Adaptive pointwise estimation in time-inhomogeneous conditional heteroscedasticity models

In this paper, a size-biased generalized logarithmic series distribution (SBGLSD) is introduced and its moments are obtained. The estimates of the parameters of SBGLSD are obtained by employing the method of moments and a pro- posed new method of estimation. The new proposed method of estimation uses the non-zero frequency of a variable only up to a finite value. In this method, the estimation of only one parameter is needed and of the other is obtained by the rela- tionship among the parameters by counting the number of non-zero frequency classes. The method is found very simple and quick to apply in practice. Extensive simulations are performed to compare the performances of the proposed and the moment method of estimation mainly with respect to their biases and mean squared errors (MSE's), for different sample sizes and of different parametric values. Comparison has been made among different estimation methods by means of Pearson's Chi-square, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) techniques.

A new method for estimating time‐varying fluxes of atmospheric trace gases using an atmospheric transport model and observed concentrations is presented. Specifically Kaiman filtering is used to estimate inputs from a state‐space model identified using unit‐pulse response functions from a transport model. The method is new in that no assumptions about initial concentrations in the model are required, although this in turn means that all flux processes must be explicitly modeled as inputs linearly related to concentrations. This also means that at least one extra measuring‐site or other measurement variable (e.g. a linear combination of emissions) than the number of input‐fluxes being estimated, is required to ensure a stable Kaiman filter.

The exponentially weighted moving average (EWMA) model is a particular modeling scheme, supported by RiskMetrics, that is capable of forecasting the current level of volatility of financial time series. It is designed to track changes in the conditional variance of financial returns by assigning exponentially decreasing weights to observed past squared measurements. The aim of this paper is twofold. First, it introduces two recursive estimation algorithms that are appropriate for the EWMA model. Both are derived by employing the general recursive prediction error scheme. Moreover, they represent a computationally effective alternative to already established nonrecursive estimation strategies since they are effective in terms of memory storage, computational complexity and detecting structural changes. Second, this paper investigates the prediction ability of the proposed recursive estimation schemes when compared with other common (nonrecursive) estimation methods. The priorities of the suggested recursive estimators are demonstrated by means of a simulation study and an extensive empirical case study of eighteen key world stock indexes. Combinations of recursive predictions are also studied. Such a strategy can be recommended due to its advantageous properties when predicting volatility.

SummaryWe propose a flexible generalized auto-regressive conditional heteroscedasticity type of model for the prediction of volatility in financial time series. The approach relies on the idea of using multivariate B-splines of lagged observations and volatilities. Estimation of such a B-spline basis expansion is constructed within the likelihood framework for non-Gaussian observations. As the dimension of the B-spline basis is large, i.e. many parameters, we use regularized and sparse model fitting with a boosting algorithm. Our method is computationally attractive and feasible for large dimensions. We demonstrate its strong predictive potential for financial volatility on simulated and real data, and also in comparison with other approaches, and we present some supporting asymptotic arguments.

An important development in the modelling of exchange rate volatility is the use of artificial neural networks (ANN) to create enhanced generalised autoregressive conditional heteroskedasticity (GARCH) models. Conventional GARCH models are good at capturing the clustering of volatility in financial time series, but they have trouble understanding complex linkages and non-linear patterns in the data. This paper aims to investigate the hybrid approach in modelling exchange rate volatility of two currency pairs: South African Rand against Brazilian Real (ZAR/REAL) and South African Rand against Chinese Yuan (ZAR/YUAN) using monthly observations over the period of January 1996-March 2024. The paper introduced ANN as an additional factor to both symmetric and asymmetric GARCH models that capture most common stylised facts about exchange rate volatility and leverage effects. The GARCH (1,1)-ANN, EGARCH (1,1)-ANN, and GJR-GARCH (1,1)-ANN models were used, and their performance was assessed using mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). The results revealed that the EGARCH (1,1)-ANN model had the best overall performance when compared to the other hybrid models based on all three evaluation measures for both the currency pairs’ data. The paper recommends further similar studies to predict future exchange rate trends and also incorporating other nonlinear methods.

Realized volatility or price range: Evidence from a discrete simulation of the continuous time diffusion process

A Bayesian conditional autoregressive geometric process model for range data

Volatility forecasting is vital important in finance to reduce risk and take better decisions. This paper proposes a spline wavelet support vector machine (SWSVM) to forecast the volatility of financial time series based on generalized autoregressive conditional heteroscedasticity model. An admissible spline wavelet kernel is constructed by incorporating the wavelet technique and spline theory into support vector machine (SVM). Since spline wavelet function can yield features that describe the stock time series both at various locations and at varying time granularities, the SWSVM gains the cluster feature of volatility well. Compared with Gaussian kernel in the standard SVM, the applicability and validity of spline wavelet kernel in SWSVM are confirmed through computer simulations and experiments on real-world stock data.

Complexity analysis based on generalized deviation for financial markets

We propose a method for improving the predictive ability of standard forecasting models used in financial economics. Our approach is based on the functional partial least squares (FPLS) model, which is capable of avoiding multicollinearity in regression by efficiently extracting information from the high‐dimensional market data. By using its well‐known ability, we can incorporate auxiliary variables that improve the predictive accuracy. We provide an empirical application of our proposed methodology in terms of its ability to predict the conditional average log return and the volatility of crude oil prices via exponential smoothing, Bayesian stochastic volatility, and GARCH (generalized autoregressive conditional heteroskedasticity) models, respectively. In particular, what we call functional data analysis (FDA) traces in this article are obtained via the FPLS regression from both the crude oil returns and auxiliary variables of the exchange rates of major currencies. For forecast performance evaluation, we compare out‐of‐sample forecasting accuracy of the standard models with FDA traces to the accuracy of the same forecasting models with the observed crude oil returns, principal component regression (PCR), and least absolute shrinkage and selection operator (LASSO) models. We find evidence that the standard models with FDA traces significantly outperform our competing models. Finally, they are also compared with the test for superior predictive ability and the reality check for data snooping. Our empirical results show that our new methodology significantly improves predictive ability of standard models in forecasting the latent average log return and the volatility of financial time series.

Estimation of volatility of financial time series plays a crucial role in pricing derivatives. Volatility is often estimated from historical data; however, it is well known that volatility varies in time. We propose a method to choose a suitable length of historical data to estimate contemporary volatility. The method is based on adaptation of a procedure used in statistical quality control - a hypothesis, that data contains a changepoint of volatility, is tested and if the test gives a positive answer, the changepoint is estimated. Then, a period of data where no changepoint is statistically significant is used to estimate contemporary volatility. The approach is illustrated on an analysis of CZK/EUR exchange rates.

A complete guide to the theory and practice of volatility models in financial engineering Volatility has become a hot topic in this era of instant communications, spawning a great deal of research in empirical finance and time series econometrics. Providing an overview of the most recent advances, Handbook of Volatility Models and Their Applications explores key concepts and topics essential for modeling the volatility of financial time series, both univariate and multivariate, parametric and non-parametric, high-frequency and low-frequency. Featuring contributions from international experts in the field, the book features numerous examples and applications from real-world projects and cutting-edge research, showing step by step how to use various methods accurately and efficiently when assessing volatility rates. Following a comprehensive introduction to the topic, readers are provided with three distinct sections that unify the statistical and practical aspects of volatility: Autoregressive Conditional Heteroskedasticity and Stochastic Volatility presents ARCH and stochastic volatility models, with a focus on recent research topics including mean, volatility, and skewness spillovers in equity markets Other Models and Methods presents alternative approaches, such as multiplicative error models, nonparametric and semi-parametric models, and copula-based models of (co)volatilities Realized Volatility explores issues of the measurement of volatility by realized variances and covariances, guiding readers on how to successfully model and forecast these measures Handbook of Volatility Models and Their Applications is an essential reference for academics and practitioners in finance, business, and econometrics who work with volatility models in their everyday work. The book also serves as a supplement for courses on risk management and volatility at the upper-undergraduate and graduate levels.

The modeling of high-frequency volatility is of utmost importance in comprehending market dynamics and the characteristics of risk. The adoption of high-frequency volatility modeling in the agricultural sector has the potential to enhance risk management for food production enterprises through the utilization of hedging strategies to mitigate the impact of food price changes. The GARCH (Generalized Autoregressive Conditional Heteroskedasticity) class of models is well-suited for the analysis and prediction of volatility in financial time series. These models effectively capture the highest level of volatility observed in the time series data. Therefore, this research utilizes one-minute trade data of the Wind Agriculture Index (886045.WI) to examine the efficacy and predictability of several GARCH class volatility models. When it comes to fitting the data within the sample, the TGARCH model demonstrates superior performance compared to both the GARCH and EGARCH models. The fluctuations in the price changes of the Wind Agriculture Index exhibit characteristics of time variability and clustering, which can be attributed to the relatively low barriers for entry and exit in the agricultural planting sector. Simultaneously, within the agricultural market, an imbalance is observed whereby the influence of positive information on price volatility surpasses that of negative information.

The role of China's crude oil futures in world oil futures market and China's financial market

Summary We propose a new generalized autoregressive conditional heteroscedastic (GARCH) model with tree-structured multiple thresholds for the estimation of volatility in financial time series. The approach relies on the idea of a binary tree where every terminal node parameterizes a (local) GARCH model for a partition cell of the predictor space. The fitting of such trees is constructed within the likelihood framework for non-Gaussian observations: it is very different from the well-known regression tree procedure which is based on residual sums of squares. Our strategy includes the classical GARCH model as a special case and allows us to increase model complexity in a systematic and flexible way. We derive a consistency result and conclude from simulation and real data analysis that the new method has better predictive potential than other approaches.