Trend–cycle–seasonal Interactions: Identification and Estimation

Abstract

Economists typically use seasonally adjusted data in which the assumption is imposed that seasonality is uncorrelated with trend and cycle. The importance of this assumption has been highlighted by the Great Recession. The paper examines an unobserved components model that permits nonzero correlations between seasonal and nonseasonal shocks. Identification conditions for estimation of the parameters are discussed from the perspectives of both analytical and simulation results. Applications to UK household consumption expenditures and US employment reject the zero correlation restrictions and also show that the correlation assumptions imposed have important implications about the evolution of the trend and cycle in the post-Great Recession period.

COVID-19 and Seasonal Adjustment

“…To fully appreciate the recommendation of Eurostat ( 2020 ) and its consequences, simulation studies are required in which we know the processes of the components of the variables. Seasonal adjustment produces latent variables, so it makes sense to design experiments in which the processes of the non-seasonal and seasonal components are known, and possibly correlated (Hindrayanto et al, 2019 ).…”

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

“…Therefore, the local level and seasonality shocks are correlated. The DCS models with stochastic local level and stochastic seasonality of this paper are alternatives to the recent Unobserved Components Model (UCM) of Hindrayanto et al (2018) that uses correlated shocks for the local level and seasonality components. Thirdly, we model the time-varying scale of the irregular component v t by using the DCS-EGARCH(1,1) model λ t = ω + βλ t−1 + αu λ,t−1 , which is updated by the score function u λ,t with respect to λ t (u λ,t is defined in Sect.…”

A Bayesian Semiparametric Approach for Trend–Seasonal Interaction: an Application to Migration Forecasts

“…As it is particularly malleable, the latter can conveniently model multiple seasonal spikes by simply increasing its order. These two components become the arguments of an unknown bivariate smooth function, which relaxes the hypothesis that trend and seasonality evolve independently (Koopman and Lee, ; Hindrayanto et al ., ). The non‐parametric nature of the interaction does not impose a rigid structure to the trend–seasonal comovements, returning an additive model with interaction (AMI).…”