Jurgen A. Doornik’s research while affiliated with University of Oxford and other places

UK top income shares have varied hugely over the past two centuries, ranging from more than 30% to less than 7% of pre‐tax national income allocated to the top 1 percentile. We build a congruent dynamic linear regression model of the top 1% income share allowing for economic, political and social factors. Saturation estimation is used to model outliers and trend breaks, proxying underlying structural changes driving income inequality in the UK. We use the model to forecast the top 1% income share over the last 15 years, and compare to a range of forecast devices. Despite a well‐specified constant parameter model conditioning on significant explanatory variables, the best performing forecasts are obtained from a random walk and a smoothed random walk. These results are explained by the presence of shifts in the income share over the forecast period, resulting in forecasts from equilibrium correction models converging to the wrong equilibrium. Our best prediction for 2026 based on the most recent data from 2021 (a 5‐year ahead projection) is that the pre‐tax top 1% income share will remain at the most recent realized value of 12.7%, but there is a large degree of uncertainty, with a 95% confidence band ranging from 10% to 15.7%.

By its emissions of greenhouse gases, economic activity is the source of climate change which affects pandemics that in turn can impact badly on economies. Across the three highly interacting disciplines in our title, time-series observations are measured at vastly different data frequencies: very low frequency at 1000-year intervals for paleoclimate, through annual, monthly to intra-daily for current climate; weekly and daily for pandemic data; annual, quarterly and monthly for economic data, and seconds or nano-seconds in finance. Nevertheless, there are important commonalities to economic, climate and pandemic time series. First, time series in all three disciplines are subject to non-stationarities from evolving stochastic trends and sudden distributional shifts, as well as data revisions and changes to data measurement systems. Next, all three have imperfect and incomplete knowledge of their data generating processes from changing human behaviour, so must search for reasonable empirical modeling approximations. Finally, all three need forecasts of likely future outcomes to plan and adapt as events unfold, albeit again over very different horizons. We consider how these features shape the formulation and selection of forecasting models to tackle their common data features yet distinct problems.

Objective: We analyze the number of recorded cases and deaths of COVID-19 in many parts of the world, with the aim to understand the complexities of the data, and produce regular forecasts. Methods: The SARS-CoV-2 virus that causes COVID-19 has affected societies in all corners of the globe but with vastly differing experiences across countries. Health-care and economic systems vary significantly across countries, as do policy responses, including testing, intermittent lockdowns, quarantine, contact tracing, mask wearing, and social distancing. Despite these challenges, the reported data can be used in many ways to help inform policy. We describe how to decompose the reported time series of confirmed cases and deaths into a trend, seasonal, and irregular component using machine learning methods. Results: This decomposition enables statistical computation of measures of the mortality ratio and reproduction number for any country, and we conduct a counterfactual exercise assuming that the United States had a summer outcome in 2020 similar to that of the European Union. The decomposition is also used to produce forecasts of cases and deaths, and we undertake a forecast comparison which highlights the importance of seasonality in the data and the difficulties of forecasting too far into the future. Conclusion: Our adaptive data-based methods and purely statistical forecasts provide a useful complement to the output from epidemiological models.

We investigate forecasting in models that condition on variables for which future values are unknown. We consider the role of the significance level because it guides the binary decisions whether to include or exclude variables. The analysis is extended by allowing for a structural break, either in the first forecast period or just before. Theoretical results are derived for a three-variable static model, but generalized to include dynamics and many more variables in the simulation experiment. The results show that the trade-off for selecting variables in forecasting models in a stationary world, namely that variables should be retained if their noncentralities exceed unity, still applies in settings with structural breaks. This provides support for model selection at looser than conventional settings, albeit with many additional features explaining the forecast performance, and with the caveat that retaining irrelevant variables that are subject to location shifts can worsen forecast performance.

Successful modeling of observational data requires jointly discovering the determinants of the underlying process and the observations from which it can be reliably estimated, given the near impossibility of pre-specifying both. To do so requires avoiding many potential problems, including substantive omitted variables; unmodeled non-stationarity and misspecified dynamics in time series; non-linearity; and inappropriate conditioning assumptions, as well as incorrect distributional shape combined with contaminated observations from outliers and shifts. The aim is to discover robust, parsimonious representations that retain the relevant information, are well specified, encompass alternative models, and evaluate the validity of the study. An approach is proposed that provides robustness in many directions. It is demonstrated how to handle apparent outliers due to alternative distributional assumptions; and discriminate between outliers and large observations arising from non-linear responses. Two empirical applications, utilizing datasets popularized in previous applications, show substantive improvements from the proposed approach to robust model discovery.

The Covid-19 pandemic has put forecasting under the spotlight, pitting epidemiological models against extrapolative time-series devices. We have been producing real-time short-term forecasts of confirmed cases and deaths using robust statistical models since 20 March 2020. The forecasts are adaptive to abrupt structural change, a major feature of the pandemic data due to data measurement errors, definitional and testing changes, policy interventions, technological advances and rapidly changing trends. The pandemic has also led to abrupt structural change in macroeconomic outcomes. Using the same methods, we forecast aggregate UK unemployment over the pandemic. The forecasts rapidly adapt to the employment policies implemented when the UK entered the first lockdown. The difference between our statistical and theory based forecasts provides a measure of the effect of furlough policies on stabilising unemployment, establishing useful scenarios had furlough policies not been implemented.

Economic forecasting is difficult, largely because of the many sources of nonstationarity influencing observational time series. Forecasting competitions aim to improve the practice of economic forecasting by providing very large data sets on which the efficacy of forecasting methods can be evaluated. We consider the general principles that seem to be the foundation for successful forecasting, and show how these are relevant for methods that did well in the M4 competition. We establish some general properties of the M4 data set, which we use to improve the basic benchmark methods, as well as the Card method that we created for our submission to that competition. A data generation process is proposed that captures the salient features of the annual data in M4.