model selection, we propose selecting significant step indicators from a saturating set added to the union of all of the candidate variables. The null retention frequency and approximate non-centrality of a selection test are derived using a ‘split-half’ analysis, the simplest specialization of a multiple-path block-search algorithm. Monte Carlo simulations, extended to sequential reduction, confirm the accuracy of nominal significance levels under the null and show retentions when location shifts occur, improving the non-null retention frequency compared to the corresponding impulse-indicator saturation (IIS)-based method and the lasso.

We have been publishing real-time forecasts of confirmed cases and deaths from coronavirus disease 2019 (COVID-19) since mid-March 2020 (published at www.doornik.com/COVID-19). These forecasts are short-term statistical extrapolations of past and current data. They assume that the underlying trend is informative regarding short-term developments but without requiring other assumptions about how the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus is spreading, or whether preventative policies are effective. Thus, they are complementary to the forecasts obtained from epidemiological models.

Practical aspects of likelihood-based inference and forecasting of series with long mem- ory are considered, based on the arfima(p; d; q) model with deterministic regressors. Sampling characteristics of approximate and exact first-order asymptotic methods are compared. The analysis is extended using modified profile likelihood analysis, which is a higher-order asymptotic method suggested by Cox and Reid (1987). The relevance of the dierences between the methods is investigated for models and forecasts of monthly core consumer price inflation in the US and quarterly overall consumer price inflation in the UK.