Predicting Time-Varying Parameters with Parameter-Driven and Observation-Driven Models

Time Varying Transition Probabilities for Markov Regime Switching Models

“…In addition, various successful applications of score models have appeared in the recent literature. For example, Creal et al (2011) and Lucas et al (2014) study dynamic volatilities and correlations under fat-tails and possible skewness; Harvey and Luati (2014) introduce new models for dynamic changes in levels under fat tails; Creal et al (2014) investigate score-based mixed measurement dynamic factor models; Oh and Patton (2013) and De Lira Salvatierra and Patton (2013) investigate factor copulas based on score dynamics; and Koopman et al (2012) show that score driven time series models have a similar fore-casting performance as correctly specified nonlinear non-Gaussian state space models over a range of model specifications.…”

Stationarity and Ergodicity of Univariate Generalized Autoregressive Score Processes

“…Other examples are the observation driven mixed measurement dynamic factor models of Creal, Schwaab, Koopman, and Lucas (2011) and the fat-tailed mixture models for duration data as proposed in Koopman, Lucas, and Scharth (2012). The latter paper also demonstrates that in terms of forecasting accuracy, GAS models perform similar to and sometimes even better than their state space or parameter driven counterparts for a range of data generating processes.…”

“…The case of volatility models is particularly interesting, as it embeds new robust volatility models such as the Student's t based GAS volatility model of and the Beta-t-Garch model of Harvey and Chakravarty (2008) as well as new models for positively valued random variables, such as the robust Gamma-Weibull mixture models for duration data as proposed in Koopman, Lucas, and Scharth (2012).…”

Intraday Stock Price Dependence Using Dynamic Discrete Copula Distributions

“…In particular, the dynamic parameters in our model, including stock return volatilities and dependence parameters, are updated using an observation driven, autoregressive updating function based on the score of the conditional observation probability mass function; for an introduction to the score driven approach, see Lucas (2011, 2013) and Harvey (2013), and for successful applications see, for example, De Lira Salvatierra and Patton (2013), Lucas, Schwaab, and Zhang (2014), Harvey andLuati (2014), andCreal, Schwaab, Koopman, and. As is known from the literature, score driven models have three main advantages: (i) they possess information theoretic optimality properties, see Blasques, Koopman, and Lucas (2015); (ii) they have similar forecasting performance as their parameter driven counterparts, even when the latter constitute the true data generating process, see Koopman, Lucas, and Scharth (2015); and (iii) as score driven models are observation driven rather than parameter driven in the classification of Cox (1981), the model's static parameters can be estimated in a straightforward way using maximum likelihood methods.…”