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The discrete Fourier transform (dft) of a fractional process is studied. An exact representation of the dft is given in terms of the component data, leading to the frequency domain form of the model for a fractional process. This representation is particularly useful in analyzing the asymptotic behavior of the dft and periodogram in the nonstationary case when the memory parameter d≥12. Various asymptotic approximations are established including some new hypergeometric function representations that are of independent interest. It is shown that smoothed periodogram spectral estimates remain consistent for frequencies away from the origin in the nonstationary case provided the memory parameter d < 1. When d = 1, the spectral estimates are inconsistent and converge weakly to random variates. Applications of the theory to log periodogram regression and local Whittle estimation of the memory parameter are discussed and some modified versions of these procedures are suggested for nonstationary cases.

There is evidence that a stationary short memory process that encounters occasional structural break can show the properties of long memory processes or persistence behaviour which may lead to extreme weather condition. In this chapter, we applied three techniques for testing the long memory for six daily rainfall datasets in Kelantan area. The results explained that all the datasets exhibit long memory. An empirical fluctuation process was employed to test for structural changes using the ordinary least square (OLS)-based cumulative sum (CUSUM) test. The result also shows that structural change was spotted in all datasets. A long memory testing was then engaged to the datasets that were subdivided into their respective break and the results displayed that the subseries follows the same pattern as the original series. Hence, this indicated that there exists a true long memory in the data generating process (DGP) although structural break occurs within the data series.

The purpose of this paper is to report on a sequential three-stage analysis of inflation persistence using monthly data from 11 inflation targeting (IT) countries and, for comparison, the USA, a non-IT country with a history of credible monetary policy.

First, the authors estimate inflation persistence in a rolling-window fractional-integration setting using the semiparametric estimator suggested by Phillips (2007). Second, the authors use tests for unknown structural breaks as a means to identify effects of the regime switch and the global financial crisis on inflation persistence. The authors use the sequences of estimated persistence measures from the first stage as dependent variables in the Bai and Perron (2003) structural break tests. Finally, the authors reapply the Phillips (2007) estimator to the subsamples defined by the breaks.

Four countries (Canada, Iceland, Mexico, and South Korea) experience a structural break in inflation persistence that coincide with the implementation of the IT regime, and three IT countries (Sweden, Switzerland, and the UK), as well as the USA experience a structural break in inflation persistence that coincides with the global financial crisis.

The authors find that in most cases the estimates of inflation persistence switch from mean-reversion nonstationarity to mean-reversion stationarity.

Monetary policy implications differ between pre- and post-global financial crisis.

Global financial crisis affected the persistence of inflation rates.

First paper to consider the effect of the global financial crisis on inflation persistence.

The recent unprecedented levels reached by financial ratios have led to a re‐examination of their time‐series properties, with evidence of long memory and nonlinearity reported. The purpose of this paper is to re‐examine the nature of these series in the light of potential time‐variation in the unconditional mean.

The paper uses econometric techniques designed to capture fractional integration, nonlinearity and time‐variation in the unconditional mean level of a series.

Reported results support such time‐variation, with cyclical behaviour evident in the unconditional mean of each ratio. Evidence of nonlinearity is still apparent in the mean‐adjusted series.

A key result that arises is that accounting for this time‐variation appears to provide improved long horizon returns predictability.

The paper demonstrates that a nonlinear model incorporating a time‐varying mean improves returns predictability. This is of interest to market participants.

The purpose of this paper is to provide empirical evidence on the long-memory behaviour of South African real estate investment trusts (SAREITs).

The study employs a battery of advanced techniques to examine the behaviour of returns of 29 SAREIT equities listed on the Johannesburg Stock Exchange. The authors analysed daily closing prices covering different periods up to 21 May 2016. The results provide support for long memory in majority of SAREIT returns.

The finding of negative fractional integration parameters provides evidence of anti-persistence in SAREIT returns.

It is recommended that the regulatory authorities adopt technologies that allow a more effective, faster means to disseminate information, and improve the electronic trading mechanism that facilitates quicker price adjustment to news entering the market.

The paper determines the fractional differencing (long-memory) parameter for SAREITs and adds value to the existing body of knowledge.

This study aims to analyse the conditional volatility of the Vietnam Index (Ho Chi Minh City) and the Hanoi Exchange Index (Hanoi) with a specific focus on their application to risk management tools such as Expected Shortfall (ES).

First, the author tests both indices for long memory in their returns and squared returns. Second, the author applies several generalised autoregressive conditional heteroskedasticity (GARCH) models to account for asymmetry and long memory effects in conditional volatility. Finally, the author back tests the GARCH models’ forecasts for Value-at-Risk (VaR) and ES.

The author does not find long memory in returns, but does find long memory in the squared returns. The results suggest differences in both indices for the asymmetric impact of negative and positive news on volatility and the persistence of shocks (long memory). Long memory models perform best when estimating risk measures for both series.

Short-time horizons to estimate the variance should be avoided. A combination of long memory GARCH models with skewed Student’s t-distribution is recommended to forecast VaR and ES.

Up to now, no analysis has examined asymmetry and long memory effects jointly. Moreover, studies on Vietnamese stock market volatility do not take ES into consideration. This study attempts to overcome this gap. The author contributes by offering more insight into the Vietnamese stock market properties and shows the necessity of considering ES in risk management. The findings of this study are important to domestic and foreign practitioners, particularly for risk management, as well as banks and researchers investigating international markets.

The main goal of this paper is to investigate whether there is long-memory behavior in the CBOE Brazil ETF volatility index (named here VIXBR). As structural breaks may create a spurious long-range dependence, the presence of structural breaks is also gauged.

The study considers the period from October 2011 to March 2021, using daily data. To test the long-memory behavior, three empirical approaches are adopted: GPH, ELW and robust GPH (RGPH) estimator. To estimate the structural break points adopted to date the subsamples, the ICSS algorithm is used.

Results considering the total period (TP) and subsamples show that the breaks did not create a spurious long-memory behavior and together with the rolling estimation, reveal strong evidence of the long-range dependence in the CBOE Brazil ETF volatility index. The higher degree of persistent of the VIXBR series suggests an extended period of increased uncertainty that agents need consider when making their investment decision.

As possible extension of this study is to investigate the behavior of long memory and structural breaks for different frequencies (weekly, monthly, among others).

The presence of long-range dependence in the CBOE Brazil ETF volatility index reveals that the past information is important for the predictability of risks, and therefore, can help to protect against market risks, which has important implications regarding the future decisions of economic agents (for example, policy makers and investors).

Brazil is an emerging capital market (ECM) that has attracted a great deal of attention from investors and investment funds seeking to diversify its assets. This paper contributes to the empirical financial literature, by studying the long-memory behavior of the CBOE Brazil ETF volatility index, considering possible structural breaks. To the best of knowledge, this has not been done so far.

Measurement of diminishing or divergent cross section dispersion in a panel plays an important role in the assessment of convergence or divergence over time in key economic indicators. Econometric methods, known as weak σ-convergence tests, have recently been developed (Kong, Phillips, & Sul, 2019) to evaluate such trends in dispersion in panel data using simple linear trend regressions. To achieve generality in applications, these tests rely on heteroskedastic and autocorrelation consistent (HAC) variance estimates. The present chapter examines the behavior of these convergence tests when heteroskedastic and autocorrelation robust (HAR) variance estimates using fixed-b methods are employed instead of HAC estimates. Asymptotic theory for both HAC and HAR convergence tests is derived and numerical simulations are used to assess performance in null (no convergence) and alternative (convergence) cases. While the use of HAR statistics tends to reduce size distortion, as has been found in earlier analytic and numerical research, use of HAR estimates in nonparametric standardization leads to significant power differences asymptotically, which are reflected in finite sample performance in numerical exercises. The explanation is that weak σ-convergence tests rely on intentionally misspecified linear trend regression formulations of unknown trend decay functions that model convergence behavior rather than regressions with correctly specified trend decay functions. Some new results on the use of HAR inference with trending regressors are derived and an empirical application to assess diminishing variation in US State unemployment rates is included.