Special Issue of the <i>Journal of Time Series Analysis</i> in Honour of the 35th Anniversary of the Publication of Geweke and Porter‐Hudak (1983): Guest Editors' Introduction

This special issue is a celebration of the 35th anniversary of the publication of John Geweke and Susan Porter-Hudak's (henceforth GPH) 1983 article, ‘The estimation and application of long memory time series models’, in the Journal of Time Series Analysis. Their article started a very large and extremely influential literature on semi-parametric estimation of long memory models. The estimation method proposed by GPH is still widely applied, even 35 years later, which is an impressive achievement considering how active this research area has been over that period and considering how early their contribution was made. The article has accumulated over 3200 Google Scholar citations in April 2019 at the time of writing this editorial, and it is currently the second-most cited article published in the history of the Journal of Time Series Analysis. It therefore seems appropriate that the article is acknowledged by this special issue in its honour. This issue contains 11 cutting-edge articles on a variety of topics dealing with long memory, fractional integration and/or fractional cointegration. The contributors include both econometricians and statisticians, and are all well known and active researchers in the field. We are grateful to all of them for responding enthusiastically to the call for a special issue, and for submitting such an interesting array of contributions on both theoretical and applied issues. We are particularly pleased that John Geweke and Susan Porter-Hudak were able to contribute to this special issue. Their contribution, which is joint with Garland Durham and Fallaw Sowell, is titled ‘Bayesian inference for ARFIMA models’. The article develops methods for Bayesian inference in autoregressive fractionally integrated moving average (ARFIMA) models that are practical even for large sample sizes by exploiting, for instance, massively parallel computing with graphics processing units. To this end, the article also identifies, discusses and solves several important numerical issues in the computation of the exact likelihood function of the ARFIMA model. Within the general topic of estimation and inference for univariate long memory models, this issue includes another four articles. In their contribution ‘A self-normalized semi-parametric test to detect changes in the long memory parameter’, Taqqu and Zhang propose a new test to detect change points in the long memory parameter based on the semi-parametric estimator of Robinson (1994). Specifically, this work extends the test of Wang and Wang (2006) in two relevant directions: the new test uses a self-normalizer to pivotalize the asymptotic distribution and multiple change points are allowed. Gupta and Hidalgo, in their contribution ‘Order selection and inference with long memory dependent data’, add to the model selection literature by proposing a criterion based on the frequency decomposition of the variance of the innovation errors, allowing the order of the short memory component to be finite with an unknown upper bound. In an empirical likelihood setting, Lahiri, Das and Nordman's contribution ‘Empirical likelihood for a long range dependent process subordinated to a Gaussian process’, derives new results for a class of long range dependent processes driven by a stationary Gaussian process. In particular, they analyse the block empirical likelihood approach and also its variant, the expansive block empirical method, justifying the advantages of the latter approach in a long memory setting. Finally, in their contribution ‘A generalised fractional differencing bootstrap for long memory processes’, Papailias, Kapetanios and Taylor analyse a bootstrap algorithm, where the time series is fractionally differenced according to an estimated fractional difference parameter and the resulting approximation to the underlying short memory series is resampled. An extension to blockwise bootstraps is also considered. A natural extension of the univariate long memory model considered by GPH is multivariate models with long memory variables, for example regression models, fractional cointegration models or panel data models. This is the topic of four articles in this issue. First, ‘Asymptotic distribution of the bias corrected least squares estimators in measurement error linear regression models under long memory’ by Koul and Surgailis presents the limiting properties of a bias corrected least squares estimator in a linear regression model when predictive variables have measurement error and when the covariate, error and measurement error processes all have long memory. In a fractionally cointegrated vector autoregressive (VAR) setting, Johansen and Nielsen's contribution ‘Nonstationary cointegration in the fractionally cointegrated VAR model’ extends Johansen and Nielsen (2012) by relaxing substantially some strong moment conditions and at the same time allowing for non-stationary cointegrating errors. In their contribution ‘Fixed bandwidth inference for fractional cointegration’, Hualde and Iacone derive fixed-bandwidth asymptotic theory for a class of estimators of the cointegration parameter based on weighted periodogram averages and investigate whether the fixed-bandwidth approach provides a more accurate approximation to the sampling distribution of relevant test statistics. In recent work on panel data models with fixed effects and persistent data and shocks, which are assumed to be fractionally integrated, Ergemen and Velasco (2017) allow the fractional integration parameters to vary across cross-sectional units, which leads to greater flexibility in modelling the dynamics of the panel. The contribution ‘Persistence heterogeneity testing in panels with interactive fixed effects’ by Ergemen and Velasco extends this work by considering the problem of testing homogeneity of the dynamics of the cross-sectional units, including the fractional integration parameters, and developing tests that have no trivial power under local departures from the null of a non-negligible fraction of the cross-sectional units. Financial economics, and particularly financial volatility modelling, has been a very successful area of application of long memory models. This issue contains two articles within this area. First, ‘The slow convergence of ordinary least squares estimators of α, β and portfolio weights under long-memory stochastic volatility’ by Liu, Deo and Hurvich considers inference for the market model coefficients based on simple linear regression when returns are generated by a long memory stochastic volatility model. Specifically, limit theorems for ordinary least squares estimators and for estimated weights of the minimum variance portfolio and the optimal portfolio are derived. Second, in ‘Long memory, realized volatility and HAR models’, Baillie, Calonaci, Cho and Rho investigate the origins of long memory in realized volatility. Specifically, the article assesses the separate roles of fractionally integrated long memory models, extended heterogeneous autoregressive (HAR) models, and time varying parameter HAR models in modelling realized volatility measures. To conclude, we would like to thank the Editor-in-Chief, Rob Taylor, for his support of our proposal to honour GPH's very influential article with this special issue of the Journal of Time Series Analysis.

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