JuliaCon 2023

Long range dependence modelling in Julia
07-27, 12:10–12:20 (US/Eastern), 32-123

This talk presents a package to analyse long-range dependence (LRD) in time series data. LRD is shown by the fact that the effects from previous disturbances take longer to dissipate than what standard models can capture. Failing to account for LRD dynamics can perversely affect forecasting performance: a model that does not account for LRD misrepresents the true prediction confidence intervals. LRD has been found in climate, political affiliation and finance data, to name a few examples.


Long-range dependence has been a topic of interest in time series analysis since Granger's study on the shape of the spectrum of economic variables. The author found that long-term fluctuations in data, if decomposed into frequency components, are such that the amplitudes of the components decrease smoothly with decreasing periods. This type of dynamics implies long-lasting autocorrelations; that is, they exhibit long-range dependence. Long-range dependence has been estimated in temperature data, political affiliation data, financial volatility measures, inflation, and energy prices, to name a few. Moreover, it has been shown that the presence of long-range dependence on data can have perverse effects on statistical methods if not included in the modelling scheme.

This talk presents a package for modelling long-range dependence in the data. We develop methods to model long-range dependence by the commonly used fractional difference operator and the theoretically based cross-sectional aggregation scheme. The fast Fourier transform and recursive implementations of the algorithms are used to speed up computations. The proposed algorithms are exact in the sense that no approximation of the number of aggregating units is needed. We show that the algorithms can be used to reduce computational times for all sample sizes.

Moreover, estimators in the frequency domain are developed to test for long-range dependence in the data. A broad range of estimators are considered: the original Geweke and Porter-Hudak (GPH) estimator, local Whittle (LW) variants that allow for non-de-meaned data, bias-reduced versions of both GPH and LW methods, and Maximum Likelihood Estimators (MLE) in the frequency domain for the fractional differenced and cross-sectional aggregated data. For the latter, the profile likelihood is obtained for efficiency.

The proposed package is simple to implement in real applications. In particular, we present an exercise using temperature data modelled using standard and long-range dependence models. The experiment shows that the standard model misrepresents the prediction confidence intervals of future global temperatures. The misrepresentation can potentially explain some of the previous underestimations of temperature increases in the last decades.

I am an Associate Professor at the Department of Mathematical Sciences at Aalborg University. Furthermore, I am a member of the National System of Researchers (SNI) of the Mexican National Council of Science and Technology (CONACYT), and a Research Fellow at CREATES -Center for Research in Econometric Analysis of Time Series-, and the Danish Finance Institute.

I obtained my PhD in Economics and Business Economics in 2016 at Aarhus University and CREATES.
My research interests are econometrics, time series, long memory, statistical learning, and climate econometrics. I have published in the Journal of Econometrics, and at Journal of Financial Econometrics, among others. Furthermore, I am a certified GitHub Campus Advisor.

I have served as a referee for the International Journal of Forecasting, the Journal of Time Series Analysis, the Journal of Computational and Graphical Statistics, Economics Letters, and for Computational Statistics & Data Analysis, among others. Moreover, I am one of the organizers of the Long Memory Conference and the Data Science Computing Conference.

Previously, I studied Mathematics at the Center for Mathematical Research (CIMAT) in 2007 in Guanajuato, Mexico, and obtained a Master’s Degree in Economics from the Center for Research and Teaching in Economics (CIDE) 2010, also in Mexico. I worked at Mexicos Central Bank and as Assistant Professor at the University of Guanajuato.