Abstract
This paper investigates the effect of seasonal adjustment filters on the identification of mixed causal-noncausal autoregressive models. By means of Monte Carlo simulations, we find that standard seasonal filters induce spurious autoregressive dynamics on white noise series, a phenomenon already documented in the literature. Using a symmetric argument, we show that those filters also generate a spurious noncausal component in the seasonally adjusted series, but preserve (although amplify) the existence of causal and noncausal relationships. This result has has important implications for modelling economic time series driven by expectation relationships. We consider inflation data on the G7 countries to illustrate these results.
Highlights
Most empirical macroeconomic studies are based on seasonally adjusted data
The present paper examines the effect of the linear approximation of X-11 seasonal adjustment on the selection of mixed causal-noncausal autoregressive processes
We investigate the effect of seasonal adjustment on selecting mixed causal-noncausal autoregressive (MAR) models for inflation rates of the G7 countries Canada, France, Germany, Italy, Japan, the United Kingdom and the United States
Summary
Most empirical macroeconomic studies are based on seasonally adjusted data. Various methods have been proposed in the literature aiming at removing unobserved seasonal patterns without affecting other properties of the time series. It has been found that the distinctive features of inflation can be captured well by MAR models due to their closeness to rational expectation models (Lanne and Luoto 2012, 2013; Lanne et al 2012a) Another reason why noncausal models can provide a good fit to this type of data is the property that they, at least in the Cauchy case, exhibit a causal recursive double autoregressive structure (Gouriéroux and Zakoïan 2016). This means that one can account for ARCH-type effects in a series by including a noncausal component in the model equation for the conditional mean.
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