Ufuk Beyaztas

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• PhD
• Professor (Associate) at Marmara University

The capital asset pricing model (CAPM) is readily used to capture a linear relationship between the daily returns of an asset and a market index. We extend this model to an intraday high-frequency setting by proposing a functional CAPM estimation approach. The functional CAPM is a stylized example of a function-on-function linear regression with a...

Accurate prediction of spatially dependent functional data is critical for various engineering and scientific applications. In this study, a spatial functional deep neural network model was developed with a novel non-linear modeling framework that seamlessly integrates spatial dependencies and functional predictors using deep learning techniques. T...

The capital asset pricing model (CAPM) is readily used to capture a linear relationship between the daily returns of an asset and a market index. We extend this model to an intraday high-frequency setting by proposing a functional CAPM estimation approach. The functional CAPM is a stylized example of a function-on-function linear regression with a...

We introduce a novel function-on-function linear quantile regression model to characterize the entire conditional distribution of a functional response for a given functional predictor. Tensor cubic $B$-splines expansion is used to represent the regression parameter functions, where a derivative-free optimization algorithm is used to obtain the est...

Streamflow (Qflow) process is one of the complex stochastic processes in the hydrology cycle owing to its associated non‐linearity and non‐stationarity characteristics. It is an essential hydrological process to address the complex time series nonlinear phenomena. In this research, a novel approach was proposed by integrating an autoregressive cond...

This paper presents a functional linear Cox regression model with frailty to tackle unobserved heterogeneity in survival data with functional covariates. While traditional Cox models are common, they struggle to incorporate frailty effects that represent individual differences not captured by observed covariates. Our model combines scalar and funct...

We introduce a spatial function-on-function regression model to capture spatial dependencies in functional data by integrating spatial autoregressive techniques with functional principal component analysis. The proposed model addresses a critical gap in functional regression by enabling the analysis of functional responses influenced by spatially c...

This paper introduces a robust estimation strategy for the spatial functional linear regression model using dimension reduction methods, specifically functional principal component analysis (FPCA) and functional partial least squares (FPLS). These techniques are designed to address challenges associated with spatially correlated functional data, pa...

A function-on-function regression model with quadratic and interaction effects of the covariates provides a more flexible model. Despite several attempts to estimate the model's parameters, almost all existing estimation strategies are non-robust against outliers. Outliers in the quadratic and interaction effects may deteriorate the model structure...

We present two innovative functional partial quantile regression algorithms designed to accurately and efficiently estimate the regression coefficient function within the function-on-function linear quantile regression model. Our algorithms utilize functional partial quantile regression decomposition to effectively project the infinite-dimensional...

Among several hydrological processes, river flow is an essential parameter that is vital for different water resources engineering activities. Although several methodologies have been adopted over the literature for modeling river flow, the limitation still exists in modeling the river flow time series curve. In this research, a functional quantile...

This study introduces a novel penalized estimation method tailored for function-on-function regression models, combining the robustness of the Tau estimator with penalization techniques to enhance resistance to outliers. Function-on-function regression is essential for modeling intricate relationships between functional predictors and response vari...

We present a novel approach for estimating a scalar-on-function regression model, leveraging a functional partial least squares methodology. Our proposed method involves computing the functional partial least squares components through sparse partial robust M regression, facilitating robust and locally sparse estimations of the regression coefficie...

We introduce a novel function-on-function linear quantile regression model to characterize the entire conditional distribution of a functional response for a given functional predictor. Tensor cubic B-splines expansion is used to represent the regression parameter functions, where a derivative-free optimization algorithm is used to obtain the estim...

Functional logistic regression is a popular model to capture a linear relationship between binary response and functional predictor variables. However, many methods used for parameter estimation in functional logistic regression are sensitive to outliers, which may lead to inaccurate parameter estimates and inferior classification accuracy. We prop...

A function-on-function regression model with quadratic and interaction effects of the covariates provides a more flexible model. Despite several attempts to estimate the model’s parameters, almost all existing estimation strategies are non-robust against outliers. Outliers in the quadratic and interaction effects may deteriorate the model structure...

Compared with the conditional mean regression-based scalar-on-function regression model, the scalar-on-function quantile regression is robust to outliers in the response variable. However, it is susceptible to outliers in the functional predictor (called leverage points). This is because the influence function of the regression quantiles is bounded...

With advancements in technology and data storage, the availability of functional data whose sample observations are recorded over a continuum, such as time, wavelength, space grids, and depth, progressively increases in almost all scientific branches. The functional linear regression models, including scalar-on-function and function-on-function, ha...

Scalar‐on‐function regression, where the response is scalar‐valued and the predictor consists of random functions, is one of the most important tools for exploring the functional relationship between a scalar response and functional predictor/s. The functional partial least squares method improves estimation accuracy for estimating the regression c...

Air temperature (AT) prediction can play a significant role in studies related to climate change, radiation and heat flux estimation, and weather forecasting. This study applied and compared the outcomes of three advanced fuzzy inference models, i.e., dynamic evolving neural-fuzzy inference system (DENFIS), hybrid neural-fuzzy inference system (HyF...

The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors. Existing methods to estimate the model parameters may be sensitive to outlying observations, common in empirical appl...

In this study, we propose a function-on-function linear quantile regression model that allows for more than one functional predictor to establish a more flexible and robust approach. The proposed model is first transformed into a finitedimensional space via the functional principal component analysis paradigm in the estimation phase. It is then app...

Scalar-on-function logistic regression, where the response is a binary outcome and the predictor consists of random curves, has become a general framework to explore a linear relationship between the binary outcome and functional predictor. Most of the methods used to estimate this model are based on the least-squares type estimators. However, the...

Scalar-on-function logistic regression, where the response is a binary outcome and the predictor consists of random curves, has become a general framework to explore a linear relationship between the binary outcome and functional predictor. Most of the methods used to estimate this model are based on the least-squares type estimators. However, the...

We propose a functional time series method to obtain accurate multi-step-ahead forecasts for age-specific mortality rates. The dynamic functional principal component analysis method is used to decompose the mortality curves into dynamic functional principal components and their associated principal component scores. Machine-learning-based multi-ste...

The scalar-on-function regression model has become a popular analysis tool to explore the relationship between a scalar response and multiple functional predictors. Most of the existing approaches to estimate this model are based on the least-squares estimator, which can be seriously affected by outliers in empirical datasets. When outliers are pre...

The scalar‐on‐function regression model has become a popular analysis tool to explore the relationship between a scalar response and multiple functional predictors. Most of the existing approaches to estimate this model are based on the least‐squares estimator, which can be seriously affected by outliers in empirical datasets. When outliers are pre...

In this study, we propose a function-on-function linear quantile regression model that allows for more than one functional predictor to establish a more flexible and robust approach. The proposed model is first transformed into a finite-dimensional space via the functional principal component analysis paradigm in the estimation phase. It is then ap...

The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors. Existing methods to estimate the model parameters may be sensitive to outlying observations, common in empirical appl...

A function-on-function linear quantile regression model, where both the response and predictors consist of random curves, is proposed by extending the classical quantile regression setting into the functional data to characterize the entire conditional distribution of functional response. In this paper, a functional partial quantile regression appr...

In this paper, a functional partial quantile regression approach, a quantile regression analog of the functional partial least squares regression, is proposed to estimate the function-on-function linear quantile regression model. A partial quantile covariance function is first used to extract the functional partial quantile regression basis functio...

In this research, a functional time series model was introduced to predict future realizations of river flow time series. The proposed model was constructed based on a functional time series’s correlated lags and the essential exogenous climate variables. Rainfall, temperature, and evaporation variables were hypothesized to have sub­stantial functi...

In this research, three water quality (WQ) indexes, namely dissolved oxygen (DO), biochemical oxygen demand (BOD), and chemical oxygen demand (COD), in Selangor River of peninsular Malaysia were simulated using a stochastic model based on vector auto-regression (VAR). The simulation was adopted based on three modeling scenarios of inputs as predict...

In this research, a functional time series model was introduced to predict future realizations of river flow time series. The proposed model was constructed based on a functional time series's correlated lags and the essential exogenous climate variables. Rainfall, temperature, and evaporation variables were hypothesized to have substantial functio...

Copper (Cu) ion in wastewater is considered as one of the crucial hazardous elements to be quantified. This research is established to predict copper ions adsorption (Ad) by Attapulgite clay from aqueous solutions using computer-aided models. Three artificial intelligent (AI) models are developed for this purpose including Grid optimization-based r...

A partial least squares regression is proposed for estimating the function-on-function regression model where a functional response and multiple functional predictors consist of random curves with quadratic and interaction effects. The direct estimation of a function-on-function regression model is usually an ill-posed problem. To overcome this dif...

A partial least squares regression is proposed for estimating the function-on-function regression model where a functional response and multiple functional predictors consist of random curves with quadratic and interaction effects. The direct estimation of a function-on-function regression model is usually an ill-posed problem. To overcome this dif...

The bootstrap procedure has emerged as a general framework to construct prediction intervals for future observations in autoregressive time series models. Such models with outlying data points are standard in real data applications, especially in the field of econometrics. These outlying data points tend to produce high forecast errors, which reduc...

Accurate solar radiation (SR) prediction is one of the essential prerequisites of harvesting solar energy. The current study proposed a novel intelligence model through hybridization of Adaptive Neuro-Fuzzy Inference System (ANFIS) with two metaheuristic optimization algorithms, Salp Swarm Algorithm (SSA) and Grasshopper Optimization Algorithm (GOA...

This paper proposes a new asymptotically valid stationary bootstrap procedure to obtain multivariate forecast densities in unrestricted vector autoregressive models. The proposed method is not based on either backward or forward representations, so it can be used for both Gaussian and non-Gaussian models. Also, it is computationally more efficient...

The bootstrap procedure has emerged as a general framework to construct prediction intervals for future observations in autoregressive time series models. Such models with outlying data points are standard in real data applications, especially in the field of econometrics. These outlying data points tend to produce high forecast errors, which reduc...

We study causality between bivariate curve time series using the Granger causality generalized measures of correlation. With this measure, we can investigate which curve time series Granger‐causes the other; in turn, it helps determine the predictability of any two curve time series. Illustrated by a climatology example, we find that the sea surfac...

We study causality between bivariate curve time series using the Granger causality generalized measures of correlation. With this measure, we can investigate which curve time series Granger-causes the other; in turn, it helps determine the predictability of any two curve time series. Illustrated by a climatology example, we find that the sea surfac...

In this paper, we propose a new resampling algorithm based on block bootstrap to obtain prediction intervals for future returns and volatilities of GARCH processes. The finite sample properties of the proposed methods are illustrated by an extensive simulation study and they are applied to Japan Yen (JPY) / U.S. dollar (USD) daily exchange rate dat...

Background/Objectives Genetic contributors to obesity are frequently studied in murine models. However, the sample sizes of these studies are often small, and the data may violate assumptions of common statistical tests, such as normality of distributions. We examined whether, in these cases, type I error rates and power are affected by the choice...

Recent technological developments have enabled us to collect complex and high-dimensional data in many scientific fields, such as population health, meteorology, econometrics, geology, and psychology. It is common to encounter such datasets collected repeatedly over a continuum. Functional data, whose sample elements are functions in the graphical...

Recent technological developments have enabled us to collect complex and high-dimensional data in many scientific fields, such as population health, meteorology, econometrics, geology, and psychology. It is common to encounter such datasets collected repeatedly over a continuum. Functional data, whose sample elements are functions in the graphical...

Functional data analysis tools, such as function-on-function regression models, have received considerable attention in various scientific fields because of their observed high-dimensional and complex data structures. Several statistical procedures, including least squares, maximum likelihood, and maximum penalized likelihood, have been proposed to...

Aggregation of large databases in a specific format is a frequently used process to make the data easily manageable. Interval-valued data is one of the data types that is generated by such an aggregation process. Using traditional methods to analyze interval-valued data results in loss of information, and thus, several interval-valued data models h...

Evaporation, one of the fundamental components of the hydrology cycle, is differently influenced by various meteorological variables in different climatic regions. The accurate prediction of evaporation is essential for multiple water resources engineering applications, particularly in developing countries like Iraq where the meteorological station...

Aggregation of large databases in a specific format is a frequently used process to make the data easily manageable. Interval-valued data is one of the data types that is generated by such an aggregation process. Using traditional methods to analyze interval-valued data results in loss of information, and thus, several interval-valued data models h...

Functional data analysis tools, such as function-on-function regression models, have received considerable attention in various scientific fields because of their observed high-dimensional and complex data structures. Several statistical procedures, including least squares, maximum likelihood, and maximum penalized likelihood, have been proposed to...

To support initiatives for global emissions targets set by the United Nations Framework Convention on climate change, sustainable extraction of usable power from freely-available global solar radiation as a renewable energy resource requires accurate estimation and forecasting models for solar energy. Understanding the Global Solar Radiation (GSR)...

Drought detection is an essential process for drought risk management and watershed sustainability. Describing a reliable predictive model for drought events has always been the motivation of the meteorology scientists. The current research proposes a functional time series analysis for the construction of a reliable predictive strategy of drought...

Functional time series whose sample elements are recorded sequentially over time are frequently encountered with increasing technology. Recent studies have shown that analyzing and forecasting of functional time series can be performed easily using functional principal component analysis and existing univariate/multivariate time series models. Howe...

Functional time series whose sample elements are recorded sequentially over time are frequently encountered with increasing technology. Recent studies have shown that analyzing and forecasting of functional time series can be performed easily using functional principal component analysis and existing univariate/multivariate time series models. Howe...

Objectives: Rigor, reproducibility and transparency (RRT) awareness has expanded over the last decade. Although RRT can be improved from various aspects, we focused on type I error rates and power of commonly used statistical analyses testing mean differences of two groups, using small (n ≤ 5) to moderate sample sizes. Methods: We compared data...

In this paper, we adapt sufficient and ordered non-overlapping block bootsrap methods into jackknife-after-bootstrap (JaB) algorithm to estimate the standard error of a statistic where observations form a stationary sequence. We also extend the JaB algorithm to obtain prediction intervals for future returns and volatilities of GARCH processes. The...

Linear models incorporating change points are very common in many scientific fields including genetics, medicine, ecology, and finance. Outlying or unusual data points pose another challenge for fitting such models, as outlying data may impact change point detection and estimation. In this paper, we propose a robust approach to estimate the change...

In this paper, we propose new Ordinary Least Squares based overlapping and non-overlapping block bootstrap methods for autoregressive time series models. The finite sample properties of the proposed methods are illustrated by an extensive simulation study and two real-world examples. Our findings reveal that the proposed methods have better perform...

This paper proposes a sufficient bootstrap method, which uses only the unique observations in the resamples, to assess the individual bioequivalence under 2 × 4 randomized crossover design. The finite sample performance of the proposed method is illustrated by extensive Monte Carlo simulations as well as a real‐experimental data set, and the result...

It is well known that under certain regularity conditions the bootstrap sampling distributions of common statistics are consistent with their true sampling distributions. However, the consistency results rely heavily on the underlying regularity conditions and in fact, a failure to satisfy some of these may lead us to a serious departure from consi...

In this paper, we propose an iterating principle in the bootstrap method to assess the individual bioequivalence under 2×4 randomized crossover design. The finite sample properties of the proposed algorithm are illustrated by an extensive simulation study and a real-world example. Our findings reveal that the proposed idea have better performance t...

In this study, we propose an approach based on the residual-based bootstrap method to obtain valid prediction intervals using monthly, short-term (three-months) and mid-term (six-months) drought observations. The effects of North Atlantic and Arctic Oscillation indexes on the constructed prediction intervals are also examined. Performance of the pr...

In this study, we propose an approach based on the residual-based bootstrap method to obtain valid prediction intervals using monthly drought observations. The effects of North Atlantic and Arctic Oscillation indexes on the constructed prediction intervals are also examined. Performance of the proposed approach is evaluated for the Palmer Drought S...

In this paper, we propose a new bootstrap algorithm to obtain prediction intervals for generalized autoregressive conditionally heteroscedastic (GARCH(1,1)) process which can be applied to construct prediction intervals for future returns and volatilities. The advantages of the proposed method are twofold: it (a) often exhibits improved performance...

Traditional resampling methods for estimating sampling distributions sometimes fail, and alternative approaches are then needed. For example, if the classical central limit theorem does not hold and the naive bootstrap fails, the m/n bootstrap, based on smaller-sized resamples, may be used as an alternative. An alternative to the naive bootstrap, t...

In this study, we propose sufficient time series bootstrap methods that achieve better results than conventional non-overlapping block bootstrap, but with less computing time and lower standard errors of estimation. Also, we propose using a new technique using ordered bootstrapped blocks, to better preserve the dependency structure of the original...

In this study, we propose a delete-2 jackknife-after-bootstrap method to refine the cut-offs for the well-known diagnostic measure Cook's distance when the data have multiple influential data points with masking and swamping effects. The performance of the proposed method is compared with one of the most recent approaches in the literature through...

The Jackknife-after-bootstrap (JaB) technique originally developed by Efron [88. B. Efron, Jackknife-after-bootstrap standard errors and influence functions, J. R. Stat. Soc. 54 (1992), pp. 83–127.View all references] has been proposed as an approach to improve the detection of influential observations in linear regression models by Martin and Robe...

In this study, we adapt sufficient bootstrap into the jackknife-after-bootstrap (JaB) algorithm. The performances of the sufficient and conventional JaB methods have been compared for detecting influential observations in linear regression. Comparison is based on two real-world examples and an extensive designed simulation study. Design includes di...

The jackknife-after-bootstrap (JaB) method has been proposed for detecting influential observations in linear regression models. The performance of JaB and the traditional methods have been compared for four different influence measures by designed simula- tion study and real world examples. Design includes different sample sizes and various modeli...

In this study, we propose using Jackknife-after-Bootstrap (JaB) method to detect influential observations in binary logistic regression model. Performance of the proposed method has been compared with the traditional method for standardized Pearson residuals, Cook's distance, change in the Pearson chi-square and change in the deviance statistics by...