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Title: On time-dependent cointegration with an application Authors:  Guy Melard - Université libre de Bruxelles (Belgium) [presenting]
Abstract: The focus is on VARMA models with deterministically time-dependent (td), coefficients, possibly dependent on the series length $n$. Previous work studied the asymptotic theory of the quasi-maximum likelihood (QML) estimators for these tdVARMA$^{(n)}$) models. Under appropriate assumptions, these estimators are consistent and asymptotically normal. Time-dependent co-integration is considered. This is done by starting from a time-dependent extension of an error correction model (ECM), denoted tdECM$^{(n)}$. Generalizing previous work, the tdECM$^{(n)}$ is expressed as a tdVARMA$^{(n)}$ model on the differenced series. Hence, the original parameters of the tdECM$^{(n)}$ can be estimated by using a QML estimation method using the exact Gaussian likelihood. The asymptotic theory is applicable, and its assumptions can be checked a posteriori. An example on the US interest rates taken from the literature will illustrate the results: a time-dependent co-integration relation exists and is statistically significant.