No abstract

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.

a b s t r a c tWe consider model selection facing uncertainty over the choice of variables and the occurrence and timing of multiple location shifts. General-to-simple selection is extended by adding an impulse indicator for every observation to the set of candidate regressors: see Johansen and Nielsen (2009). We apply that approach to a fat-tailed distribution, and to processes with breaks: Monte Carlo experiments show its capability of detecting up to 20 shifts in 100 observations, while jointly selecting variables. An illustration to US real interest rates compares impulse-indicator saturation with the procedure in Bai and Perron (1998).

We outline a range of criteria for evaluating model selection approaches that have been used in the literature. Focusing on three key criteria, we evaluate automatically selecting the relevant variables in an econometric model from a large candidate set. General-tospecific selection is outlined for a regression model in orthogonal variables, where only one decision is required to select, irrespective of the number of regressors. Comparisons with an automated model selection algorithm, Autometrics (Doornik, 2009), show similar properties, but not restricted to orthogonal cases. Monte Carlo experiments examine the roles of post-selection bias corrections and diagnostic testing, and evaluate selection in dynamic models by costs of search versus costs of inference.JEL classifications: C51, C22.

We have been publishing real-time forecasts of confirmed cases and deaths for COVID-19 from mid-March 2020 onwards, 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 of short term developments, without requiring other assumptions of how the SARS-CoV-2 virus is spreading, or whether preventative policies are effective. As such they are complementary to forecasts from epidemiological models. The forecasts are based on extracting trends from windows of the data, applying machine learning, and then computing forecasts by applying some constraints to this flexible extracted trend. The methods have previously been applied to various other time series data and have performed well. They are also effective in this setting, providing better forecasts in the earlier stages than some epidemiological models.

a b s t r a c tA new test for non-linearity in the conditional mean is proposed using functions of the principal components of regressors. The test extends the non-linearity tests based on Kolmogorov-Gabor polynomials (Thursby and Schmidt, 1977;Tsay, 1986;Teräsvirta et al., 1993), but circumvents problems of high dimensionality, is equivariant to collinearity, and includes exponential functions, so is a portmanteau test with power against a wide range of possible alternatives. A Monte Carlo analysis compares the performance of the test to the optimal infeasible test and to alternative tests. The relative performance of the test is encouraging: the test has the appropriate size and has high power in many situations.

a b s t r a c tWhen location shifts occur, cointegration-based equilibrium-correction models (EqCMs) face forecasting problems. We consider alleviating such forecast failure by updating, intercept corrections, differencing, and estimating the future progress of an 'internal' break. Updating leads to a loss of cointegration when an EqCM suffers an equilibrium-mean shift, but helps when collinearities are changed by an 'external' break with the EqCM staying constant. Both mechanistic corrections help compared to retaining a prebreak estimated model, but an estimated model of the break process could outperform. We apply the approaches to EqCMs for UK M1, compared with updating a learning function as the break evolves.

We consider the reasons for nowcasting, the timing of information and sources thereof, especially contemporaneous data, which introduce different aspects compared to forecasting. We allow for the impact of location shifts inducing nowcast failure and nowcasting during breaks, probably with measurement errors. We also apply a variant of the nowcasting strategy proposed in Castle and Hendry (2009) to nowcast Euro Area GDP growth. Models of disaggregate monthly indicators are built by automatic methods, forecasting all variables that are released with a publication lag each period, then testing for shifts in available measures including survey data, switching to robust forecasts of missing series when breaks are detected.