Testing for jumps in conditionally Gaussian ARMA–GARCH models, a robust approach

Abstract

Financial series occasionally exhibit large changes. To deal with those events, we assume that the observed return series consists of a conditionally Gaussian ARMA-GARCH (or -GJR) model contaminated by an additive jump component. In this framework, we propose a new test for additive jumps. The test is based on standardised returns, where the first two conditional moments of the non-contaminated observations are estimated in a robust way. Simulation results indicate that the test has very good finite sample properties, i.e. correct size and high proportion of correct jump detection. We apply our test on daily returns and detect less than 1% of jumps for the three exchange rates and between 1 and 3% of jumps for about 50 large capitalization stocks from the NYSE. Once jumps have been filtered out, all series are found to be conditionally Gaussian. We also find that simple GARCH-type models estimated on filtered returns deliver better out-of-sample forecasts of the conditional variance than GARCH and GAS models estimated on raw data.

Jumps in energy and non‐energy commodities

“…We follow Laurent et al (2016) 5 by testing for additive jumps in AR-GARCH-GJR models 6 . Random returns (r t ) are described by an AR(1)-GARCH(1,1) model: We provide here the pairwise correlation coefficients based on the full sample period (22 September 2008 to 16 April 2019).…”

Realized EquiCorrelation: a bird’s-eye view of financial stress on equity markets

“…Merton (1976) is often considered as one of the seminal contributions to this field: he proposed to add jumps to the pure Gaussian Black and Scholes's (1973) model. Following Lee and Mykland (2008), Laurent et al (2011) have proposed a test based on daily data making it possible to estimate the number of days over which a jump may have happened. The test is based on the standardization of returns: returns are scaled through the estimation of their expectation and volatility.…”

The role of outliers and oil price shocks on volatility of metal prices

“…methods to detect outliers in nonlinear models (see e.g., Sakata and White, 1998;Hotta and Tsay 1999;Franses and Chijsels, 1999;Charles and Darné, 2005;Zhand and King, 2005;Doornik and Ooms, 2005;Laurent et al, 2013). In this study we apply the Doornik and Ooms (2005) procedure to detect the additive outliers in the GARCH-type models.…”

“…Moreover, Charles andDarné (2014a and2014b) estimate the price volatility of crude oil and Dow Jones industrial average index, respectively, after detecting and correcting outliers in the GARCHtype models, applying the Laurent et al (2013) outlier detection method. However, to the best of our knowledge, there is no study in the literature that takes into account the presence of outliers in volatility of non-energy commodity markets.…”