Long Memory Persistence Research Articles

Impact of COVID-19 on Stock Indices Volatility: Long-Memory Persistence, Structural Breaks, or Both?

The onset of the COVID-19 pandemic has increased volatility in financial markets, motivating researchers to investigate its impact. Some use the GARCH family of models to focus on long-memory persistence, while others use Markov chain models to better identify structural breaks and regimes. However, no study has addressed the occurrence of these two phenomena in a unified framework. Since both are important features of the data, to ignore one or the other could lead to poorly specified models. The outcome would be incorrect risk measurement, with implications for risk management, Value at risk, portfolio decisions, forecasting, and option pricing. This paper aims to fill this gap in the literature. We assemble an international dataset for 16 stock market indices in three continents over the period from August 1, 2019 to February 18, 2022, totalling 669 business days. Using R, we estimate 80 GARCH family models, 16 pure Markov-Switching models, and 900 combined GARCH/ Markov-Switching models using daily stock market log-returns. We allow for two volatility regimes (low and high). We also measure and incorporate News Impact Curves, which show how past shocks affect contemporaneous volatility. Our main finding, across estimated models, is that COVID-19 affected both long-memory persistence and volatility regimes in most markets. To describe the specific impact in each market, we report News Impact Curves. Lastly, the first wave of COVID-19 had a much greater impact on volatility than did subsequent waves linked to the emergence of new variants.

Long-memory and volatility spillovers across petroleum futures

Return volatility usually presents a degree of persistence, which, although still consistent with an essential stationary process, cannot be adequately captured by standard autoregressive specifications. In this study, we examine the transmission mechanism across petroleum volatilities accounting for this stylized fact. To do so, we compute both time and frequency domain measures of connectedness based on variance decompositions from a fractionally integrated VAR (FIVAR). Our main findings summarize: (1) there is strong evidence of long-memory in petroleum volatilities, but no evidence of infinite variances; (2) an adequate quantification of spillovers must consider long-memory persistence explicitly; (3) spillovers are relatively high, but considerably lower than predicted in the traditional short-memory framework, especially at low frequencies. Thus, accounting for long-memory has asymmetric implications for different market participants.

A novel time-varying FIGARCH model for improving volatility predictions

The FIGARCH model has received wide attention due to its ability to capture the features of volatility long-memory persistence and clustering. The classical FIGARCH model is based on the difference scheme of Grünwald–Letnikov fractional operators. This paper introduces the new class of FIGARCH processes for improving time-varying volatility predictions. Firstly, a novel FIGARCH model based on the Caputo fractional operators (FIGARCH-C model for short) is proposed. Secondly, a quasi-maximum likelihood estimation (QMLE) is used to estimate the parameters of the FIGARCH-C(1, d, 1), the FIGARCH(1, d, 1) and GARCH(1, 1) models. Finally, we apply the three models to Brent crude oil and S&P 500 returns and provide the comparison results of the three models. The results show that the FIGARCH and FIGARCH-C models outperformed the GARCH model in capturing the long memory in volatility. It is also found that the FIGARCH-C model is more sensitive to capture the change in the volatile period.

Regional analysis of wind velocity patterns in complex terrain

Wind energy is a weather and climate-dependent energy resource with natural spatio-temporal variabilities at time scales ranging from fraction of seconds to seasons and years, while at spatial scales it is strongly affected by the terrain and vegetation. To optimize wind energy systems and maximize the energy extraction, wind measurements on various time scales as well as wind energy forecasts are required and needed. This study focuses on spatio-temporal characteristics of the wind velocity in complex terrain, relevant to wind energy assessment, operation, and grid integration, using data collected at 11 towers ranging from 40 to 80 m tall over a 12-year period in complex terrain of western-central and northern Nevada, USA. The autocorrelation analysis, Detrended Fluctuation Analysis (DFA) and Detrended Cross-Correlation Analysis (DCCA) showed strong coherence between the wind speed and direction with slowly decreasing amplitude of the multi-day periodicity with increasing lag periods. Besides pronounced diurnal periodicity at all locations, statistical analysis and DFA also showed significant seasonal and annual periodicities, long-memory persistence with similar characteristics at all sites and towers with a relatively narrow range of the Weibull parameters. The DCCA indicates similar wind patterns at each tower, and strong correlations between measurement sites in spite of separations of about 300 km across the towers’ setup. The northern Nevada area exhibits higher wind resource potential and higher wind persis-tence compared to the western-central region. Overall, the DFA and DCCA results suggest higher degree of complementarity among wind data at measure-ment sites compared to previous standard statistical analysis.

Modeling high-frequency volatility with three-state FIGARCH models

Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity (FIGARCH) models have enjoyed considerable popularity over the past decade because of their ability to capture the features of volatility clustering and long-memory persistence. However, in the presence of structural changes, it is well known that the estimate of long memory will be spurious. Consequently, two modeling approaches are developed to incorporate structural changes into the FIGARCH framework. One approach is to model the intercept in the conditional variance equation via a certain function of time. Based on this approach, the Adaptive-FIGARCH (A-FIGARCH) and Time-Varying FIGARCH (TV-FIGARCH) models are proposed. The second approach is to model the time-series in separate stages. In the first stage, a certain algorithm is applied to detect the change points. The FIGARCH model is fitted to the time-series in the next stage, with the intercept (and other parameters) being allowed to vary between change points. An example of a recently developed algorithm for detecting change points is the Nonparametric Change Point Model (NPCPM), which can be readily applied to the standard FIGARCH framework (NPCPM-FIGARCH). In this paper, we adopt the second approach but use the Markov Regime-Switching (MRS) model to detect the change points and identify three economic states depending on the scale of volatility. This new 2-stage Three-State FIGARCH (3S-FIGARCH) framework is compared with other FIGARCH-type models via Monte-Carlo simulations and high-frequency datasets. From the comparison, we find that the 3S-FIGARCH model can largely improve the fit and potentially lead to a more reliable estimator of the long-memory parameter.

Economic Growth under Stochastic Population and Pollution Shocks

We study dynamics of interactions among economic growth, population, and environmental quality when stochastic shocks in these systems display long-memory property. We make two important contributions. First, we show that the long-memory persistence in economic growth is determined jointly by the convergence speed of shocks in both environmental quality and population. Second, by simulating a modified Solow-Swan economy we demonstrate that the convergence-speed of shocks in these systems significantly affects the long-run growth trajectory of output. Our empirical examination evince that adjustment of output to long-run equilibrium is very slow, thanks to the slowly dissipating population and pollution shocks.