Conditional Heteroskedasticity Process Research Articles

Test of parameter changes in a class of observation-driven models for count time series

This paper investigates the parameter-change tests for a class of observation-driven models for count time series. We propose two cumulative sum (CUSUM) test procedures for detection of changes in model parameters. Under regularity conditions, the asymptotic null distributions of the test statistics are established. In addition, the integer-valued generalized autoregressive conditional heteroskedastic (INGARCH) processes with conditional negative binomial distributions are investigated. The developed techniques are examined through simulation studies and also are illustrated using an empirical example.

Random coefficient autoregressive processes and the PUCK model with fluctuating potential

The potentials of unbalanced complex kinetics (PUCK) model consists of a random walker subjected to a potential centered at its moving average position. We study the PUCK model with fluctuating quadratic potential, showing that it is a special case of the random coefficient autoregressive (RCAR) process and thus a member of the same class of processes as the autoregressive conditional heteroskedasticity (ARCH) process; both RCAR processes but with different coefficient dependence. For the general Gaussian RCAR process, we use generalized Fibonacci numbers to derive explicit expressions for the mean squared displacement and the autocovariance function. We also obtain the conditions for divergence of variance, which imply tail index of the power-law-tailed cumulative probability distribution. Translating the results to the PUCK model, we analyze US Dollar/Japanese Yen market data and demonstrate that the model simultaneously reproduces empirical facts of price time series: diffusion and autocorrelation of prices and heavy-tailed distribution of price changes.

Effects of Price Insurance Programs on Supply Response: A Case Study of Corn Farmers in Quebec

Aims: This study examines the supply response of corn in the province of Quebec. Study Design: A time series design is implemented. Place and Duration of Study: Our analysis covers the period from 1985 to 2013 and uses the data of corn production in the province of Quebec. Methodology: A generalised autoregressive conditional heteroskedasticity (GARCH) process is used to model output price expectations and its volatility. Results: We found that application of the Farm Income Stabilisation Insurance in Quebec neutralises the adverse effects of price volatilities on corn production and generates a market power for corn producers. The change in the producers' attitude towards risk is other implication of the insurance program. Conclusion: These results imply that implementation of the insurance program in the province of Quebec leads to an increase of corn production and consequently this increase in production can impose more compensation cost (paid by the insurance program) to governments.

Conditional maximum likelihood estimation in negative binomial INGARCH processes with known number of successes when the true parameter is at the boundary of the parameter space

The paper establishes the asymptotic distribution of the conditional maximum likelihood estimator for integer-valued generalized autoregressive conditional heteroskedastic (INGARCH) processes of conditional negative binomial distributions, with the number of successes in the definition of the negative binomial distribution being assumed to be known, when the true parameter is at the boundary of the parameter space. Based on the result, coefficient nullity tests are developed for model simplification. The proposed tests are investigated through a simulation study.

Financial Scandal and China’s Stock Market Couplings

This paper examines the impact of CITIC Securities (CITICS)’ insider trading on five state-owned banks’ stock returns in China. We first conduct a structural Vector Autoregression model together with Granger causality to investigate the response of banks’ returns to that of CITICS. Next an Exponential Generalised AutoRegressive Conditional Heteroskedasticity process is employed to capture the volatilities of stock returns, and therefore investigate the response of five banks to that of CITICS. The dataset for three months after the scandal is obtained and the estimation results show some significant coupling effects do exist within stock returns of financial sector in stock market as well as within their volatilities. The core findings in this study suggest that Chinese stock prices could reflect all relevant information available from past changes in the share price as well as publicly available information. To some extent, China’s stock market is semi-strong efficiency, implying the quality of investors’ rationality and providing regulators with empirical evidence to policy-making.

Effect of petroleum product prices on Thailand's economic growth

Thailand has long been familiar with price control for petroleum products of economic or social importance. This paper applies the model of Garen et al. (2011) to investigate whether increases in petroleum product prices can reduce real gross domestic product (GDP). Time series analysis of data for the 24 quarters from 2009 to 2014 is used to determine real GDP. Two models use an autoregressive conditional heteroskedasticity process with regard to GARCH(1, 1) and EGARCH, and employ lagged variables to incorporate feedback over time. Price increases for both gasoline with 85% ethanol (E85) and unleaded regular gasoline with research octane number of 91 (UGR91) appear to have a positive effect on real GDP. This might be a result of government subsidies and taxes, including the effect of oil companies' income on real GDP. Contrastingly, low sulphur diesel (LSD) price increases appear to have a negative effect on real GDP.

A Nonlinear ARMA-GARCH Model With Johnson $S_u$ Innovations and Its Application to Sea Clutter Modeling

In this paper, a novel time series heteroskedastic model is proposed for sea clutter modeling application. In the light of characteristics of the practical clutter at low grazing angle, the original generalized autoregressive conditional heteroskedasticity process, which has been widely used in various fields of economics, is extended from three aspects. First, the autoregressive moving-average terms are introduced for modeling the temporal correlation of both clutter returns and innovations. Second, the exponential of the conditional variance is generalized from one to arbitrary positive value, to capture the nonlinearity existing in the practical clutter. Third, the traditional Gaussian innovation is replaced by the Johnson $S_{u}$ random variable, which is a monotonic transformation of the Gaussian random variable and is capable of modeling the skewness and kurtosis. By systematically analyzing a large number of practical sea clutter data sets, we show that the proposed time series model fits the data better than some commonly used statistic-based distributions, such as the Weibull and compound Gaussian distributions.

On the tail behavior of a class of multivariate conditionally heteroskedastic processes

Conditions for geometric ergodicity of multivariate autoregressive conditional heteroskedasticity (ARCH) processes, with the so-called BEKK (Baba, Engle, Kraft, and Kroner) parametrization, are considered. We show for a class of BEKK-ARCH processes that the invariant distribution is regularly varying. In order to account for the possibility of different tail indices of the marginals, we consider the notion of vector scaling regular variation (VSRV), closely related to non-standard regular variation. The characterization of the tail behavior of the processes is used for deriving the asymptotic properties of the sample covariance matrices.

An Online Sequential Learning Non-parametric Value-at-Risk Model for High-Dimensional Time Series

Online Value-at-Risk (VaR) analysis in high-dimensional space remains a challenge in the era of big data. In this paper, we propose an online sequential learning non-parametric VaR model called OS-GELM which is an autonomous cognitive system. This model uses a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) process and an online sequential extreme learning machine (OS-ELM) to cognitively calculate VaR, which can be used for online risk analysis. The proposed model not only learns the data one-by-one or chunk-by-chunk but also calculates VaR in real time by extending OS-ELM from machine learning to the non-parametric GARCH process. The GARCH process is also extended to one-by-one and chunk-by-chunk mode. In OS-GELM, the parameters of hidden nodes are randomly selected. The output weights are analytically determined based on the sequentially arriving data. In addition, the generalization performance of the OS-GELM model attains a small training error and generates the smallest norm of weights. Experimentally obtained VaRs are compared with those given by GARCH-type models and conventional OS-ELM. The computational results demonstrate that the OS-GELM model obtains more accurate results and is better at forecasting the online VaR. OS-GELM model is an autonomous cognitive system to dynamically calculate Value-at-Risk, which can be used for online financial risk assessment about human being’s behavior. The OS-GELM model can calculate VaR in real time, which can be used as a tool for online risk management. OS-GELM can handle any bounded, non-constant, piecewise-continuous membership function to realize real-time VaR monitoring.

QMLE for Quadratic ARCH Model with Long Memory

We discuss parametric quasi‐maximum likelihood estimation for quadratic autoregressive conditional heteroskedasticity (ARCH) process with long memory introduced in Doukhan emphet al. (2016) and Grublytė and Škarnulis (2016) with conditional variance involving the square of inhomogeneous linear combination of observable sequence with square summable weights. The aforementioned model extends the quadratic ARCH model of Sentana () and the linear ARCH model of Robinson () to the case of strictly positive conditional variance. We prove consistency and asymptotic normality of the corresponding quasi‐maximum likelihood estimates, including the estimate of long memory parameter 0 < d < 1/2. A simulation study of empirical mean‐squared error is included.

CAUSALITY-IN-VARIANCE BETWEEN THE STOCK MARKET AND MACROECONOMIC VARIABLES IN SINGAPORE

The present study investigates the causality-in-variance between macroeconomic variables and the stock market in Singapore from November 1990 to March 2013. This study utilizes the [Sanso, A, V Arago and JL Carrion (2004). Testing for change in the unconditional variance of financial time series. Revista de Economia Financiera, 4, 32–53.] test to detect the structural break in variance; a generalized autoregressive conditional heteroskedasticity (GARCH) process to model volatility; and the cross correlation function (CCF) causality method. The results demonstrate that the most important macroeconomic causes of stock market volatility in Singapore is exchange rate volatility. The findings provide preliminary insights on risk elements for policy makers monitoring the stability of financial markets by providing insights about volatility spillovers and risk transmission between the stock market and macroeconomic variables in Singapore.

Dynamic and Asymmetric Contagion Reactions of Financial Markets During the Last Subprime Crisis

To analyze the dynamic and asymmetric contagion reactions of financial markets during the last subprime crisis, this paper proposes a contagion reaction equation combined with the generalized auto regressive conditional heteroskedasticity process to develop a dynamic asymmetric contagion model, and then provides the Markov chain Monte Carlo estimation method of this new model. This paper then constructs an empirical study of two metals futures in China during the last subprime crisis period, applying the model to measure the impact of the contagion reactions as well as assess the model’s effectiveness. Our results show: (1) the financial contagion phenomenon is the reason why some financial markets experienced almost corresponding reactions during the subprime crisis; (2) financial contagion reactions behave conspicuously in three particular phases during the subprime crisis; (3) financial contagion reactions have predictive functions for financial market changes and can provide indicators for risk management during crisis periods.

DAY-OF-THE-WEEK EFFECT IN US BIOTECHNOLOGY STOCKS — DO POLICY CHANGES AND ECONOMIC CYCLES MATTER?

This study examines the presence of the day-of-the-week effect on daily returns of biotechnology stocks over a 16-year period from January 2002 to December 2015. Using daily returns from the NASDAQ Biotechnology Index (NBI), we find that the stock returns were the lowest on Mondays, and compared to the Mondays the stock returns were significantly higher on Wednesdays, Thursdays, and Fridays. The day-of-the-week effect on returns of biotechnology stocks remained significant even after controlling for the Fama–French and Carhart factors. Moreover, the results from using the asymmetric generalized autoregressive conditional heteroskedastic (GARCH) processes reveal that momentum and small-firm effect were positively associated with the market risk-adjusted returns of the biotechnology stocks during this period. The findings of our study suggest that active portfolio managers need to consider the day of the week, momentum, and small-firm effect when making trading decisions for biotechnology stocks. Implications for portfolio managers, small investors, scholars, and policymakers are included.

Chaoticity Properties of Fractionally Integrated Generalized Autoregressive Conditional Heteroskedastic Processes

Fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) arises in modeling of financial time series. FIGARCH is essentially governed by a system of nonlinear stochastic difference equations.In this work, we have studied the chaoticity properties of FIGARCH (p,d,q) processes by computing mutual information, correlation dimensions, FNNs (False Nearest Neighbour), the largest Lyapunov exponents (LLE) for both the stochastic difference equation and for the financial time series by applying Wolf’s algorithm, Kant’z algorithm and Jacobian algorithm. Although Wolf’s algorithm produced positive LLE’s, Kantz’s algorithm and Jacobian algorithm which are subsequently developed methods due to insufficiency of Wolf’s algorithm generated negative LLE’s constantly.So, as well as experimenting Wolf’s methods’ inefficiency formerly pointed out by Rosenstein (1993) and later Dechert and Gencay (2000), based on Kantz’s and Jacobian algorithm’s negative LLE outcomes, we concluded that it can be suggested that FIGARCH (p,d,q) is not deterministic chaotic process.

Functional Generalized Autoregressive Conditional Heteroskedasticity

Heteroskedasticity is a common feature of financial time series and is commonly addressed in the model building process through the use of autoregressive conditional heteroskedastic and generalized autoregressive conditional heteroskedastic (GARCH) processes. More recently, multivariate variants of these processes have been the focus of research with attention given to methods seeking an efficient and economic estimation of a large number of model parameters. Because of the need for estimation of many parameters, however, these models may not be suitable for modelling now prevalent high‐frequency volatility data. One potentially useful way to bypass these issues is to take a functional approach. In this article, theory is developed for a new functional version of the GARCH process, termed fGARCH. The main results are concerned with the structure of the fGARCH(1,1) process, providing criteria for the existence of strictly stationary solutions both in the space of square‐integrable and continuous functions. An estimation procedure is introduced, and its consistency and asymptotic normality are verified. A small empirical study highlights potential applications to intraday volatility estimation.

Liquidation discount—a novel application of ARFIMA–GARCH

Urgent liquidation of a large stock portfolio entails a liquidity cost—i.e., a “liquidation discount”. This is the market impact discount in value yielded by the immediate sale of the portfolio relative to its in-hand market value calculated from prevailing market prices. For any portfolio, the day-to-day liquidation discount “at risk” (i.e., the liquidation discount that would be suffered if liquidation were undertaken) is variable. This liquidation discount risk is additional to price risk and will be of concern to portfolio managers that may, at short notice, wish to convert substantial stockholdings to cash. We obtain daily time series of instantaneous log liquidation discount for variously sized portfolios of Australian stocks and determine that these time series are best modeled with an Autoregressive Fractionally Integrated Moving Average-Generalized Autoregressive Conditional Heteroskedasticity (ARFIMA–GARCH) process. We then formulate a liquidation discount-at-risk measure with which portfolio managers can budget for the future cost of portfolio liquidity for a chosen liquidation horizon and confidence level.

On the Distribution Estimation of Power Threshold Garch Processes

The aim of this article is to estimate the probability distribution of power threshold generalized autoregressive conditional heteroskedasticity processes by establishing bounds for their finite dimensional laws. These bounds only depend on the parameters of the model and on the distribution function of its independent generating process. The application of this study to some particular models allows us to conjecture that this procedure is an adequate alternative to the corresponding estimation using the empirical distribution functions, particularly useful in the development of control charts for this kind of models.

Composite quantile regression estimation for P-GARCH processes

We consider the periodic generalized autoregressive conditional heteroskedasticity (P-GARCH) process and propose a robust estimator by composite quantile regression. We study some useful properties about the P-GARCH model. Under some mild conditions, we establish the asymptotic results of proposed estimator. The Monte Carlo simulation is presented to assess the performance of proposed estimator. Numerical study results show that our proposed estimation outperforms other existing methods for heavy tailed distributions. The proposed methodology is also illustrated by VaR on stock price data.

Supply Response of Corn Farmers in Quebec: Analyzing the Impact of Prices Volatility?

This study examines the supply response and the effect of price predictability of corn in the province of Quebec. A generalized autoregressive conditional heteroskedasticity (GARCH) process is used to model output price expectations and its volatility. The empirical results show that price predictability has a positive effect on producers’ decisions. Estimation of supply elasticity illustrates that expected output price is the most important risk factor for corn producers in Quebec.As expected, we found that the Farm Income Stabilization Insurance (ASRA) in Quebec leads producers to be more sensitive to effective prices than to market prices. Our results also show that application of this program causes less sensitivity to input prices than to output prices. Reducing producers’ risk aversion is another implication of this program.

Signal Processing Technique for Combining Numerous MEMS Gyroscopes Based on Dynamic Conditional Correlation

A signal processing technique is presented to improve the angular rate accuracy of Micro-Electro-Mechanical System (MEMS) gyroscope by combining numerous gyroscopes. Based on the conditional correlation between gyroscopes, a dynamic data fusion model is established. Firstly, the gyroscope error model is built through Generalized Autoregressive Conditional Heteroskedasticity (GARCH) process to improve overall performance. Then the conditional covariance obtained through dynamic conditional correlation (DCC) estimator is used to describe the correlation quantitatively. Finally, the approach is validated by a prototype of the virtual gyroscope, which consists of six-gyroscope array. The experimental results indicate that the weights of gyroscopes change with the value of error. Also, the accuracy of combined rate signal is improved dramatically compared to individual gyroscope. The results indicate that the approach not only improves the accuracy of the MEMS gyroscope, but also discovers the fault gyroscope and eliminates its influence.