Semiparametric lag dependent functions

This paper introduces a suite of tests for linear and general non-linear serial dependence. The problem is complex as the number ofvariations of realistic non-linear alternatives is very large.The alternative model is dened in terms of penalized truncatedpolynomial splines, making the approximation capable of accuratelyapproximating a large class of linear and non-linear processes.The asymptotic distribution for the test statistic is derived, and weshow using Monte Carlo simulations that one test is equivalent to theLjung-Box test, other linear tests corresponds to ordinary or partialsample autocorrelation while the non-linear versions are capable of de-tecting non-linear eects, even when other tests fail to do so.