Time‐series models with an EGB2 conditional distribution

Abstract

A time‐series model in which the signal is buried in noise that is non‐Gaussian may throw up observations that, when judged by the Gaussian yardstick, are outliers. We describe an observation‐driven model, based on an exponential generalized beta distribution of the second kind (EGB2), in which the signal is a linear function of past values of the score of the conditional distribution. This specification produces a model that is not only easy to implement but which also facilitates the development of a comprehensive and relatively straightforward theory for the asymptotic distribution of the maximum‐likelihood (ML) estimator. Score‐driven models of this kind can also be based on conditional t distributions, but whereas these models carry out what, in the robustness literature, is called a soft form of trimming, the EGB2 distribution leads to a soft form of Winsorizing. An exponential general autoregressive conditional heteroscedastic (EGARCH) model based on the EGB2 distribution is also developed. This model complements the score‐driven EGARCH model with a conditional t distribution. Finally, dynamic location and scale models are combined and applied to data on the UK rate of inflation.

Robust time series models with trend and seasonal components

“…If desired, λ and σ can be updated at each step using the sample variance of the u t s. The relationship between variance of the u t s and λ for the t-distribution is given in Harvey (2013, p. 62). For the EGB2 (with ξ = ς) it follows from Caivano and Harvey (2014) that σ 2 u = σ 2 h 2 ξ 2 /(2ξ + 1). The seasonally adjusted observations are constructed as…”

“…Similarly a parametric form of Winsorizing is given by the exponential generalized beta distribution of the second kind (EGB2) distribution. The article by Caivano and Harvey (2014) sets out the theory for the DCS location model with an EGB2 distribution and illustrates its practical value.…”

Time Series Models with an EGB2 Conditional Distribution

“…For many puposes, it is better to parameterize the scale in terms of the standard deviation in (4) and so is replaced by h exp( ). Unfortunately, the presence of h = h( ; &) complicates the information matrix, as shown inCaivano and Harvey (2013). Thus it is simpler to just replace by exp( ); where = ln h; if asymptotic standard errors are to be computed.…”

Score-driven currency exchange rate seasonality as applied to the Guatemalan Quetzal/US Dollar

“…With respect to Beta-t-EGARCH, we refer to the recent applications of Blazsek and Villatoro (2015), Blazsek and Mendoza (2016), and Blazsek and Monteros (2017). Another example of DCS models is QAR (Harvey 2013), which is a nonlinear and outlier-robust alternative to the AR Moving Average (ARMA) model (Box and Jenkins 1970). An additional recent example of DCS models is QVAR (Blazsek et al , 2018b, which is a nonlinear and outlier-robust alternative to the VARMA model (see, for example, Lütkepohl 2005).…”

“…3.3). DCS-EGARCH models for the Student's-t, Skew-Gen-t, EGB2 and NIG distributions are named Beta-t-EGARCH (Harvey and Chakravarty 2008), Skew-Gen-t-EGARCH (Harvey and Lange 2017), EGB2-EGARCH (Caivano and Harvey 2014) and NIG-EGARCH (Blazsek et al 2018c), respectively. We initialize λ t by using parameter λ 0 .…”