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Author (up) Araya, H.; Bahamonde, N.; Fermin, L.; Roa, T.; Torres, S. doi  openurl
  Title ON THE CONSISTENCY OF THE LEAST SQUARES ESTIMATOR IN MODELS SAMPLED AT RANDOM TIMES DRIVEN BY LONG MEMORY NOISE: THE RENEWAL CASE Type
  Year 2023 Publication Statistica Sinica Abbreviated Journal Stat. Sin.  
  Volume 33 Issue 1 Pages 1-26  
  Keywords Least squares estimator; long-memory noise; random times; regression model; renewal process.  
  Abstract In this study, we prove the strong consistency of the least squares estimator in a random sampled linear regression model with long-memory noise and an independent set of random times given by renewal process sampling. Additionally, we illustrate how to work with a random number of observations up to time T = 1. A simulation study is provided to illustrate the behavior of the different terms, as well as the performance of the estimator under various values of the Hurst parameter H.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1017-0405 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:001021573400001 Approved  
  Call Number UAI @ alexi.delcanto @ Serial 1692  
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Author (up) Araya, H.; Bahamonde, N.; Fermin, L.; Roa, T.; Torres, S. doi  openurl
  Title ON THE CONSISTENCY OF LEAST SQUARES ESTIMATOR IN MODELS SAMPLED AT RANDOM TIMES DRIVEN BY LONG MEMORY NOISE: THE JITTERED CASE Type
  Year 2023 Publication Statistica Sinica Abbreviated Journal Stat. Sin.  
  Volume 33 Issue 1 Pages 331-351  
  Keywords Least squares estimator; long-memory noise; random times; regression model  
  Abstract In numerous applications, data are observed at random times. Our main purpose is to study a model observed at random times that incorporates a longmemory noise process with a fractional Brownian Hurst exponent H. We propose a least squares estimator in a linear regression model with long-memory noise and a random sampling time called “jittered sampling”. Specifically, there is a fixed sampling rate 1/N, contaminated by an additive noise (the jitter) and governed by a probability density function supported in [0, 1/N]. The strong consistency of the estimator is established, with a convergence rate depending on N and the Hurst exponent. A Monte Carlo analysis supports the relevance of the theory and produces additional insights, with several levels of long-range dependence (varying the Hurst index) and two different jitter densities.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1017-0405 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:001021364800009 Approved  
  Call Number UAI @ alexi.delcanto @ Serial 1840  
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Author (up) Araya, H.; Plaza-Vega, F. doi  openurl
  Title Parameter estimation for fractional power type diffusion: A hybrid Bayesian-deep learning approach Type
  Year 2023 Publication Communications In Statistics-Theory And Methods Abbreviated Journal Commun. Stat.-Theory Methods  
  Volume Early Access Issue Pages  
  Keywords Parameter estimation; power-type fractional diffusion; fractional Brownian motion; ABC  
  Abstract In this article, we consider the problem of parameter estimation in a power-type diffusion driven by fractional Brownian motion with Hurst parameter in (1/2,1). To estimate the parameters of the process, we use an approximate bayesian computation method. Also, a particular case is addressed by means of variations and wavelet-type methods. Several theoretical properties of the process are studied and numerical examples are provided in order to show the small sample behavior of the proposed methods.  
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  Language Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0361-0926 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:001120573700001 Approved  
  Call Number UAI @ alexi.delcanto @ Serial 1919  
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Author (up) Barrera, J.; Araya, H. doi  openurl
  Title Modeling Chile Fishing Data Using Environmental Exogenous Variables with GARCH-X Model Type
  Year 2023 Publication Journal of the Iranian Statistical Society Abbreviated Journal J. Iran. Stat. Soc.  
  Volume 21 Issue 1 Pages 19-35  
  Keywords Environmental Modeling; Exogenous Variables; Fishing Data; GARCH-X; Time Series  
  Abstract Fishing industry has always been an economic motor in many countries around the world, but the fisheries production faces a lot of uncertainty and instability due to the complex factors involved in its operations. In this article, we consider the problem of modeling Chile fishing data using environmental exogenous variables with generalized autoregressive conditional heteroskedasticity (GARCH-X) type models. We carried out this by proposing an ARMA type model for the mean with GARCH-X noise. First, the ARMA, GARCH and GARCH-X models are briefly introduced and the data is described. The exogenous variables are selected from a group of environmental and climatic indicators by correlational analysis. Then, ARMA GARCH and ARMA GARCH-X models with exogenous variables are fitted and compared by information criteria and classical error measures, and stability of its parameters are checked. The statistical tests and comparisons evidenced that a model with inclusion of external variables in mean and variance with the ARMA GARCH-X specification performed better and adjusted the observed values more rigorously. Finally, some conclusions and possible refinations of the applied techniques are given.  
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  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1726-4057 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:001078337200002 Approved  
  Call Number UAI @ alexi.delcanto @ Serial 1903  
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Author (up) Plaza, F.; Araya, H.; Yanez, E. doi  openurl
  Title Environmental effect on the variability of anchovy (Engraulis ringens) in northern Chile: Autoregressive conditional heteroskedastic approach with exogenonus variable and missing values Type
  Year 2023 Publication Fisheries Research Abbreviated Journal Fish. Res.  
  Volume 260 Issue Pages 106607  
  Keywords Anchovy; Environment; Sea surface temperature; ARCH models; Estimation  
  Abstract This article studies the monthly variability of anchovy (Engraulis ringens) in northern Chile, related with the environmental effect of sea surface temperature on the landings of the fishery. In order to achieve that goal, a variant of the autoregressive conditional heteroskedastic (ARCH) model is proposed, in which an additional covariate is included (sea surface temperature) and missing values are considered. To estimate the parameters of the model we use a least square type estimation procedure. The proposed model considers monthly data from the anchovy fishery in northern Chile from 2010 to 2020 with the sea surface temperature as an environmental exogenous variable. The results show the good performance of the model and its capability to further represent the anchovy variability by means of its estimated conditional variance.  
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  Language Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0165-7836 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000918851900001 Approved  
  Call Number UAI @ alexi.delcanto @ Serial 1743  
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Author (up) Plaza-Vega, F.; Araya, H. doi  openurl
  Title Anchovy (Engraulis ringens) and Pacific sardine (Sardinops sagax) variability changes in northern Chile associated with the environment and inter species synchronicity: GARCH model with exogenous variable and hybrid Bayesian deep learning estimation approach Type
  Year 2024 Publication Progress in Oceanography Abbreviated Journal Prog. Oceanogr.  
  Volume 221 Issue Pages 103190  
  Keywords Small; pelagic; environment; GARCH; variability; exogenous variables; parameters; estimation  
  Abstract Small pelagic fish species, such as anchovy (Engraulis ringens) and Pacific sardine (Sardinops sagax), play a crucial role in marine ecosystems worldwide as they serve as an important food source for higher-order predators, such as seabirds, marine mammals, and larger fish species; also from their high productivity in terms of fishery landings, they help with maintaining food security. However, small pelagic populations are known for their variability, with fluctuations in their distribution and abundance influenced by interactions with environmental and human-related factors in different spatio-temporal scales. This study aims to investigate the variability in anchovy and sardine populations in northern Chile and their potential environmental drivers by using a class of models that address the changes in variability (i.e. variance) over time, namely Generalized autoregressive conditional heteroskedasticity (GARCH) models. In particular, this work considers a GARCH model that includes an additional term in the variance, that could help to better model the variability fluctuations of both anchovy and sardine, explained by environmental factors. Since there is no estimation procedures for those type of models, we propose a hybrid Approximate Bayesian Computation (ABC) procedure that involves the use of Deep Learning structures for estimating the parameters of the model and obtain posterior distributions. The results are two-fold: First, the proposal of a new time series model that better explain conditional variance with exogenous variables and a novel estimation procedure, and second, a novel approach for establishing explicit models that address the variability of small pelagic fisheries and their interaction with the environment.  
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  Language Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0079-6611 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:001158438200001 Approved  
  Call Number UAI @ alexi.delcanto @ Serial 1938  
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