Time-varying Variance Research Articles

Modeling streamflow time series using nonlinear SETAR-GARCH models

Although hydrological processes are generally nonlinear, linear time series models are commonly adopted in the field of water sciences. Nonlinear approaches such as threshold time series and conditional heteroscedasticity models are still seldom used. In this study, first, two- and three-regime Self-Exciting Threshold Autoregressive (SETAR) models are used to model the mean behavior of daily streamflows. The residual time series computed from the difference between observations and lag-one time-ahead best-estimates of the fitted models are also obtained. Second, the conditional variance behavior of the residual series obtained from the two- and three-regime SETAR models is modeled using the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. The GARCH model is hence used to capture the time-varying variance behavior of residuals as a nonlinear phenomenon and thus it removes the existence of autoregressive conditional heteroscedasticity so-called ARCH effect. Finally, the performance of SETAR models and their combination with the GARCH model are evaluated. Six deseasonalized daily streamflow series from upstream watershed rivers of Zarrineh Rood dam, in the southern part of Lake Urmia in Iran, are used to illustrate and test the procedure. The McLeod-Li test, a formal test for demonstrating the ARCH effect, indicates that the ARCH effect exists in all residual series, which means that the residuals of streamflow time series are nonstationary in terms of the variance. Results indicate that the hybrid SETAR-GARCH models performed better than the models without GARCH component. Results demonstrate also that the use of nonlinear SETAR and GARCH improves streamflow modeling efficiency by capturing the heteroscedasticity in the residuals of nonlinear threshold time series.

Noise-Statistics Learning of Automotive-Grade Sensors Using Adaptive Marginalized Particle Filtering

This paper presents a method for real-time identification of sensor statistics especially aimed for low-cost automotive-grade sensors. Based on recent developments in adaptive particle filtering (PF) and under the assumption of Gaussian distributed noise, our method identifies the slowly time-varying sensor offsets and variances jointly with the vehicle state, and it extends to banked roads. While the method is primarily focused on learning the noise characteristics of the sensors, it also produces an estimate of the vehicle state. This can then be used in driver-assistance systems, either as a direct input to the control system or indirectly to aid other sensor-fusion methods. The paper contains verification against several simulation and experimental data sets. The results indicate that our method is capable of bias-free estimation of both the bias and the variance of each sensor, that the estimation results are consistent over different data sets, and that the computational load is feasible for implementation on computationally limited embedded hardware typical of automotive applications.

Multiple streamflow time series modeling using VAR–MGARCH approach

Multivariate time series modeling approaches are known as valuable methods for simulating and forecasting the temporal evolution of hydroclimatic variables. These approaches are also useful for modeling the temporal dependence and cross-dependence between variables and sites. Although multiple linear time series approaches, such as vector autoregressive (VAR) and multiple generalized autoregressive conditional heteroscedasticity (MGARCH) approaches are ordinarily applied in finance and econometrics, these methods have not been broadly applied in hydrology science. The present research employs the VAR and VAR–MGARCH methods to model the mean and conditional variance (heteroscedasticity) of daily streamflow data in the Zarrineh Rood dam watershed, in northwestern Iran. The bivariate diagonal vectorization heteroscedasticity (DVECH) model, as one of the key MGARCH models, demonstrates how the conditional variance, covariance, and correlation structures change in time between the residual time series from VAR model. In this regards, in the present study, five experiments which present different combinations of twofold streamflows (including both upstream and downstream stations) are conducted. The VAR approach is fitted to the twofold daily time series in each of the experiments with different orders. The Portmanteau test, as a formal test for demonstrating time-varying variance (or so-called ARCH effect), indicates the existence of conditional heteroscedastic behavior in the twofold residual time series obtained from the VAR models fitted to the twofold streamflows. Thus, the VAR–DVECH approach is suggested to capture the inherent heteroscedasticity in daily streamflow series. The bivariate DVECH approach indicates short-term and long-term persistency in the conditional variance–covariance structure of the twofold residuals of streamflows. Results show also that the use of the nonlinear bivariate DVECH model improves streamflow modeling efficiency by capturing the heteroscedasticity in the twofold residuals obtained from the VAR model for all experiments. The assessment criteria indicate also that the VAR–DVECH approach leads to a better performance than the VAR model.

Analyzing the Dynamic Equicorrelation Between Shanghai Composite (SSEC) and Austral African Stock Market Indices

In this article, we employ the GARCH-DECO (1,1) to investigate empirically the dependence between Shanghai Composite (SSEC) and Austral African stock market indices. We utilize daily return indices over the period from January 4, 2006 to December 30, 2016. From the empirical findings, the conditional dependence between Shanghai Composite (SSEC) and Austral African stock market indices show the existence of high volatility and confirm the existence of a significantly time-varying variance in the conditional linkages between time series returns obtained after the estimation of the GARCH-DECO (1,1) model. Additionally, the conditional heteroscedasticity volatility prediction attains the maximum after the financial crisis of 2007, especially in 2008 and 2009. Our empirical results indicate the existence of high dependency between Shanghai Composite (SSEC) and Austral African stock market indices which prove the financialization of Chinese stock market and Austral African stock market indices. We also find some evidence on the leadership of China in the African region. We discuss implications for the financial integration literature.

Object Tracking Over Distributed WSNs With Consensus on Estimates and Missing Data

Wireless sensor network (WSN) technologies are used to provide mobile object tracking due to advantages such as mobility, scalability, and flexibility. However, wireless interaction between the network nodes is often accompanied by missing data, which requires robustness from the estimator. This paper develops an iterative distributed unbiased finite impulse response (dUFIR) filtering algorithm for object tracking via WSNs with consensus on estimates and shows that it has higher robustness than the distributed Kalman filter (dKF). The tracking problem is viewed as a real-time position estimation of an unmanned ground vehicle (UGV). The extensive simulations are provided using real sensor parameters and measurements of the UGV position with missing data. Two different scenarios are considered when: 1) each sensor is capable of measuring the UGV position and 2) sensors have different time-varying noise variances, as in practical WSNs. The higher robustness of the dUFIR against the dKF is demonstrated under diverse operation conditions.

MV Benchmark for Networked Control Systems with Random Communication Delays

Abstract This work considers the control performance assessment (CPA) of networked control systems (NCSs) with random communication delays. Two kinds of communication delays are considered simultaneously: sensor-to-controller communication delay and controller-to-actuator communication delay A closed-form solution of the linear time-variant (LTV) minimum variance (MV) control law is derived for this class of systems. Correspondingly the MV benchmark value is calculated based on the achieved output with minimum variance. These results can be used for evaluating the potential improvement of control performance for NCSs with random communication delays. Further, the proposed results are illustrated based on a numerical example.

Co-movements in volatility of dependency between US dollar and euro: analysing by conditional heteroscedasticity models

In this study, we use for the first time the conditional heteroscedasticity specifications (GARCH, AGARCH, APARCH, Asymmetry MEM, MEM, EGARCH, GJR GARCH, and GAS-GARCH Student t models) to examine the volatility of exchange rate returns between the US dollar and the euro. So, the conditional heteroscedasticity models are used to capture the time-varying parameter by the function of the likelihood function. Methodologically, we utilise a daily data of the exchange rate between the US dollar and the euro during the period of study from 2 January 2000 to 30 June 2015. From the empirical findings, we remark that the exchange rate returns between the US dollar and the euro show a highly volatility and validate the presence of a greatly time-varying variance in the exchange rate time series obtained after the estimation of the conditional heteroscedasticity models. Besides, we can remark that the conditional heteroscedasticity volatility prediction attains their maximum after the financial crisis of 2008, especially on 2009. Our empirical findings indicate the existence of highly dependency between the US dollar and the euro which prove the economic and financial integration between the USA and the Euro zone.

Identification and estimation of acoustic signals parameters in telecommunication systems of audio exchange

The paper studies the formation of models of stationary signals by linear systems with constant parameters and nonlinear systems described by second-order and third-order functional series. It is also shown that the nonstationary nature of signals, in general, can be represented by a system with variable parameters. The equations obtained in the work solve the problem of identifying the parameters of a model of a non-stationary signal with a time-varying mean value and variance. The object of the study are stationary and nonstationary processes and their statistical characteristics. The aim of the work is to develop methods for identifying and evaluating process parameters describing the acoustic signal in telecommunication systems.

Time-varying Variance Scaling: Application of the Fractionally Integrated ARMA Model

Time-varying variance scaling is the technique by which a mean-variance investor can volatility manage a portfolio by adjusting allocation according to the attractiveness of the mean-variance trade-off, μt/σt2. This study shows that the choice of volatility forecasting models significantly affects performance. We find that the fractionally integrated ARMA model provides significantly better scaling input than the simple historical average volatility for most test portfolios examined by this study. For standard momentum portfolios, however, using the simple historical average as input for volatility scaling resulted in the best performance in many cases.

Option Pricing with Arima-Garch Models of Underlying Asset Returns

ARIMA-GARCH models are used in the analysis of financial series with time-varying conditional variance. A calibrated model of underlying asset returns allows computing all derivatives of the original money flow. The article describes an ARIMA-GARCH model of the underlying asset returns, the forms of ARIMA- and GARCH-components, and the corresponding stationarity conditions. A survey of the results on option pricing by ARIMA-GARCH and GARCH models of underlying asset returns is presented.

Valuing executive stock options under correlated employment shocks

In this paper, we present a valuation framework for pricing executive stock options that incorporates the vesting period, employment shocks as well as time-varying variances of the stock. A GARCH process is used to describe the variance of the stock and employment shocks are captured by a doubly stochastic Poisson process. Additionally, the proposed model allows for the correlation between the intensity and the variance of the stock. In the proposed framework, we derive a closed-form expression for executive stock options and investigate executive stock option prices numerically.

Incipient Fault Detection for Complex Industrial Processes with Stationary and Nonstationary Hybrid Characteristics

For a nonstationary process which has a time-varying mean, a time-varying variance, or both, it can be difficult to detect incipient disturbances which may be hidden by the time-varying process variations. Besides, stationary and nonstationary characteristics may coexist in complex industrial processes which, however, have not been studied for process monitoring. In the present work, a triple subspace decomposition based dissimilarity analysis algorithm is developed to detect incipient abnormal behaviors in complex industrial processes with both stationary and nonstationary hybrid characteristics. The novelty is how to comprehensively separate the stationary and nonstationary process characteristics and describe them, respectively. First, a stationarity evaluation and separation strategy is proposed to decompose the data space into three subspaces, revealing the linear stationary process characteristics, the nonlinear stationary process characteristics, and the final nonstationary process characteristics....

Mutual information identifies spurious Hurst phenomena in resting state EEG and fMRI data.

Long-range memory in time series is often quantified by the Hurst exponent H, a measure of the signal's variance across several time scales. We analyze neurophysiological time series from electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) resting state experiments with two standard Hurst exponent estimators and with the time-lagged mutual information function applied to discretized versions of the signals. A confidence interval for the mutual information function is obtained from surrogate Markov processes with equilibrium distribution and transition matrix identical to the underlying signal. For EEG signals, we construct an additional mutual information confidence interval from a short-range correlated, tenth-order autoregressive model. We reproduce the previously described Hurst phenomenon (H>0.5) in the analytical amplitude of alpha frequency band oscillations, in EEG microstate sequences, and in fMRI signals, but we show that the Hurst phenomenon occurs without long-range memory in the information-theoretical sense. We find that the mutual information function of neurophysiological data behaves differently from fractional Gaussian noise (fGn), for which the Hurst phenomenon is a sufficient condition to prove long-range memory. Two other well-characterized, short-range correlated stochastic processes (Ornstein-Uhlenbeck, Cox-Ingersoll-Ross) also yield H>0.5, whereas their mutual information functions lie within the Markovian confidence intervals, similar to neural signals. In these processes, which do not have long-range memory by construction, a spurious Hurst phenomenon occurs due to slow relaxation times and heteroscedasticity (time-varying conditional variance). In summary, we find that mutual information correctly distinguishes long-range from short-range dependence in the theoretical and experimental cases discussed. Our results also suggest that the stationary fGn process is not sufficient to describe neural data, which seem to belong to a more general class of stochastic processes, in which multiscale variance effects produce Hurst phenomena without long-range dependence. In our experimental data, the Hurst phenomenon and long-range memory appear as different system properties that should be estimated and interpreted independently.

An Empirical Research on Marketing Strategies of Different Risk Preference Merchant

Holiday merchandise has unique demand characteristics, unofficial start data, and a limited life cycle. In an intensely competitive market, individual merchants are able to get more sales opportunities if they display their products earlier. In this study, a time-variant variance and time-variant expected market demand model are introduced to investigate the order strategies that are used by risk-averse holiday merchants. Our results show that risk preference, market uncertainty, and market power have a significant effect on the merchant’s market strategies. Risk-averse merchants prefer to enhance forecast accuracy rather than using an early-display advantage. They can even give up their early-display advantage if they are faced with increased market uncertainty and small market power. Compared with the fixed purchase cost, the time-sensitive purchase cost can stimulate the merchant to purchase in advance, but this can decrease the merchant’s profit. Consequently, risk-averse merchants always display their merchandise later, decrease the order quantity, and, finally, miss the market opportunity.

Blind Source Separation Using Temporal Correlation, Non-Gaussianity and Conditional Heteroscedasticity

Independent component analysis separates latent sources from a linear mixture by assuming sources are statistically independent. In real world applications, hidden sources are usually non-Gaussian and have dependence among samples. In such case, both attributes should be considered jointly to obtain a successful separation. To capture sample dependence, a latent source is sometimes modeled by autoregressive or moving average models with an independent and identically distributed error or residual. However, these models are limited by assuming only linear dependence among a source’s samples. This paper proposes a new blind source separation algorithm based on an autoregressive-autoregressive conditional heteroscedasticity (AR-ARCH) model, which captures linear correlations, non-Gaussianity, and squared residuals’ dependence. The AR part of the AR-ARCH model captures the correlation among samples. The ARCH part of the model captures the non-Gaussianity and nonlinear dependence among samples. The ARCH model also assumes the time-varying conditional variances for sources. We derive the Cramer Rao lower bound (CRLB) for the mixing matrix based on the AR-ARCH model. We perform simulations on both synthetic and real data. The results show that the proposed method outperforms the baseline algorithms especially for a small number of samples and approaches the CRLB.

Within and Cross Volatility Contagion Effects among Stock, Crude and Forex Returns: Empirical Evidence from Five Emerging Economies

The paper examines the spillover effects of return volatility among stock market index, foreign exchange market and WTI crude oil market across five emerging nations. Here a Trivariate Diagonal BEKK-GARCH model is used to estimate the time-varying conditional variance and to test the own-volatility spillover effects of returns among the three underlying variables. We find that significant own volatility spillover exists in the WTI returns followed by that of stock returns and forex returns. Further, fluctuations in WTI returns exert considerable influence over the stock market volatilities. The lagged variance of the variables as well as their lagged squared residuals from the mean equation has a positive and significant impact on the current volatility in most cases. The findings of the study are of pertinent importance to financiers, economists, investors and policymakers.

A comprehensive evaluation of value-at-risk models and a comparison of their performance in emerging markets

This paper aims to evaluate the performance of different value-at-risk (VaR) calculation methods, allowing us to identify models that are valid for use in emerging markets. We apply several widely used methods for calculating VaR, including both parametric and nonparametric methods. We consider different confidence levels for the VaR as well as different sample sizes. To test our models’ validity, we use both unconditional and conditional coverage backtests. In addition, we use a ranking method (which entails a backtesting approach based on the regulatory loss function) to appropriately compare the VaR calculation methods. Obtained from data for three different indexes (namely, Iranian, Turkish and Russian), our backtesting results indicate that parametric models from the generalized autoregressive conditional heteroscedasticity family, with asymmetric effects and fat tails (associated with their use of a t distribution), display the best performance. That is, the best-performing models under emerging market conditions are those that satisfy three important criteria simultaneously. First, they account for the time-varying variance. Second, they capture the asymmetric nature of shocks. Third, they are able to deal with fat tails in the distribution. These can also be regarded as the main features of emerging markets.

Risk factors and their associated risk premia: An empirical analysis of the crude oil market

Abstract This paper sheds new light on higher-order price risks in crude oil markets. A model-free analysis reveals that crude oil variance risk behaves fundamentally different from variance risk in equity markets. Most importantly, a skewness swap is no valid hedge for a variance swap and investors fear large price jumps in both directions. A model-based assessment confirms this and reveals that while stochastic volatility is important to capture the statistical properties such as volatility clusters and time-varying variance swap rates, only jump risk seems to be priced with a premium. Empirical evidence from a pricing and hedging exercise confirms these findings.

A Bayesian Structural Time Series Approach to Constructing Rent Indexes: An Application to Indian Office Markets

We introduce new methodology for constructing real estate rent indices. Using unique data on contract rents from six Indian metropolitan markets, we pair subsequent rented units in the same building to create over 12,000 pseudo repeat rent pairs. We impose an autoregressive structure on the log rent returns in a structural time series variant of the repeat sales model widely used in real estate price indexing. We also allow for time-varying index signal and noise variance parameters. This method has several advantages, including low statistical estimation noise (even in small samples), fewer historical revisions, and the ability to capture changes in market volatility and its subsequent effect on the rent index and estimation error. Finally, we estimate the model using full Bayesian inference that gives the entire posterior distribution. The resulting indices are robust to property heterogeneity and omitted variables, and present well behaved quarterly depictions of the recent history of office market rents in the six cities.

Non-stationary random response analysis of structures with uncertain parameters

This paper proposes a non-stationary random response analysis method of structures with uncertain parameters. The structural physical parameters and the input parameters are considered as random variables or interval variables. By using the pseudo-excitation method and the direct differentiation method (DDM), the analytical expression of the time-varying power spectrum and the time-varying variance of the structure response can be obtained in the framework of first order perturbation approaches. In addition, the analytical expression of the first-order and second-order partial derivative (e.g., time-varying sensitivity coefficient) for the time-varying power spectrum and the time-varying variance of the structure response expressed via the uncertainty parameters can also be determined. Based on this and the perturbation technique, the probabilistic and non-probabilistic analysis methods to calculate the upper and lower bounds of the time-varying variance of the structure response are proposed. Finally the effectiveness of the proposed method is demonstrated by numerical examples compared with the Monte Carlo solutions and the vertex solutions.