Restricted estimation of an adjusted time series: application to Mexico's industrial production index

The inclusion of linear deterministic effects in a time series model is important to get an appropriate specification. Such effects may be due to calendar variation, outlying observations or interventions. This article proposes a two-step method for estimating an adjusted time series and the parameters of its linear deterministic effects simultaneously. Although the main goal when applying this method in practice might only be to estimate the adjusted series, an important by-product is a substantial increase in efficiency in the estimates of the deterministic effects. Some theoretical examples are presented to demonstrate the intuitive appeal of this proposal. Then the methodology is applied on two real datasets. One of these applications investigates the importance of the 1995 economic crisis on Mexico's industrial production index.