A Long Memory Time Series Approach to Convergence: The COVID19 pandemic and other applications
The concept of convergence (or lack of it) over time among different indicators of economic or social activity is central in the study of many economic phenomena. For example, one of the main predictions of (neoclassical) economic growth theory is that economies with the same productivity would grow at the same rate and converge to the same equilibrium. This is the so called growth convergence hypothesis, which has been one of the main focal points of the empirical economic growth literature. Currently, with the COVID‑19 pandemic, there has been a heated discussion in policy circles about the possible merits of different policy initiatives (such as strict lockdowns or more voluntary social distancing measures) to deal with its spread and its effect on economic activity. An analysis of convergence (divergence) of COVID‑19 cases and deaths among different countries that adopted similar (different) policies would shed some light on this debate. Given that the spread of COVID‑19 may follow recurring phases with different variants with higher infection rates coupled with the presence of vaccines, the approach that we propose may prove very useful in capturing the speed that different policy options converge in their outcome so that one can assess their relative economic and human costs.
We will use a long memory analytical framework to examine the convergence of COVID‑19 case gaps relying on the estimation of d, the parameter that describes the underlying (long-memory) process and determines the speed of convergence gaps between different countries, see Stengos and Yazgan (2014a, 2014b). We will develop a general Markov-Switching-Autoregressive Fractional Integrated Moving Average (MS-ARFIMA(p,d,q) model that allows for the presence of structural breaks in the long memory parameter d as well as in the mean function we would examine the contamination effect of structural breaks between the mean parameters and the long memory parameter and analyze the properties of these parameter estimators both analytically and by means of Monte Carlo simulations. Secondly, we will combine the above MS-ARFIMA(p,d,q) model with the maximal clique method of Bron and Kerbosch (1973) and Konc and Janezic (2007), examined extensively by Beylunioglu, Stengos and Yazgan (2020) as a clustering algorithm within an I(1)/I(0) framework to study the evolution of membership into a (convergent) group of countries as it may change over time. However, the above framework does not allow for movement between different regimes and the properties of the maximal clique method as a clustering algorithm are unknown if a long memory framework is adopted and the plan is to examine its properties by means of extensive Monte Carlo simulations as in by Beylunioglu, Stengos and Yazgan (2020) and Corrado et al (2021).
We will develop a unified methodology to examine the process of convergence in cases and reported deaths in the different possible phases of the COVID‑19 spread among different territories (provinces) and countries that have adopted different measures to cope with the pandemic. Our methodology would be useful in general when long available time series data exist to empirically assess whether economic policies that are designed to establish convergence in living standards between different countries or regions are successful. Within the boundaries of a given country such as Canada, that would allow for a more accurate examination of the success for example of regional transfers in establishing the equalization of prosperity across all regions in the country. Across countries, the same will be done over time within a geographical region such as the European Union for example. The different situations described above will lead to different academic papers