Robust estimation and forecasting of climate change using score-driven ice-age models

ScScore-driven models applied to finance and economics have attracted significant attention in the last decade. In this paper, we apply those models to climate data. We study the robustness of a recent climate econometric model, named ice-age model, and we extend that model by using score-driven filters in the measurement and transition equations. The climate variables considered are Antarctic ice volume Icet, atmospheric carbon dioxide level CO2,t, and land surface temperature Tempt, which during the history of the Earth were driven by exogenous variables. The influence of humanity on climate started approximately 10-15 thousand years ago, and it has significantly increased since then. We forecast the climate variables for the last 100 thousand years, by using data for the period of 798 thousand years ago to 101 thousand years ago for which humanity did not influence the Earth’s climate. For the last 10-15 thousand years of the forecasting period, we find that: (i) the forecasts of Icet are above the observed Icet, (ii) the forecasts of the CO2,t level are below the observed CO2,t, and (iii) the forecasts of Tempt are below the observed Tempt. Our results are robust, and they disentangle the effects of humanity and orbital variables.Blazsek acknowledges funding from Universidad Francisco Marroquín. Escribano acknowledges funding from Ministerio de Economía, Industria y Competitividad (ECO2016-00105-001 and MDM 2014-0431), Comunidad de Madrid (MadEco-CM S2015/HUM-3444), and Agencia Estatal de Investigación (2019/00419/001)

Anticipating extreme losses using score-driven shape filters

We suggest a new value-at-risk (VaR) framework using EGARCH (exponential generalized autoregressive conditional heteroskedasticity) models with score-driven expected return, scale, and shape filters. We use the EGB2 (exponential generalized beta of the second kind), NIG (normal-inverse Gaussian), and Skew-Gen-t (skewed generalized-t) distributions, for which the score-driven shape parameters drive the skewness, tail shape, and peakedness of the distribution. We use daily data on the Standard & Poor"s 500 (S&P 500) index for the period of February 1990 to October 2021. For all distributions, likelihood-ratio (LR) tests indicate that several EGARCH models with dynamic shape are superior to the EGARCH models with constant shape. We compare the realized volatility with the conditional volatility estimates, and we find two Skew-Gen-t specifications with dynamic shape, which are superior to the Skew-Gen-t specification with constant shape. The shape parameter dynamics are associated with important events that affected the stock market in the United States (US). VaR backtesting is performed for the dot.com boom (January 1997 to October 2020), the 2008 US Financial Crisis (October 2007 to March 2009), and the coronavirus disease (COVID-19) pandemic (January 2020 to October 2021). We show that the use of the dynamic shape parameters improves the VaR measurementsAyala and Blazsek acknowledge funding from Universidad Francisco Marroquín. Escribano acknowledges funding from the Spanish Ministry of Economy, Industry and Competitiveness (ECO2015-68715-R, ECO2016-00105-001), Consolidation Grant (#2006/04046/002), and Maria de Maeztu Grant (MDM 2014-0431)

Prediction accuracy of bivariate score-driven risk premium and volatility filters: an illustration for the Dow Jones

In this paper, we introduce Beta-t-QVAR (quasi-vector autoregression) for the joint modelling of score-driven location and scale. Asymptotic theory of the maximum likelihood (ML) estimatoris presented, and sufficient conditions of consistency and asymptotic normality of ML are proven. Forthe joint score-driven modelling of risk premium and volatility, Dow Jones Industrial Average (DJIA)data are used in an empirical illustration. Prediction accuracy of Beta-t-QVAR is superior to theprediction accuracies of Beta-t-EGARCH (exponential generalized AR conditional heteroscedasticity),A-PARCH (asymmetric power ARCH), and GARCH (generalized ARCH). The empirical results motivate the use of Beta-t-QVAR for the valuation of DJIA options