Testing of seasonal integration and cointegration with fractionally integrated techniques: An application to the Danish labour demand

This article examines seasonal quarterly data of several labour demand variables in Denmark by means of fractional integration techniques. We use the same dataset as in Engsted and Haldrup [Engsted, T., Haldrup, N., 1994, The linear quadratic adjustment cost model and the demand for labour. Journal of Applied Econometrics 9, 145-159] and Fanelli [Fanelli, L., 2002. A new approach for estimating and testing the linear quadratic adjustment cost model under rational expectations and I(1) variables. Journal of Economic Dynamics and Control 26, 117-139]. In these two papers they examine the demand for labour using classic cointegration techniques at the long run or zero frequency, based on error correction models. In this paper, we argue that some of the variables used in these models might be misspecified due to the seasonal structure underlying the processes. In fact, a seasonal fractional model may be a more adequate specification for some of the series. A small empirical application based on seasonal fractional cointegration is also carried out at the end of the article.