Stock Return Volatility and World War II: Evidence From Garch and Garch-X Models

External energy security elements and the riskiness of clean energy stocks: a volatility analysis

“…ARIMA-X( p , i , q ) is an extension of the standard univariate ARIMA( p , i , q ) but the former incorporates exogenous variables which may be crucial in determining the forecast value of the stationary stock returns (Bierens, 1987; Choudhry, 1995; Engle and Patton, 2001). Consequently, following Bierens (1987) and Kur et al (2021), this paper uses ARIMA model that incorporates exogenous variables, ARIMA-X( p , i , q ), to build the conditional mean equation generally specified as follows: where y t is the response variable which must be stationary; ψ 0 is the constant intercept; ϕ i , φ k and θ j are the coefficients of the autoregressive term, k exogenous variables and the moving average respectively; p and q are the lag limits of the autoregressive and the moving average variables respectively; r denotes the number of exogenous variables; x tk represents r number of exogenous variables and ε t is the white-noised residual.…”

“…Supported by this position, and the argument derived from a careful review of the relevant literature, ESEs are included in the variance equation as external factors that may explain CERs volatility. Therefore, following Lamoureux and Lastrapes (1990) and Choudhry (1995), the variance equation is modelled as GARH(1,1) containing ESEs such as Brent oil futures price, Henry Hub natural gas price, coal futures price, carbon futures price and GIT stock price as exogenous variables: where β 1 to β 5 are the constant parameters of the five ESEs external to CERs, introduced as exogenous variables in the conditional variance equation. Following Engle and Patton (2001), these variables are lagged once indicating that it will take one day for news about shocks from these variables to fully reach the NASDAQ clean energy stock market.…”

“…3.3.1 Mean equation. ARIMA-X(p,i,q) is an extension of the standard univariate ARIMA (p,i,q) but the former incorporates exogenous variables which may be crucial in determining the forecast value of the stationary stock returns (Bierens, 1987;Choudhry, 1995;Engle and Patton, 2001). Consequently, following Bierens (1987) and Kur et al (2021), this paper uses ARIMA model that incorporates exogenous variables, ARIMA-X(p, i, q), to build the conditional mean equation generally specified as follows:…”

“…Supported by this position, and the argument derived from a careful review of the relevant literature, ESEs are included in the variance equation as external factors that may explain CERs volatility. Therefore, following Lamoureux and Lastrapes (1990) and Choudhry (1995), the variance equation is modelled as GARH(1,1) containing ESEs such as Brent oil futures price, Henry Hub natural gas price, coal futures price, carbon futures price and GIT stock price as exogenous variables:…”

Optimal hedging efficiency in global freight markets: Comparing FFAs and time charter strategies

“…The importance of cointegration between spot and future prices is underscored by Kroner and Sultan (1993), Chou et al (1993), and Lien and Tse (1999). Choudhry (1997) utilizes a GARCH (1,1) model with a BEKK formation to examine spot and futures stock indices. Kavussanos and Visvikis (2006) have pioneered empirical work on FFAs, as most studies focus on the delisted BIFFEX futures contract due to data availability issues with FFAs.…”