Showing papers on "Heteroscedasticity published in 2018"

Forecasting the volatility of stock price index: A hybrid model integrating LSTM with multiple GARCH-type models

Abstract: Volatility plays crucial roles in financial markets, such as in derivative pricing, portfolio risk management, and hedging strategies. Therefore, accurate prediction of volatility is critical. We propose a new hybrid long short-term memory (LSTM) model to forecast stock price volatility that combines the LSTM model with various generalized autoregressive conditional heteroscedasticity (GARCH)-type models. We use KOSPI 200 index data to discover proposed hybrid models that combine an LSTM with one to three GARCH-type models. In addition, we compare their performance with existing methodologies by analyzing single models, such as the GARCH, exponential GARCH, exponentially weighted moving average, a deep feedforward neural network (DFN), and the LSTM, as well as the hybrid DFN models combining a DFN with one GARCH-type model. Their performance is compared with that of the proposed hybrid LSTM models. We discover that GEW-LSTM, a proposed hybrid model combining the LSTM model with three GARCH-type models, has the lowest prediction errors in terms of mean absolute error (MAE), mean squared error (MSE), heteroscedasticity adjusted MAE (HMAE), and heteroscedasticity adjusted MSE (HMSE). The MAE of GEW-LSTM is 0.0107, which is 37.2% less than that of the E-DFN (0.017), the model combining EGARCH and DFN and the best model among those existing. In addition, the GEW-LSTM has 57.3%, 24.7%, and 48% smaller MSE, HMAE, and HMSE, respectively. The first contribution of this study is its hybrid LSTM model that combines excellent sequential pattern learning with improved prediction performance in stock market volatility. Second, our proposed model markedly enhances prediction performance of the existing literature by combining a neural network model with multiple econometric models rather than only a single econometric model. Finally, the proposed methodology can be extended to various fields as an integrated model combining time-series and neural network models as well as forecasting stock market volatility.

German Value Set for the EQ-5D-5L

Abstract: The objective of this study was to develop a value set for EQ-5D-5L based on the societal preferences of the German population. As the first country to do so, the study design used the improved EQ-5D-5L valuation protocol 2.0 developed by the EuroQol Group, including a feedback module as internal validation and a quality control process that was missing in the first wave of EQ-5D-5L valuation studies. A representative sample of the general German population (n = 1158) was interviewed using a composite time trade-off and a discrete choice experiment under close quality control. Econometric modeling was used to estimate values for all 3125 possible health states described by EQ-5D-5L. The value set was based on a hybrid model including all available information from the composite time trade-off and discrete choice experiment valuations without any exclusions due to data issues. The final German value set was constructed from a combination of a conditional logit model for the discrete choice experiment data and a censored at −1 Tobit model for the composite time trade-off data, correcting for heteroskedasticity. The value set had logically consistent parameter estimates (p < 0.001 for all coefficients). The predicted EQ-5D-5L index values ranged from −0.661 to 1. This study provided values for the health states of the German version of EQ-5D-5L representing the preferences of the German population. The study successfully employed for the first time worldwide the improved protocol 2.0. The value set enables the use of the EQ-5D-5L instrument in economic evaluations and in clinical studies.

HAR Inference: Recommendations for Practice

Abstract: The classic papers by Newey and West (1987) and Andrews (1991) spurred a large body of work on how to improve heteroscedasticity- and autocorrelation-robust (HAR) inference in time series regressio...

Small-Sample Methods for Cluster-Robust Variance Estimation and Hypothesis Testing in Fixed Effects Models

Abstract: In panel data models and other regressions with unobserved effects, fixed effects estimation is often paired with cluster-robust variance estimation (CRVE) to account for heteroscedasticity and un-modeled dependence among the errors. Although asymptotically consistent, CRVE can be biased downward when the number of clusters is small, leading to hypothesis tests with rejection rates that are too high. More accurate tests can be constructed using bias-reduced linearization (BRL), which corrects the CRVE based on a working model, in conjunction with a Satterthwaite approximation for t-tests. We propose a generalization of BRL that can be applied in models with arbitrary sets of fixed effects, where the original BRL method is undefined, and describe how to apply the method when the regression is estimated after absorbing the fixed effects. We also propose a small-sample test for multiple-parameter hypotheses, which generalizes the Satterthwaite approximation for t-tests. In simulations covering a wide...

Change Detection and the Causal Impact of the Yield Curve

Abstract: Causal relationships in econometrics are typically based on the concept of predictability and are established by testing Granger causality. Such relationships are susceptible to change, especially during times of financial turbulence, making the real‐time detection of instability an important practical issue. This article develops a test for detecting changes in causal relationships based on a recursive evolving window, which is analogous to a procedure used in recent work on financial bubble detection. The limiting distribution of the test takes a simple form under the null hypothesis and is easy to implement in conditions of homoskedasticity and conditional heteroskedasticity of an unknown form. Bootstrap methods are used to control family‐wise size in implementation. Simulation experiments compare the efficacy of the proposed test with two other commonly used tests, the forward recursive and the rolling window tests. The results indicate that the recursive evolving approach offers the best finite sample performance, followed by the rolling window algorithm. The testing strategies are illustrated in an empirical application that explores the causal relationship between the slope of the yield curve and real economic activity in the United States over the period 1980–2015.

Onewaytests: An R package for one-way tests in independent groups designs

Abstract: One-way tests in independent groups designs are the most commonly utilized statistical methods with applications on the experiments in medical sciences, pharmaceutical research, agriculture, biology, engineering, social sciences and so on. In this paper, we present the onewaytests package to investigate treatment effects on the dependent variable. The package offers the one-way tests in independent groups designs, which include ANOVA, Welch's heteroscedastic F test, Welch's heteroscedastic F test with trimmed means andWinsorized variances, Brown-Forsythe test, Alexander- Govern test, James second order test and Kruskal-Wallis test. The package also provides pairwise comparisons, graphical approaches, and assesses variance homogeneity and normality of data in each group via tests and plots. A simulation study is also conducted to give recommendations for applied researchers on the selection of appropriate one-way tests under assumption violations. Furthermore, especially for non-R users, a user-friendly web application of the package is provided. This application is available at http://www.softmed.hacettepe.edu.tr/onewaytests.

Leave-out estimation of variance components

Abstract: We propose leave-out estimators of quadratic forms designed for the study of linear models with unrestricted heteroscedasticity. Applications include analysis of variance and tests of linear restrictions in models with many regressors. An approximation algorithm is provided that enables accurate computation of the estimator in very large datasets. We study the large sample properties of our estimator allowing the number of regressors to grow in proportion to the number of observations. Consistency is established in a variety of settings where plug-in methods and estimators predicated on homoscedasticity exhibit first-order biases. For quadratic forms of increasing rank, the limiting distribution can be represented by a linear combination of normal and non-central $\chi^2$ random variables, with normality ensuing under strong identification. Standard error estimators are proposed that enable tests of linear restrictions and the construction of uniformly valid confidence intervals for quadratic forms of interest. We find in Italian social security records that leave-out estimates of a variance decomposition in a two-way fixed effects model of wage determination yield substantially different conclusions regarding the relative contribution of workers, firms, and worker-firm sorting to wage inequality than conventional methods. Monte Carlo exercises corroborate the accuracy of our asymptotic approximations, with clear evidence of non-normality emerging when worker mobility between blocks of firms is limited.

Heteroskedastic PCA: Algorithm, Optimality, and Applications

Abstract: A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance matrix to remove estimation bias due to heteroskedasticity. This procedure is computationally efficient and provably optimal under the generalized spiked covariance model. A key technical step is a deterministic robust perturbation analysis on singular subspaces, which can be of independent interest. The effectiveness of the proposed algorithm is demonstrated in a suite of problems in high-dimensional statistics, including singular value decomposition (SVD) under heteroskedastic noise, Poisson PCA, and SVD for heteroskedastic and incomplete data.

Conditional Density Estimation with Bayesian Normalising Flows

Abstract: Modeling complex conditional distributions is critical in a variety of settings Despite a long tradition of research into conditional density estimation, current methods employ either simple parametric forms or are difficult to learn in practice This paper employs normalising flows as a flexible likelihood model and presents an efficient method for fitting them to complex densities These estimators must trade-off between modeling distributional complexity, functional complexity and heteroscedasticity without overfitting We recognize these trade-offs as modeling decisions and develop a Bayesian framework for placing priors over these conditional density estimators using variational Bayesian neural networks We evaluate this method on several small benchmark regression datasets, on some of which it obtains state of the art performance Finally, we apply the method to two spatial density modeling tasks with over 1 million datapoints using the New York City yellow taxi dataset and the Chicago crime dataset

Inference on multivariate heteroscedastic time varying random coefficient models

Abstract: In this article, we introduce the general setting of a multivariate time series autoregressive model with stochastic time-varying coefficients and time-varying conditional variance of the error process. This allows modelling VAR dynamics for non-stationary time series and estimation of time-varying parameter processes by the well-known rolling regression estimation techniques. We establish consistency, convergence rates, and asymptotic normality for kernel estimators of the paths of coefficient processes and provide pointwise valid standard errors. The method is applied to a popular seven-variable dataset to analyse evidence of time variation in empirical objects of interest for the DSGE (dynamic stochastic general equilibrium) literature.

Beyond expectation: Deep joint mean and quantile regression for spatio-temporal problems

Abstract: Spatio-temporal problems are ubiquitous and of vital importance in many research fields. Despite the potential already demonstrated by deep learning methods in modeling spatio-temporal data, typical approaches tend to focus solely on conditional expectations of the output variables being modeled. In this paper, we propose a multi-output multi-quantile deep learning approach for jointly modeling several conditional quantiles together with the conditional expectation as a way to provide a more complete "picture" of the predictive density in spatio-temporal problems. Using two large-scale datasets from the transportation domain, we empirically demonstrate that, by approaching the quantile regression problem from a multi-task learning perspective, it is possible to solve the embarrassing quantile crossings problem, while simultaneously significantly outperforming state-of-the-art quantile regression methods. Moreover, we show that jointly modeling the mean and several conditional quantiles not only provides a rich description about the predictive density that can capture heteroscedastic properties at a neglectable computational overhead, but also leads to improved predictions of the conditional expectation due to the extra information and a regularization effect induced by the added quantiles.

Real-Time Prediction of Seasonal Heteroscedasticity in Vehicular Traffic Flow Series

Abstract: Over the past decade, traffic heteroscedasticity has been investigated with the primary purpose of generating prediction intervals around point forecasts constructed usually by short-term traffic condition level forecasting models. However, despite considerable advancements, complete traffic patterns, in particular the seasonal effect, have not been adequately handled. Recently, an offline seasonal adjustment factor plus GARCH model was proposed in Shi et al. 2014 to model the seasonal heteroscedasticity in traffic flow series. However, this offline model cannot meet the real-time processing requirement proposed by real-world transportation management and control applications. Therefore, an online seasonal adjustment factors plus adaptive Kalman filter (OSAF+AKF) approach is proposed in this paper to predict in real time the seasonal heteroscedasticity in traffic flow series. In this approach, OSAF and AKF are combined within a cascading framework, and four types of online seasonal adjustment factors are developed considering the seasonal patterns in traffic flow series. Empirical results using real-world station-by-station traffic flow series showed that the proposed approach can generate workable prediction intervals in real time, indicating the acceptability of the proposed approach. In addition, compared with the offline model, the proposed online approach showed improved adaptability when traffic is highly volatile. These findings are important for developing real-time intelligent transportation system applications.

Group-Linear Empirical Bayes Estimates for a Heteroscedastic Normal Mean

Abstract: The problem of estimating the mean of a normal vector with known but unequal variances introduces substantial difficulties that impair the adequacy of traditional empirical Bayes estimators. By taking a different approach that treats the known variances as part of the random observations, we restore symmetry and thus the effectiveness of such methods. We suggest a group-linear empirical Bayes estimator, which collects observations with similar variances and applies a spherically symmetric estimator to each group separately. The proposed estimator is motivated by a new oracle rule which is stronger than the best linear rule, and thus provides a more ambitious benchmark than that considered in the previous literature. Our estimator asymptotically achieves the new oracle risk (under appropriate conditions) and at the same time is minimax. The group-linear estimator is particularly advantageous in situations where the true means and observed variances are empirically dependent. To demonstrate the meri...

A review on missing hydrological data processing.

Abstract: Like almost all fields of science, hydrology has benefited to a large extent from the tremendous improvements in scientific instruments that are able to collect long-time data series and an increase in available computational power and storage capabilities over the last decades. Many model applications and statistical analyses (e.g., extreme value analysis) are based on these time series. Consequently, the quality and the completeness of these time series are essential. Preprocessing of raw data sets by filling data gaps is thus a necessary procedure. Several interpolation techniques with different complexity are available ranging from rather simple to extremely challenging approaches. In this paper, various imputation methods available to the hydrological researchers are reviewed with regard to their suitability for filling gaps in the context of solving hydrological questions. The methodological approaches include arithmetic mean imputation, principal component analysis, regression-based methods and multiple imputation methods. In particular, autoregressive conditional heteroscedasticity (ARCH) models which originate from finance and econometrics will be discussed regarding their applicability to data series characterized by non-constant volatility and heteroscedasticity in hydrological contexts. The review shows that methodological advances driven by other fields of research bear relevance for a more intensive use of these methods in hydrology. Up to now, the hydrological community has paid little attention to the imputation ability of time series models in general and ARCH models in particular.

New Approaches for Estimation of Monthly Rainfall Based on GEP-ARCH and ANN-ARCH Hybrid Models

Abstract: Accurate estimation of rainfall has an important role in the optimal water resources management, as well as hydrological and climatological studies. In the present study, two novel types of hybrid models, namely gene expression programming-autoregressive conditional heteroscedasticity (GEP-ARCH) and artificial neural networks-autoregressive conditional heteroscedasticity (ANN-ARCH) are introduced to estimate monthly rainfall time series. To fulfill this purpose, five stations with various climatic conditions were selected in Iran. The lagged monthly rainfall data was utilized to develop the different GEP and ANN scenarios. The performance of proposed hybrid models was compared to the GEP and ANN models using root mean square error (RMSE) and coefficient of determination (R2). The results show that the proposed GEP-ARCH and ANN-ARCH models give a much better performance than the GEP and ANN in all of the studied stations with various climates. Furthermore, the ANN-ARCH model generally presents better performance in comparison with the GEP-ARCH model.

Time series copulas for heteroskedastic data

Abstract: We propose parametric copulas that capture serial dependence in stationary heteroskedastic time series. We suggest copulas for first-order Markov series, and then extend them to higher orders and multivariate series. We derive the copula of a volatility proxy, based on which we propose new measures of volatility dependence, including co-movement and spillover in multivariate series. In general, these depend upon the marginal distributions of the series. Using exchange rate returns, we show that the resulting copula models can capture their marginal distributions more accurately than univariate and multivariate generalized autoregressive conditional heteroskedasticity models, and produce more accurate value-at-risk forecasts.

Generalised spatial and spatiotemporal autoregressive conditional heteroscedasticity

Abstract: In this paper, we introduce a new spatial model that incorporates heteroscedastic variance depending on neighbouring locations. The proposed process is considered as the spatial equivalent to the temporal autoregressive conditional heteroscedasticity (ARCH) model. We also show how the newly introduced spatial ARCH model can be used in spatiotemporal settings. In contrast to the temporal ARCH model, in which the distribution is known given the full information set for the prior periods, the distribution is not straightforward in the spatial and spatiotemporal setting. However, the model parameters can be estimated using the maximum-likelihood approach. Via Monte Carlo simulations, we demonstrate the performance of the estimator for a specific spatial weighting matrix. Moreover, we combine the known spatial autoregressive model with the spatial ARCH model assuming heteroscedastic errors. Eventually, the proposed autoregressive process is illustrated by an empirical example. Specifically, we model lung cancer mortality in 3108 U.S. counties and compare the newly introduced model with four benchmark approaches.

A new bivariate integer-valued GARCH model allowing for negative cross-correlation

Abstract: Univariate integer-valued time series models, including integer-valued autoregressive (INAR) models and integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models, have been well studied in the literature, but there is little progress in multivariate models. Although some multivariate INAR models were proposed, they do not provide enough flexibility in modeling count data, such as volatility of numbers of stock transactions. Then, a bivariate Poisson INGARCH model was suggested by Liu (Some models for time series of counts, Dissertations, Columbia University, 2012), but it can only deal with positive cross-correlation between two components. To remedy this defect, we propose a new bivariate Poisson INGARCH model, which is more flexible and allows for positive or negative cross-correlation. Stationarity and ergodicity of the new process are established. The maximum likelihood method is used to estimate the unknown parameters, and consistency and asymptotic normality for estimators are given. A simulation study is given to evaluate the estimators for parameters of interest. Real and artificial data examples are illustrated to demonstrate good performances of the proposed model relative to the existing model.

Modelling and predicting the Bitcoin volatility using GARCH models

Abstract: This paper is the first to forecast the volatility of the Bitcoin/USD exchange rate. It assesses and compares the predictive ability of the generalised autoregressive conditional heteroscedasticity (GARCH) (1,1), the exponentially weighted moving average (EWMA), and the exponential generalised autoregressive conditional heteroscedasticity (EGARCH) (1,1). Models' parameters are first estimated from the in sample Bitcoin/USD exchange rate returns and in sample volatility is calculated. Out of sample volatility is forecasted afterward. Estimated volatilities are then compared to realised volatilities relying on error statistics, after which the models are ranked. The EGARCH (1,1) model outperforms the GARCH (1,1) and EWMA models in both in sample and out of sample contexts with increased accuracy in the out of sample period. Results show an original reflection concern with regard to the nature of the Bitcoin, which behaves differently than traditional currencies. Given the early-stage behaviour of the Bitcoin, results might change in the future.

Evaluation of three statistical prediction models for forensic age prediction based on DNA methylation

Abstract: DNA methylation is a promising biomarker for forensic age prediction. A challenge that has emerged in recent studies is the fact that prediction errors become larger with increasing age due to interindividual differences in epigenetic ageing rates. This phenomenon of non-constant variance or heteroscedasticity violates an assumption of the often used method of ordinary least squares (OLS) regression. The aim of this study was to evaluate alternative statistical methods that do take heteroscedasticity into account in order to provide more accurate, age-dependent prediction intervals. A weighted least squares (WLS) regression is proposed as well as a quantile regression model. Their performances were compared against an OLS regression model based on the same dataset. Both models provided age-dependent prediction intervals which account for the increasing variance with age, but WLS regression performed better in terms of success rate in the current dataset. However, quantile regression might be a preferred method when dealing with a variance that is not only non-constant, but also not normally distributed. Ultimately the choice of which model to use should depend on the observed characteristics of the data.