Given the nutritional relevance and health benefits of fishery products consumption, this article examines the statistical properties of fishery products consumption in 25 OECD countries from 1961 to 2017, focusing on the degree of persistence. Using a methodology based on fractional integration, we explore if mean reversion takes place in the series or, if on the contrary, shocks do have a permanent nature. The empirical results show the existence of positive time trends in the majority of countries, the only exceptions being Greece, Japan, Portugal and the UK. Mean reversion is found in 17 out of the 25 countries examined; the unit root null hypothesis cannot be rejected in 7, while Japan is the only country with an order of integration significantly higher than 1. These findings suggest that short-term measures are more effective than long-term interventions in promoting fishery products consumption in most OECD countries. The policy implications are discussed in the final part of the manuscript.

We attempt in this paper to identify financial cycles in 43 countries using data from 1970 to 2019. We use a model based on stochastic cycles that employ fractional integration. The results indicate that the average duration of the cycles is 23 years for Denmark, India, South Korea, Sweden, Spain, Switzerland, and the United States. Our study contributes to the field of research by proposing an alternative model and method for researching financial cycles. The advantage of using such an approach is the ability to isolate more robust stochastic cycles allowing for the possibility of the existence of multiple financial cycles in financial data. It is also found that the credit-GDP ratio exhibits long memory and persistent behavior at the long run frequency. Long memory is found in a number of countries at the cyclical structure with shock of the dynamics of the financial cycle lasting long before disappearing in some of the countries examined.

This paper investigates the persistence of CO2 emissions in the US and per Intergovernmental Panel on Climate Change (IPCC) category contribution, evaluating its persistence across time (1970-2022). The structure of the integration factor and major structural breaks are examined to determine the degree of persistence across sectors and to assess policy effectiveness. Empirical results show clear evidence of persistence and non-mean reversion patterns in the long-term CO2 emissions in all sectors; though, log-data show weak mean reversion across global bioenergetic emissions and fossil manufacturing-civil airline emissions. Moreover, structural breaks results suggest that these breaks are mostly related to economic shocks rather than to environmental policies. Excepting Road and Transportation, all IPCC sectors show decreasing emission patterns since 2000. Thus, this persistent profile would suggest that emissions from these sectors would maintain this decreasing pattern in the future. However, Road and Transportation (29 % of total emissions) exhibit a different growing pattern, that suggests further increases if no additional measures are taken. Therefore, to accomplish IPCC commitments, more efforts are recommended with a special focus in the Road and Transportation sector to change the long-term US CO2 emission pattern.

This paper investigates time series persistence in obesity and severe obesity rates in a group of 38 OECD countries by using techniques based on fractional integration. The idea is to determine if there are trends in the time series and if the impact of health policy exposure might have permanent or transitory effects. The results based on aggregated and disaggregated data by sex indicate high levels of persistence in all cases, with orders of integration of magnitude higher than three. Trends in these rates are also of high magnitudes, particularly in Australia, New Zealand and United Kingdom. An implication of the findings is that long-term measures are required to tame obesity rates and severe obesity rates in OECD countries. The paper finally highlights the long-term measures needed to reduce the alarmingly high obesity rates in the developed countries.

We introduce the fractionally integrated quasi-autoregressive moving average model for the t distribution (t-FI-QARMA), the first fractionally integrated score-driven location model. We apply tFI-QARMA to annual black carbon emissions data for 38 countries from 1820 to 2019. We estimate t-FI-QARMA using the maximum likelihood method for the fractional integration parameter in the interval (-1/2;1/2). We use statistical performance metrics to compare the t-FI-QARMA with its special cases: Gaussian-FI-ARMA, t-QARMA, and Gaussian-ARMA. Heteroscedasticity-robust tests indicate that t-FI-QARMA is superior to all alternatives, finding evidence of long memory patterns in most countries examined.

In this paper, we examine energy demand in a group of Latin American regions using a fractional integration approach. Employing annual data from 1965 to 2023 on primary energy consumption in exajoules (EJ) and per capita consumption in gigajoules (GJ), we investigate the persistence and mean-reverting properties of energy demand over time. The application of fractional integration techniques allows us to capture both short- and long-term dependencies, offering a more flexible framework compared to traditional time series models. Our findings indicate that energy demand in Latin America exhibits long-memory characteristics, implying that shocks to consumption may have prolonged effects, with some countries displaying a slow mean-reverting process while others show evidence of permanent shocks. These heterogeneous results suggest that structural factors, such as economic development, energy policies, and technological advancements, play a crucial role in shaping consumption patterns. Additionally, the study highlights the importance of considering long-run dynamics in energy demand forecasting and policymaking, particularly in the context of economic growth and environmental sustainability. The results emphasize the need for adaptive energy strategies that consider the varying degrees of persistence across countries, aiming for a balance between economic development and the transition towards cleaner energy sources.

Time trends are examined in Arctic temperatures by using a fractionally integrated model. The results indicate that globally, the time trend coefficient is significantly positive and the degree of differentiation is equal to 0.32. Looking at subsamples of 25 years, the time trend is only found to be significantly positive in the last two subsamples, being particularly high in the final one corresponding to data starting at January 2001. For this period, the degree of integration is also the highest across all subsamples. This result supports the hypothesis that temperatures in the Arctic region have increased in recent years.

This note analyses how shocks caused by the Covid-19 and the Russia-Ukraine crisis impact on inflation persistence G7 countries. Using data ending at December-2019, high estimates of the persistence parameter d indicate a strong persistence of inflation. The unit root hypothesis could not be refuted for Germany, Japan, and the United States, while this hypothesis is rejected in favour of higher orders of integration in the remaining cases. Expanding the dataset to include the pandemic and the Russia-Ukraine crisis reveal that d-values remain significantly elevated across all countries, reinforcing the persistence of inflation. Interestingly, Canada, previously excluded from the group, now aligns with Germany, Japan, and the United States. This suggests a change in inflation dynamics for Canada during these extraordinary periods. Additionally, employing a recursive estimate reveals a slight increase in inflation persistence for most countries, except Japan, which exhibits an almost flat trend in the evolution of the differencing parameter.

In this article, we examine the statistical properties of 15 international renewable commodity prices by looking at the degree of persistence from January 1960 to March 2023. Moreover, we also explored if the incidence of the COVID-19 pandemic or Russia-Ukraine war caused a change in persistence or mean reversion of renewable commodity prices. The results suggest that all series are highly persistent, and evidence of mean reversion and transitory shocks are only obtained in some cases for bananas and tea. The COVID-19 pandemic or Russia-Ukraine war has not significantly affected the persistence of the series.

We estimate models of fractional integration to determine the degree of persistence for two recently developed metrics of carbon price uncertainty: the Carbon VIX and Carbon Implied Volatility (CIV) covering the period of the 1st week of September 2013 to the 4th week of December 2022. First, we find the two metrics to be highly persistent but depicting mean-reversion with long-memory. Second, time-varying (recursive) estimation revealed that the underlying persistence is on a downward trend. Third, we show that the recent reduction in persistence of carbon price uncertainties is a result of declining carbon policy uncertainty — a metric we develop using aggregate information on squared surprises of carbon futures price of various maturities. Given that carbon price uncertainty has been shown to negatively affect decarbonization investments, our findings have important implications for the European Union Emissions Trading System (EU-ETS).

Purpose As a result, the primary purpose of the study is to assess the influence of these two shocks on the inflation persistence of the BRICS countries. Design/methodology/approach The most current occurrence of global instability, the COVID-19 outbreak and the ongoing Russia/Ukraine war, provide a unique research opportunity to determine if inflation volatility, generated by the pandemic and the war, is irrevocably linked to its persistence. We apply fractional integration techniques to the price series. Findings Our results indicate high levels of persistence in all countries, with orders of integration higher than 1 in practically all cases. This result holds independently of using data ending in January 2020 or January 2024. India is the only country with an order of integration significantly below 1 in the two cases, and thus showing evidence of mean reversion and transitory shocks. Originality/value

This paper uses fractional integration methods to obtain new evidence on polar amplification. The adopted modelling framework is very general since it allows the differencing parameter to take any real value, including fractional ones, and provides useful information on both the short and the long run. The analysis is carried out using monthly temperature anomaly data for both the Arctic and the Antarctic, as well as the Northern and Southern Hemisphere, which have been obtained from the NOAA (National Center for Environmental Information) archive. The main findings can be summarised as follows. There is evidence of Arctic amplification, since the upward trend in the Arctic data is more pronounced compared to that in the Northern Hemisphere series, but not of Antarctic amplification, where the opposite holds. Also, the effects of forcings are more long-lived in the Arctic/Northern hemisphere than in the other pole/hemisphere. These results are robust to whether or not seasonality is explicitly modelled. In addition, temperature changes in the poles have bigger effects on those in the corresponding hemisphere if they occur in the Antarctic rather than in the Arctic.

This paper analyses US nominal house prices at an annual frequency over the period from 1927 to 2022 by means of a very general time series model. This includes both a (linear and non-linear) deterministic and a stochastic component, with the latter allowing for fractional orders of integration at both the long-run and the cyclical frequencies. The results are heterogeneous depending on the model specification and on whether or not the series have been logged. Specifically, a linear model appears to be more appropriate for the logged data whilst a non-linear one appears to be a better fit for the original ones. Further, the order of integration at the zero or long-run frequency is much higher than at the cyclical one. The former is in fact around 1 in all specified models, which implies a high degree of persistence of this component. Finally, the order of integration of the cyclical structure implies that cycles have a periodicity of about 8 years, but it is almost insignificant in all cases.

This paper uses fractional integration methods to obtain comprehensive evidence on the evolution of the number of hot days, defined as those with temperatures above 35 °C, in 54 countries from various regions of the world over the period from 1950 to 2022. The variable analysed is a key indicator of global warming, and the chosen modelling approach is most informative about the behaviour of the series as it provides evidence on the possible presence of time trends, on whether or not mean reversion occurs, and on the degree of persistence. In brief, the findings indicate the presence of considerable heterogeneity among the countries studied and highlight the importance of tailored climate policies based on both global and local factors.

This paper investigates the presence of long-run trends and persistence in various pollutants in the city of Ulaanbaatar, Mongolia using fractional integration. Using daily data from January 1st, 2022 until May 31st, 2024 we investigate the statistical properties of four pollutants, namely, NO2, SO2, PM10, and PM2.5. The results indicate the presence of significant negative time trends in the cases of SO2 and PM2.5 and evidence of long memory and mean reverting patterns in all four pollutants. Policy implications of the results obtained are reported at the end of the paper.

In this article, daily CO2 emissions for the years 2019–2022 are examined using fractional integration for Brazil, China, EU-27 (and the UK), India, and the USA. According to the findings, all series exhibit long memory mean-reversion tendencies, with orders of integration ranging between 0.22 in the case of India (with white noise errors) and 0.70 for Brazil (under autocorrelated disturbances). Nevertheless, the differencing parameter estimates are all considerably below 1, which supports the theory of mean reversion and transient shocks. These results suggest the need for a greater intensification of green policies complemented with economic structural reforms to achieve the zero-emissions target by 2050.

In this paper we propose a statistical model that combines both autoregressions and fractional differentiation in a unified treatment. However, instead of imposing that the roots are strictly on the unit circle, we also allow them to be within the unit circle. This permits a higher degree of flexibility in the specification of the model, with rates of dependence combining exponential with hyperbolic decays. Monte Carlo experiments and empirical applications to climatological and financial data show that the proposed approach performs well.

PurposeThis paper deals with the stock market prices in Africa. In particular, we focus on data from 14 African countries that have stock exchanges with a market capitalisation of more than US$1bn also capturing stock market dynamics during the COVID-19 pandemic.Design/methodology/approachThe methodology is based on the concept of fractional integration that indicates that the number of differences to be taken in a series to render it stationary I(0) may be a fractional value.FindingsAssuming a white noise process, only the South African stock market displays transitory shocks. Allowing for autocorrelation, the time trend is statistically significant in four countries: Namibia, South Africa, Tunisia and Zimbabwe, although mean reversion is found in two countries: Morocco and South Africa. These two countries are the ones where the random walk can be rejected and thus are informationally inefficient. There is one country (Rwanda) with an estimated value of d above 1, while the unit root null hypothesis cannot be rejected in the remaining countries, implying that in all of them, other than Morocco and South Africa, the random walk hypothesis cannot be rejected.Research limitations/implicationsA limitation of this work is the number of countries examined, 14, due to the lack of available data. Dealing with the methodology, a limitation is also the linear nature of the trend structure examined, which may be extended to non-linear approaches.Practical implicationsThe practical implication is the mean-reverting nature of some of the series examined, implying that no strong measures should be adopted in these cases if exogenous negative shocks occur.Social implicationsThe academia and also practitioners can be interested in the present work, in particular in relation to the mean-reverting nature of the series and the efficient market hypothesis.Originality/valueThe originality in this work comes from the use of fractional integration, a methodology that is not very usual in the analysis of time series data.