Estimation of Stochastic Volatility with a Compensated Poisson Jump Using Quadratic Variation

Considering the dynamic diffusion in degradation process, we propose an integrated Wiener process with a nonlinear drift and a stochastic volatility for degradation modelling. In our model, the drift and stochastic volatility are estimated nonparametrically to avoid the model misspecification issue. The key innovation of this study is the estimation of stochastic volatility which adopts the functional principal component analysis method and applies it to bipower variance. This estimation approach is able to effectively capture both cross-unit variations and time-varying features within the diffusion process. Also, the proposed model can reduce the estimation bias caused by jump points, which are common phenomenon in degradation process. Furthermore, the distribution of remaining useful life and the mean time to failure are both obtained in explicit forms. Finally, the proposed model and the nonparametric estimation method are illustrated by two simulation experiments and two real cases.

Owing to enormous advances in data acquisition and processing technology the study of high (or ultra) frequency data has become an important area of econometrics. At least three avenues of econometric methods have been followed to analyze high frequency financial data: Models in tick time ignoring the time dimension of sampling, duration models specifying the time span between transactions and, finally, fixed time interval techniques. Starting from the strong assumption that quotes are irregularly generated from an underlying exogeneous arrival process, fixed interval models promise feasibility of familiar time series techniques. Moreover, fixed interval analysis is a natural means to investigate multivariate dynamics. In particular, models of price discovery are implemented in this venue of high frequency econometrics. Recently, a sound statistical theory of ‘realized volatility’ has been developed. In this framework high frequency log price changes are seen as a means to observe volatility at some lower frequency.

Econometric analysis of high frequency data

Chaos and nonlinear theory has significant impact on the analysis of economic and financial time series. Nonlinearity plays an important role in explaining the empirical features of asymmetric business cycles, clustered volatility, and regime switching in finance data. In this Chapter, we will focus the popular local polynomial prediction method and its applications to chaotic time series prediction and financial volatility estimation. Volatility and conditional covariance estimation is important in many aspects of modern finance theory. We introduce a nonparametric volatility model, called local ARCH, and propose a weighted least square method for goodness of fit. The statistical theory is based on a martingale regression framework developed in Lu (1999a,b), which includes a wide variety of nonlinear time series models, such as nonlinear autoregression, ARCH, and nonlinear vector autoregressive models. The daily AOL stock data is used as an example to illustrate the developed techniques. First, we apply the nonlinear regression procedure to model the spread-volume relationship—We find a nice power-law relationship in all appropriate periods after discovering that the spurious nonlinearity in the overall data is due to nonstationarity. We also find a vastly changing structure in GARCH models fitted to different parts of the return rate series based on closing prices. We apply the developed local ARCH theory to a stationary subseries of the return series, and find some encouraging results.

We compare distributional properties of high frequency (tick by tick) returns of stocks traded at the NASDAQ, NYSE, and BSE (Budapest Stock Exchange). In particular, we model returns with a mixture of a degenerate (zero) and a symmetric stable distribution. We measure time with the number of successive price changes on the market and study the convergence of the index of stability on increasing time horizons. We apply results to calculate expected waiting times to reach given levels of value at risk.

Editor's Introduction to Panel Discussion on Analysis of High-Frequency Data

Profitability is a financial ratio that measures the ability of an entity, whether individual or company, to generate profit or earnings. Bank risk is the potential occurrence of an event that could potentially harm the bank. The Covid-19 pandemic caused banks to be highly selective in providing loans and impacted the interest income which is the main income source of the banking industry. This research aims to investigate the influence of income diversification on profitability and bank risk in the Covid-19 pandemic. The population in this study comprises all conventional commercial banking companies listed on the Indonesia Stock Exchange (IDX) from 2020 to 2022. The selected sample for this study consists of 42 companies. The data analysis method used is panel data regression analysis. The results indicate that income diversification has a positive impact on Profitability measured using Return on Assets (ROA) and Return on Equity (ROE). On the other hand, income diversification has a negative impact on Risk measured using the Standard Deviation of Return on Assets (SDROA) and Standard Deviation of Return on Equity (SDROE).
 Profitabilitas merupakan rasio keuangan yang mengukur kemampuan suatu entitas, baik perorangan maupun perusahaan, dalam menghasilkan keuntungan atau pendapatan. Risiko bank adalah potensi terjadinya suatu peristiwa yang berpotensi merugikan bank. Pandemi Covid-19 menyebabkan perbankan menjadi sangat selektif dalam memberikan pinjaman dan berdampak pada pendapatan bunga yang merupakan sumber pendapatan utama industri perbankan. Penelitian ini bertujuan untuk mengetahui pengaruh diversifikasi pendapatan terhadap profitabilitas dan risiko bank pada masa pandemi Covid-19. Populasi dalam penelitian ini adalah seluruh perusahaan perbankan umum konvensional yang terdaftar di Bursa Efek Indonesia (BEI) pada tahun 2020 hingga 2022. Sampel yang dipilih untuk penelitian ini terdiri dari 42 perusahaan. Metode analisis data yang digunakan adalah analisis regresi data panel. Hasil penelitian menunjukkan bahwa diversifikasi pendapatan berpengaruh positif terhadap Profitabilitas yang diukur menggunakan Return on Assets (ROA) dan Return on Equity (ROE). Di sisi lain, diversifikasi pendapatan berdampak negatif terhadap Risiko yang diukur menggunakan Standar Deviasi Return on Assets (SDROA) dan Standar Deviasi Return on Equity (SDROE).

<p style='text-indent:20px;'>This paper provides invariance theorems that facilitate testing for the existence of an asset price bubble in a market where the price evolves as a Markov diffusion process. The test involves only the properties of the price process' quadratic variation under the statistical probability. It does not require an estimate of either the equivalent local martingale measure or the asset's drift. To augment its use, a new family of stochastic volatility price processes is also provided where the processes' strict local martingale behavior can be characterized.</p>

Volatility forecasts crucial to many financial applications usually assume implicitly that the frequency of the data should match the forecast horizon; portfolio managers typically rely on risk models estimated using monthly data to produce monthly volatility forecasts, for example. For longer–term forecasts, this practice has two drawbacks: Volatility estimates can be based on stale data; and return events occurring within long sampling intervals are obscured, confounding estimation. Monthly volatility risk measures constructed using higher–frequency data seem to be more robust than those using low–frequency data. Microstructure effects can explain the differences in estimates.

Quasi-fiscal policies in times of crisis: A high-frequency data analysis

A nonparametric eigenvalue-regularized integrated covariance matrix estimator for asset return data

This study examines volatility transmission between major European indices (CAC 40, DAX, FTSE MIB, IBEX 35, EURO STOXX 50) and Tunisia’s TUNINDEX amid global crises (2008 financial crisis, COVID-19, Russo-Ukrainian war). Using GARCH(1,1) and BEKK models, the analysis reveals low correlation and weak volatility spillovers between the TUNINDEX and European markets, indicating relative decoupling. ARCH-LM tests confirm conditional heteroskedasticity, while GARCH models show persistent volatility. The BEKK model underscores marginal shock transmission, affirming the TUNINDEX’s independence. These findings suggest diversification benefits for investors but highlight local risk considerations. Practical recommendations are provided for stakeholders, with future research directions including asymmetric effects and high-frequency data analysis.

<p>Using volatility estimation as the underlying commonality this thesis traverses the statistical problem of robust estimation of scale, through to the financial problem of valuing call options over stock. We use a large simulation study of robust scale estimators to benchmark a nonparametric volatility estimation procedure, which not only uses techniques which are particularly suited to observed financial returns, but also addresses the problem of bias in any robust volatility estimation procedure. Existing option pricing models are discussed with careful study of the assumed volatility and elasticity of volatility with respect to stock price relationships for each of these models. An option pricing formula is derived which extends existing methods, and provides a closed form solution which can be readily computed. Preliminary analysis of real price data suggests this model is able to explain observed leverage phenomena.</p>

This paper aims to empirically examine long memory and bi-directional information flow between estimated volatilities of highly volatile time series datasets of five cryptocurrencies. We propose the employment of Garman and Klass (GK), Parkinson’s, Rogers and Satchell (RS), and Garman and Klass-Yang and Zhang (GK-YZ), and Open-High-Low-Close (OHLC) volatility estimators to estimate cryptocurrencies’ volatilities. The study applies methods such as mutual information, transfer entropy (TE), effective transfer entropy (ETE), and Rényi transfer entropy (RTE) to quantify the information flow between estimated volatilities. Additionally, Hurst exponent computations examine the existence of long memory in log returns and OHLC volatilities based on simple R/S, corrected R/S, empirical, corrected empirical, and theoretical methods. Our results confirm the long-run dependence and non-linear behavior of all cryptocurrency’s log returns and volatilities. In our analysis, TE and ETE estimates are statistically significant for all OHLC estimates. We report the highest information flow from BTC to LTC volatility (RS). Similarly, BNB and XRP share the most prominent information flow between volatilities estimated by GK, Parkinson’s, and GK-YZ. The study presents the practicable addition of OHLC volatility estimators for quantifying the information flow and provides an additional choice to compare with other volatility estimators, such as stochastic volatility models.

This data set provides Daymet output data as mosaicked gridded estimates of daily weather parameters for North America, including continuous surfaces of day length, precipitation, shortwave radiation, snow water equivalent, maximum air temperature, minimum air temperature, and water vapor pressure. The Daymet data product was derived from selected meteorological station data by interpolation and extrapolation algorithms. The data product covers the period January 1, 1980 to December 31 of the most recently processed calendar year for Canada and the United States. Data for additional calendar years will become available by June of the following year. For Mexico, data are available for the period January 1, 1980 to December 31, 2009. Data are available on a daily time step at a 1-km x 1-km spatial resolution in Lambert Conformal Conic projection with a spatial extent that covers the conterminous United States, Mexico, and Southern Canada as meteorological station density allows. Data are assembled by parameter and year with each yearly file containing a time dimension of 365 days. Data are provided in Climate and Forecast (CF) metadata convention compliant (version 1.4) netCDF file formats.