Incorporating relevant multivariate information for characterizing half-life with an application to purchasing power parity

Half-lives are summary measures of persistence, and are usually characterized from impulse response functions (IRFs) of univariate time series models. Two issues which occur with half-life characterization in multivariate time series are IRFs become conditional on specific shocks and are often also not uniquely identified. I introduce an approach for characterizing the half-life in multivariate time series models which circumvents both issues. An empirical application suggests the half-life of the real exchange rate estimated from multivariate models is generally longer relative to univariate models.