Search Results (17)

Fractional cointegration has been extensively examined in time series analysis, but its extension to heterogeneous panel data with unobserved heterogeneity and cross-sectional dependence remains underdeveloped. This paper develops a robust framework for testing fractional cointegration in heterogeneous panel data, where unobserved heterogeneity, cross-sectional dependence, and persistent shocks complicate traditional approaches. We propose the Bayesian Tapered Narrowband Least Squares (BTNBLS) estimator, which addresses three critical challenges: (1) spectral leakage in long-memory processes, mitigated via tapered periodograms; (2) precision loss in fractional parameter estimation, resolved through narrowband least squares; and (3) unobserved heterogeneity in cointegrating vectors (${\theta }_i$) and memory parameters ($\nu ,\delta$), modeled via hierarchical Bayesian priors. Monte Carlo simulations demonstrate that BTNBLS outperforms conventional estimators (OLS, NBLS, TNBLS), achieving minimal bias (0.041–0.256), near-nominal coverage probabilities (0.87–0.94), and robust control of Type 1 errors (0.01–0.07) under high cross-sectional dependence ($\rho =0.8$), while the Bayesian Chen–Hurvich test attains near-perfect power (up to 1.00) in finite samples. Applied to Purchasing Power Parity (PPP) in 18 fragile Sub-Saharan African economies, BTNBLS reveals statistically significant fractional cointegration between exchange rates and food price ratios in 15 countries ($p<0.05$), with a pooled estimate ($\widehat{\theta }=0.33$, $p<0.001$) indicating moderate but resilient long-run equilibrium adjustment. These results underscore the importance of Bayesian shrinkage and spectral tapering in panel cointegration analysis, offering policymakers a reliable tool to assess persistence of shocks in institutionally fragmented markets. Full article

In analyzing the decoupling of emissions from economic growth, current literature foregoes the nonlinear complexities of macroeconomic systems, leading to ineffective energy transition policies, specifically for developing countries. This study focuses on the Indian energy–economy–emission nexus to establish a control system that internalizes inflation, trade openness, and fossil fuel imports with economic growth and macro-emissions to visualize the complex pathways of decoupling. Through long-term cointegration and vector error correction modeling, it was found that GDP and energy affect capital, inflation and energy imports, which are locked in a long-run negative feedback loop that ultimately increases emissions. Capital growth enables decoupling at 0.7% CO₂ emissions reduction for every 1% capital growth, while 1% inflation growth inhibits decoupling by increasing CO₂ emissions by 0.8%. A cybernetic fractional circuit of R-C elements and operational amplifiers was utilized to examine the delay of pulses from GDP to the loop elements, which revealed that capital is periodic with GDP pulses. However, inflation, being aperiodic with the clock pulses of GDP, causes the pulse-width of capital to decrease and fossil fuel imports to increase. Through the circuital model, it was possible to determine the exact policy intervention schedule in business cycle growth and recession phases that could build clean energy capital and limit inflation-induced recoupling. Full article

Fractional cointegration in time series data has been explored by several authors, but panel data applications have been largely neglected. A previous study of ours discovered that the Chen and Hurvich fractional cointegration test for time series was fairly robust to a moderate degree of heterogeneity across sections of the six tests considered. Therefore, this paper advances a customized version of the Chen and Hurvich methodology to detect cointegrating connections in panels with unobserved fixed effects. Specifically, we develop a test statistic that accommodates variation in the long-term cointegrating vectors and fractional cointegration parameters across observational units. The behavior of our proposed test is examined through extensive Monte Carlo experiments under various data-generating processes and circumstances. The findings reveal that our modified test performs quite well comparatively and can successfully identify fractional cointegrating relationships in panels, even in the presence of idiosyncratic disturbances unique to each cross-sectional unit. Furthermore, the proposed modified test procedure established the presence of long-run equilibrium between the exchange rate and labor wage of 36 countries’ agricultural markets. Full article

This paper investigates the relationships of the Bloomberg Gender Equality Index and the MSCI World Index in global financial markets. The main objective is to analyze the degree of integration of each index from a fractional perspective for the years 2014–2021. The methodology involves fractional integration to assess the consistency and integration levels of both indices, revealing that they are remarkably consistent with integration orders close to 1 and no evidence of mean-reverting behavior. When examining potential cointegrating relationships between the two indices using the classical two-step method of Engle and Granger, the order of integration of the estimated errors is very close to 1, showing no evidence of cointegration. However, employing the more robust fractional CVAR (FCVAR) approach, the results strongly support the hypothesis of cointegration, indicating evidence of long-term co-movements between the two indices. The findings suggest that investment strategies should incorporate gender diversity criteria, as companies aligning with these benchmarks may enhance co-movements with the Bloomberg Gender Equality Index. Policymakers should promote transparency and initiatives that support gender diversity to improve market stability. Full article

Asymptotic theories for fractional cointegrations have been extensively studied in the context of time series data, with numerous empirical studies and tests having been developed. However, most previously developed testing procedures for fractional cointegration are primarily designed for time series data. This paper proposes a generalized residual-based test for fractionally cointegrated panels with fixed effects. The test’s development is based on a bivariate panel series with the regressor assumed to be fixed across cross-sectional units. The proposed test procedure accommodates any integration order between $[0,1]$, and it is asymptotically normal under the null hypothesis. Monte Carlo experiments demonstrate that the test exhibits better size and power compared to a similar residual-based test across varying sample sizes. Full article

This paper analyzes the stochastic properties of consumer sentiment to understand how they affected the luxury sector in the United States before and after COVID-19. The results were derived using fractional integration methodologies and suggest that, before the pandemic episode, both variables were expected to be mean reverting and the shocks were transitory, having similar behavior. However, after the appearance of COVID-19, results suggest that consumer sentiment recovered before the luxury sector. Results from the use of cointegration methodologies show that the effects of COVID-19 disappeared in the short-run. Finally, the sentiment of consumers acts as a leading indicator of the behavior of the luxury sector according to wavelet analysis. Thus, an increase in consumer sentiment implies an increase of 3.6% in the luxury sector. Full article

This paper deals with the analysis of the temperatures in a group of 36 African countries. By looking at the maximum, minimum and the range (the difference between the maximum and the minimum) and using a long memory model based on fractional integration and cointegration, we first show that all series display a long memory pattern, with a significant positive time trend in 29 countries for the maximum temperatures and in 33 for the minimum ones. Looking at the range, the estimated value for the order of integration is smaller than the one based on maximum or minimum temperatures in 17 countries. Performing fractional cointegration tests between the maximum and minimum temperatures, our results indicate that the two series cointegrate in the classical sense (i.e., with a short memory equilibrium relationship) in a group of 11 countries, and there is another group of eight countries displaying cointegration in the fractional sense. The remaining 17 countries with no evidence of cointegration are therefore at a very high risk of climate change due to the absence of long-term co-movement in their maximum and minimum temperatures. Findings in this paper are of tremendous interpretations and relevance for the analysis and climate projections in Africa. Full article

This paper analyzes the stochastic properties in clinical disorders to understand how they have manifested in consumer sentiment in the USA since 1990. The results obtained via fractional integration methodologies exhibit a high degree of persistence, finding non-mean reversion behavior in all of the time series analyzed, except for depressive disorder. Using a causality test, we find that mental and substance use disorders, anxiety disorder, schizophrenia, and alcohol use disorder influence consumer sentiment. Focusing on the cointegrating part, we conclude that an increase in the previously cited mental disorders produces a decrease in the Consumer Sentiment Index. Full article

In this paper, we use a copula to examine the relationship and dynamic dependence structure between the crude oil market and the BRICS countries’ stock indices expressed through financial crises, from the 2008 global financial crisis to COVID-19, based on daily data. We characterize the long-term relationship as well as the short-term dynamics and represent the interdependence between them. We also study the short-run conditional links through the considered variables under the effects of long-run interactions and the asymmetric volatility spillover relationship. In addition, we establish that the volatility transmission is stubborn and that the impact of the crises and our empirical findings prove that there is fractional co-integration between crude oil and financial markets. We notice that there are lengthy correlations between the variables, as we detect significant bidirectional causal links. In particular, we see positive short-run links and use an optimal copula coefficient to measure the risk spillovers between oil markets and financial markets that represent the dependence structure. For robustness purposes, based on a sliding-window analysis, we complement our investigation with VaR analysis. Full article

At the beginning of the COVID-19 pandemic, the entire world was waiting for a medical solution (for example, vaccines) in order to return to normality. Sanitary restrictions changed our consumption behaviors and feelings. Therefore, this paper analyzes the stochastic properties of consumer sentiment during the COVID-19 episode and the appearance of vaccines against the virus in December 2020 in the United States of America. This study adds a new dimension to the literature because it is the first research paper that uses advanced methodologies based on fractional integration and fractional cointegration analysis to understand the statistical properties of these time series and their behavior in the long term. The results using fractional integration methodologies exhibit a high degree of persistence, finding behavior of mean reversion during the pandemic episode. Therefore, the shock duration in consumer sentiment will be transitory, recovering to its previous trend in the short run. Focusing on the cointegrating part, we arrive at two main conclusions. First, an increase in total vaccination produces a positive reaction or impact on the behavior of consumers. On the other hand, an increase in new COVID-19 cases negatively affects the behavior of the consumer. Full article

This article was prepared for the Special Issue “Celebrated Econometricians: Katarina Juselius and Søren Johansen” of Econometrics. It is based on material recorded on 30 October 2018 in Copenhagen. It explores Søren Johansen’s research, and discusses inter alia the following issues: estimation and inference for nonstationary time series of the I(1), I(2) and fractional cointegration types; survival analysis; statistical modelling; likelihood; econometric methodology; the teaching and practice of Statistics and Econometrics. Full article

This paper aims to both fit and predict crop biophysical variables with a SAR image series by performing a factorial experiment and estimating time series models using a combination of forecasts. Two plots of barley grown under rainfed conditions in Spain were monitored during the growing cycle of 2015 (February to June). The dataset included nine field estimations of agronomic parameters, 20 RADARSAT-2 images, and daily weather records. Ten polarimetric observables were retrieved and integrated to derive the six agronomic and monitoring variables, including the height, biomass, fraction of vegetation cover, leaf area index, water content, and soil moisture. The statistical methods applied, namely double smoothing, ARIMAX, and robust regression, allowed the adjustment and modelling of these field variables. The model equations showed a positive contribution of meteorological variables and a strong temporal component in the crop’s development, as occurs in natural conditions. After combining different models, the results showed the best efficiency in terms of forecasting and the influence of several weather variables. The existence of a cointegration relationship between the data series of the same crop in different fields allows for adjusting and predicting the results in other fields with similar crops without re-modelling. Full article

We estimate fundamental pricing relationships in selected European day-ahead electricity markets. Using a fractionally integrated panel data model with unobserved common effects, we quantify the responsiveness of hourly electricity prices to two fundamental leading indicators of day-ahead markets: the predicted load and renewable generation. The application of fractional cointegration analysis techniques gives further insight into the pricing mechanism of power delivery contracts, enabling us to measure the persistence of fundamental shocks. Full article

It is commonly found that the markets for long-term government bonds of Economic and Monetary Union (EMU) countries were integrated prior to the EMU debt crisis. Contrasting this, we show, based on the interrelation between market integration and fractional cointegration, that there were periods of integration and disintegration that coincide with bull and bear market periods in the stock market. An econometric argument about the spectral behavior of long-memory time series leads to the conclusion that there is a stronger differentiation between bonds with different default risks. This implied the possibility of macroeconomic and fiscal divergence between the EMU countries before the crisis periods. Full article

This paper revisits the question whether volatilities of different markets and trading zones have a long-run equilibrium in the sense that they are fractionally cointegrated. We consider the U.S., Japanese and German stock, bond and foreign exchange markets to see whether there is fractional cointegration between the markets in one trading zone or for one market across trading zones. Also the other combinations of different markets in different trading zones are considered. Applying a purely semiparametric approach through the whole analysis shows fractional cointegration can only be found for a small minority of different cases. Investigating further we find that all volatility series show persistence breaks during the observation period which may be a reason for different findings in previous studies. Full article