Conditional Mean Equation Research Articles

An examination of impact of gold and oil prices on the stock markets indices during COVID-19

Understanding stock market volatility has remained significantly important because of its diverse implications. The current pandemic COVID-19 has brutally exaggerated the financial market across the board. This study inspects the volatility of Pakistan, India and USA stock markets due to pandemic of COVID-19 using the GARCH model. Furthermore, the price of oil and gold is used as exogenous variables in the conditional mean equation of the GARCH (1,1) model to assess the volatility of stock indices KSE-100 (Pakistan), BSESN (India) and NASDAQ (USA). Moreover, the data covering the period from 1st June 2018 to 31st December 2022 are divided into pre-COVID-19 (1st June 2018 to 30th January 2020) and during-COVID-19 (31st January 2020 to 31st December 2022. Findings reveal that the stock market dependency of NASDAQ experienced oil and gold impact followed by pre-COVID-19 and during-COVID-19 periods, respectively. Whereas, the Indian stock market had a significant impact on gold and oil during the COVID-19 period but the Pakistani stock market was not influenced by oil and gold in the entire considered study period. In addition, NASDAQ market and BSESN have the highest risk-return trade-off and are more persistent followed by pre-COVID-19 and during-COVID-19 periods, respectively.

Effects of Multiple Financial News Shocks on Tourism Demand Volatility Modelling and Forecasting

Even though both symmetric and asymmetric conceptions of news impacts are well-established in the disciplines of economics and financial markets, the effects of combining multiple news shocks on the volatility of tourism demand have not yet been delved into or gauged in any tourist destination. This work hypothesises and verifies that the news impact curve (NIC), conditional heteroscedastic volatility models, and multiple news shocks are suitable for forecasting the volatility of the Malaysian tourist industry. Among them, three primarily volatility models (GARCH, EGARCH, and GJRGARCH) are used in conjunction with five financial news shocks (FFNSs), namely the Kuala Lumpur Composite Index (KLCI), the United States Dollar Index (DXY), the stock performance of 500 large companies listed on stock exchanges (S&P500), Crude Oil (CO), and Gold Price (GP). Among the most significant findings of this study are the demonstration of monthly seasonality using conditional mean equations, asymmetry effects in EGARCH-FFNSs, and GJRGARCH-FFNSs models in conditional variance equations and 50 NICs, and the GARCH-FFNSs model’s evaluation of the persistence influence of news shocks on monthly visitor arrivals in Malaysia. The GJRGARCH-FFNSs model is the best model for Malaysian tourism demand volatility forecasting accuracy. Furthermore, KLCI and Gold Price have the most substantial impact on the number of tourists to Malaysia. In addition, it should be emphasised that the methodological framework utilised in this study can be a useful tool for creating and forecasting the performance of symmetry and asymmetry impacts on tourism demand volatility.

Forecasting electricity prices with expert, linear, and nonlinear models

This paper compares several models for forecasting regional hourly day-ahead electricity prices, while accounting for fundamental drivers. Forecasts of demand, in-feed from renewable energy sources, fossil fuel prices, and physical flows are all included in linear and nonlinear specifications, ranging in the class of ARFIMA-GARCH models—hence including parsimonious autoregressive specifications (known as expert-type models). The results support the adoption of a simple structure that is able to adapt to market conditions. Indeed, we include forecasted demand, wind and solar power, actual generation from hydro, biomass, and waste, weighted imports, and traditional fossil fuels. The inclusion of these exogenous regressors, in both the conditional mean and variance equations, outperforms in point and, especially, in density forecasting when the superior set of models is considered. Indeed, using the model confidence set and considering northern Italian prices, predictions indicate the strong predictive power of regressors, in particular in an expert model augmented for GARCH-type time-varying volatility. Finally, we find that using professional and more timely predictions of consumption and renewable energy sources improves the forecast accuracy of electricity prices more than using predictions publicly available to researchers.

Estimation of large dimensional time varying VARs using copulas

This paper provides a simple, yet reliable, alternative to the (Bayesian) estimation of large multivariate VARs with time variation in the conditional mean equations and/or in the covariance structure. The original multivariate, n-dimensional model is treated as a set of n univariate estimation problems, and cross-dependence is handled through the use of a copula. This makes it possible to run the estimation of each univariate equation in parallel. Thus, only univariate distribution functions are needed when estimating the individual equations, which are often available in closed form, and easy to handle with MCMC (or other techniques). Thereafter, the individual posteriors are combined with the copula, so obtaining a joint posterior which can be easily resampled. We illustrate our approach using various examples of large time-varying parameter VARs with 129 and even 215 macroeconomic variables.

Stationarity and ergodicity of Markov switching positive conditional mean models

A general Markov‐Switching autoregressive conditional mean model, valued in the set of non‐negative numbers, is considered. The conditional distribution of this model is a finite mixture of non‐negative distributions whose conditional mean follows a GARCH‐like dynamics with parameters depending on the state of a Markov chain. Three different variants of the model are examined depending on how the lagged‐values of the mixing variable are integrated into the conditional mean equation. The model includes, in particular, Markov mixture versions of various well‐known non‐negative time series models such as the autoregressive conditional duration model, the integer‐valued GARCH (INGARCH) model, and the Beta observation driven model. For the three variants of the model, conditions are given for the existence of a stationary and ergodic solution. The proposed conditions match those already known for Markov‐switching GARCH models. We also give conditions for finite marginal moments. Applications to various mixture and Markov mixture count, duration and proportion models are provided.

Stochastic analysis of oscillatory hydraulic tomography

This paper investigates the effectiveness of different oscillatory hydraulic tomography (OHT) frequencies for estimating heterogeneous fields. The analysis first formulates the effects of uncharacterized aquifer responses, T, and S fields as the ensemble mean residual flux and residual storage terms in the stochastic unconditional and conditional mean equations. These terms persist unless the T, S, or head fields are specified everywhere. We then conducted OHT to estimate the T and S fields using Monte Carlo experiments. The experiments show that using the heads in response to periodic pumping with different frequencies or multifrequency, the estimates' performance metrics vary from one realization to others. The mean performance metrics over many realizations are, however, indistinguishable, despite the frequency. We attribute the variation in the performance metrics to the lack of parameter or state variable ergodicity. Lastly, we emphasize the importance of dense monitoring networks and a cost-effective data collection strategy to improve the resolution of characterizing aquifer heterogeneity.

The Influence of the Economic Variables on the Chinese B-Share Markets

This paper analyzed how economic variables affect the Chinese B-share market. For this purpose, we investigated the monthly data of major economic variables (consumer price index, imports and exports volume, money supply, real estate index and retail sales volume) and B-share price index of Shanghai and Shenzhen Exchange of China from 2009 to 2019 by employing the multivariate VAR-GARCH-BEKK model. We measured the return spillover effect between Chinese major economic variables and B-share market index from the estimation results of VAR conditional mean equation, and volatility spillover effect between the economic variables and B-share index from the estimation results of GARCH-BEKK conditional variance equation. From these results, we investigated whether there is any difference between the Shanghai and Shenzhen Exchange markets. The main findings are as follows. First, the return spillover effect does not exist in both markets except the Consumer Price Index (CPI). Second, there is the volatility spillover effect between economic variables and Shenzhen B-share market, implying that the volatility spillover effect is more important than the return spillover effect in the Chinese B-share market. Third, compared with Shanghai, the change of the Shenzhen stock market is more affected by the change of economic variables. These findings have some important policy implications. First, investors in Chinese stock market need to make good use of the information inherent in China’s economic changes to increase returns and reduce investment risks. Second, the investors should pay close attention to the overall trends of the Chinese economy and the global economy, not just to the trends of the Chinese market.

Improved ACD-Based Financial Trade Durations Prediction Leveraging LSTM Networks and Attention Mechanism

The liquidity risk factor of security market plays an important role in the formulation of trading strategies. A more liquid stock market means that the securities can be bought or sold more easily. As a sound indicator of market liquidity, the transaction duration is the focus of this study. We concentrate on estimating the probability density function p Δ t i + 1 | G i , where Δ t i + 1 represents the duration of the (i + 1)-th transaction and G i represents the historical information at the time when the (i + 1)-th transaction occurs. In this paper, we propose a new ultrahigh-frequency (UHF) duration modelling framework by utilizing long short-term memory (LSTM) networks to extend the conditional mean equation of classic autoregressive conditional duration (ACD) model while retaining the probabilistic inference ability. And then, the attention mechanism is leveraged to unveil the internal mechanism of the constructed model. In order to minimize the impact of manual parameter tuning, we adopt fixed hyperparameters during the training process. The experiments applied to a large-scale dataset prove the superiority of the proposed hybrid models. In the input sequence, the temporal positions which are more important for predicting the next duration can be efficiently highlighted via the added attention mechanism layer.

Non-linear filter design for a counter-flow heat exchanger: some investigations

This article presents a second-order non-linear filtering technique for a non-trivial state-dependent noise perturbation case of a counter-flow heat exchanger. The conditional mean and variance evolution equations are derived for the non-linear stochastic differential equations relating the dynamics of a counter-flow heat exchanger. The efficacy of the proposed filtering technique is adjudged through detailed parametric investigations for different flow, temperature and noise intensity conditions. These parametric investigation results and that obtained by employing Extended Kalman Filter are compared. The proposed filtering technique is validated using Computational Fluid Dynamics. Theoretical, as well as simulation results, demonstrate the superiority of the proposed filtering technique for estimating stochastically perturbed counter-flow heat exchanger.

Econometric Model Used in the Portfolio Optimization over Several Periods

"The classic problem of optimizing a portfolio can be extended to a multi-stage programming problem. The purpose of the multi-period portfolio optimization problem is to determine the optimal portfolio for a certain finite time horizon. In a multi-period model in which investors are allowed to change the composition of the portfolio, it is essential to take into account trading costs, a solution in this regard being the use of tree-type scenarios. The study undertaken by the authors considered the construction of a portfolio optimization model in case there is a certain constraint on returns. ARMA type processes were used to model the conditional mean equation."

A nonlinear Bayesian filtering approach to estimating adaptive market effciency

Abstract The adaptive market hypothesis (AMH) supplies a convincing motivation for why market efficiency should not be regarded as a stable property in time. This paper explores a Bayesian methodology for estimating weak-form market efficiency under the AMH using a test of evolving efficiency (TEE). More precisely, a generalized TEE (GTEE) approach is proposed in which the conditional first moment of a time series is assumed to be a nonlinear function of its conditional second moment, i.e., a nonlinear feedback term is present in the conditional mean equation. We then discuss a maximum likelihood estimation procedure for the resulting nonlinear model using the state-space approach and extended Kalman filtering. This methodology is used to estimate time-varying, weak-form market efficiency in four, specifically chosen, markets over a time-period that includes the global financial crisis of 2007/2008.

Bayesian Analysis of Extended Auto Regressive Model with Stochastic Volatility

This paper proposes an extension of the autoregressive model with stochastic volatility error. The Bayes analysis of the proposed model using vague priors for the parameters of the conditional mean equation and informative prior for the parameters of conditional volatility equation is done. The Gibbs sampler with intermediate Metropolis steps is used to find out posterior inferences for the parameters of autoregressive model and independent Metropolis–Hastings algorithm is used to simulate the volatility of the mean equation. The two data sets in the form of gross domestic product growth rate of India at constant prices and exchange rate of Indian rupees relative to US dollar are considered for numerical illustration. These data are used after assuring the stationarity by differencing the data once. The retrospective as well as prospective short term predictions of the data are provided based on the two simple components of the general autoregressive process. The findings based on the real data are expected to assist the policy makers and managers to make economic and business strategies more precisely.

The ethanol mandate and crude oil and biofuel agricultural commodity price dynamics

We investigate mean and volatility spillovers between the crude oil market and the main biofuel feedstock markets (corn, soybean, and sugar). In doing so, we estimate a four-variable vector error correction (VEC)–GARCH–in–Mean model with a BEKK representation for the variance equation, and also examine the possible effects of the ethanol mandate by including a dummy variable in both the conditional mean and variance equations. We find that the oil market and the biofuel feedstock markets are tightly interconnected and that the ethanol mandate has strengthened their linkages in terms of volatility spillovers.

Does Indian Spot Electricity Price Series Exhibit Inverse-Leverage Effect?

In this study, we investigate whether Indian Spot Electricity Price Series exhibit Inverse-Leverage effect by modeling Indian spot electricity price using ARIMA-EGARCH model using data given by Indian Energy Exchange from January 1st 2014 to 31st December 2015 accounting for 730 days and 17,520 hourly spot prices for all the five regions of Indian electricity market. Conditional mean and conditional variance equations are estimated. The results of the study provide crucial insights for power market participants/open access consumers whose numbers have surpassed 3530 in Indian Energy Exchange to strategically plan their exposure in Indian spot electricity market.

The Ethanol Mandate and Crude Oil and Biofuel Agricultural Commodity Price Dynamics

We investigate mean and volatility spillovers between the crude oil market and the main biofuel feedstock markets (corn, soybean, and sugar). In doing so, we estimate a four-variable vector error correction (VEC) GARCH-in-Mean model with a BEKK representation for the variance equation, and also examine the possible effects of the ethanol mandate by including a dummy variable in both the conditional mean and variance equations. We find that the oil market and the biofuel feedstock markets are tightly interconnected and that the ethanol mandate has strengthened their linkages in terms of volatility spillovers.

Calendar anomaly: unique evidence from the Indian stock market

PurposeThe purpose of this paper is to ascertain the monthly seasonality in the Indian stock market after taking into consideration the market features of leptokurtosis, volatility clustering and the leverage effect.Design/methodology/approachAugmented Dickey-Fuller, Phillips-Perron and Kwaitkowski-Phillips-Schmidt-Shin tests are deployed to check stationarity of the series. Autocorrelation function, partial autocorrelation function and Ljung-Box statistics are employed to check the applicability of volatility models. An exponential generalized auto regressive conditionally heteroskedastic model is deployed to test the seasonality, where the conditional mean equation is a switching model with dummy variables for each month of the year.FindingsThough the financial year in India stretches from April to March, the stock market exhibits a November effect (returns in November are the highest). Cultural factors, misattribution bias and liquidity hypothesis seem to explain the phenomenon.Research limitations/implicationsThe paper endeavors to provide a review of possible explanations behind month-of-the-year effect documented in literature in the past four decades. Further, the unique evidence from the Indian stock market supports the argument in the literature that monthly seasonality, by nature, may not be a consistent/robust phenomenon. Therefore, it needs to be examined from time to time.Originality/valueAs the seasonality in the stock market and resultant anomalies are dynamic phenomena, the paper reports the current seasonality/anomalies prevalent in the Indian market. This would aid investors in designing short-term investment portfolios (based on anomalies present) in order to earn abnormal returns.

Spot electricity price forecasting in Indian electricity market using autoregressive-GARCH models

In this study we investigate Spot electricity price forecasting performance of Autoregressive-GARCH models on Indian spot electricity price series. Hourly spot electricity price data for each of the five regions of Indian Electricity market from 1st of October 2010 to 15th November 2013 is used for the study to evaluate forecasting performance of the calibrated models. The conditional mean and conditional variance equations are estimated and one-step-ahead forecasts with a rolling window is performed. The fact that India being the only country in the world having power exchanges in-spite of demand outstripping supply and peak power shortage even to this day, further emphasizes the significance and criticality of spot electricity price forecasting from a power market participant's perspective and its practical relevance for Open access consumers in India.

THE ZERO LOWER BOUND AND CRUDE OIL AND FINANCIAL MARKETS SPILLOVERS

We investigate mean and volatility spillovers between the crude oil market and the debt, stock, and foreign exchange markets. In doing so, we estimate a four-variable VARMA–GARCH model with a BEKK representation and also examine the possible effects of monetary policy at the zero lower bound by including a dummy variable in both the conditional mean and variance equations. We find that the crude oil market and the financial markets are tightly interconnected and that monetary policy at the zero lower bound has strengthened their linkages.

Price and volatility transmissions between natural gas, fertilizer, and corn markets

Purpose – The purpose of this paper is to investigate the price and volatility transmission between natural gas, fertilizer (ammonia), and corn markets, an issue that has been traditionally ignored in the literature despite its significant importance. Design/methodology/approach – The authors jointly estimate a vector error correction model for the conditional mean equation and a multivariate generalized autoregressive heteroskedasticity model for the conditional volatility equation to investigate the interactions between natural gas, ammonia, and corn prices and their volatility. Findings – The authors find significant interplay between fertilizer and corn markets, while only a mild linkage in prices and volatility exist between those markets and natural gas during the period 1994-2014. There is not only a positive relationship between corn and ammonia prices in the short run, but both prices react to deviations from the long-run parity. Furthermore, the lagged conditional volatility of ammonia prices positively affects conditional volatility in the corn market and vice versa. This result is robust to a specification using crude oil price as an alternative to natural gas price to account for the large transportation cost built into ammonia prices. Results for the period of 2006-2014 indicate virtually no linkage between natural gas prices and those of fertilizer and corn during that period, while linkages in price level and volatility between the latter remain strong. Originality/value – This paper is the first in the literature to comprehensively examine the role of fertilizer on corn prices and volatility, and its relation to natural gas prices.

New Evidence on Sources of Leverage Effects in Individual Stocks

AbstractI test Black's leverage effect hypothesis on a panel of U.S. stocks from 1997 to 2012. I find that negative stock return innovations increase the future volatility of equity returns by about 36% more than positive ones. There is a strong and positive relation between variation in the size of these leverage effects and variation in the firm's use of debt. I uncover this relation by applying the Fama/French/Carhart 4‐factor asset pricing model in the exponential generalized autoregressive conditional heteroskedasticity mean equation and by using panel data to control for firm‐ and time‐invariant unobservables via first differences and two‐way fixed effects.