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Theory"],"published-print":{"date-parts":[[2012,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The family of multiplicative error models, introduced by Engle (2002, <jats:italic>Journal of Applied Econometrics<\/jats:italic> 17, 425\u2013446), has attracted considerable attention in recent literature for modeling positive random variables, such as the duration between trades at a stock exchange, volume transactions, and squared log returns. Such models are also applicable to other positive variables such as waiting time in a queue, daily\/hourly rainfall, and demand for electricity. This paper develops a new method for testing the lack-of-fit of a given parametric multiplicative error model having a Markov structure. The test statistic is of Kolmogorov\u2013Smirnov type based on a particular martingale transformation of a marked empirical process. The test is asymptotically distribution free, is consistent against a large class of fixed alternatives, and has nontrivial asymptotic power against a class of nonparametric local alternatives converging to the null hypothesis at the rate of <jats:italic>O<\/jats:italic> (<jats:italic>n<\/jats:italic><jats:sup>\u20131\/2<\/jats:sup>). In a simulation study, the test performed better overall than the general purpose Ljung\u2013Box <jats:italic>Q<\/jats:italic>-test, a Lagrange multiplier type test, and a generalized moment test. We illustrate the testing procedure by considering two data examples.<\/jats:p>","DOI":"10.1017\/s0266466612000102","type":"journal-article","created":{"date-parts":[[2012,5,21]],"date-time":"2012-05-21T09:56:46Z","timestamp":1337594206000},"page":"1283-1312","source":"Crossref","is-referenced-by-count":18,"title":["LACK-OF-FIT TESTING OF THE CONDITIONAL MEAN FUNCTION IN A CLASS OF MARKOV MULTIPLICATIVE ERROR MODELS"],"prefix":"10.1017","volume":"28","author":[{"given":"Hira L.","family":"Koul","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Indeewara","family":"Perera","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mervyn J.","family":"Silvapulle","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2012,5,21]]},"reference":[{"key":"S0266466612000102_ref29","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1214\/aos\/1018031108","article-title":"Nonparametric model checks for time series","volume":"27","author":"Koul","year":"1999","journal-title":"Annals of Statistics"},{"key":"S0266466612000102_ref42","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600004898"},{"key":"S0266466612000102_ref24","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.2010.00681.x"},{"key":"S0266466612000102_ref37","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1963-0153046-2"},{"key":"S0266466612000102_ref1","first-page":"1","article-title":"Econometric analysis of intra-daily trading activity on the Tokyo stock exchange","volume":"24","author":"Bauwens","year":"2006","journal-title":"Monetary and Economic Studies"},{"key":"S0266466612000102_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2004.06.003"},{"key":"S0266466612000102_ref7","doi-asserted-by":"publisher","DOI":"10.1093\/jjfinec\/nbq016"},{"key":"S0266466612000102_ref22","doi-asserted-by":"publisher","DOI":"10.2139\/ssrn.951399"},{"key":"S0266466612000102_ref14","doi-asserted-by":"publisher","DOI":"10.1162\/REST_a_00167"},{"key":"S0266466612000102_ref36","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-6419.2007.00547.x"},{"key":"S0266466612000102_ref38","doi-asserted-by":"crossref","first-page":"1916","DOI":"10.1214\/aos\/1024691363","article-title":"Model checks for regression: An innovation process approach","volume":"26","author":"Stute","year":"1998","journal-title":"Annals of Statistics"},{"key":"S0266466612000102_ref20","doi-asserted-by":"publisher","DOI":"10.21314\/JCF.2001.071"},{"key":"S0266466612000102_ref35","doi-asserted-by":"publisher","DOI":"10.1198\/073500105000000081"},{"key":"S0266466612000102_ref11","doi-asserted-by":"publisher","DOI":"10.3103\/S106653070902001X"},{"key":"S0266466612000102_ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2009.10.008"},{"key":"S0266466612000102_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2005.01.018"},{"key":"S0266466612000102_ref10","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1995.10476633"},{"key":"S0266466612000102_ref32","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/65.2.297"},{"key":"S0266466612000102_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(03)00201-X"},{"key":"S0266466612000102_ref8","doi-asserted-by":"publisher","DOI":"10.1353\/mcb.2005.0027"},{"key":"S0266466612000102_ref6","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176347506"},{"key":"S0266466612000102_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-0062-5"},{"key":"S0266466612000102_ref27","doi-asserted-by":"publisher","DOI":"10.1214\/009053604000000274"},{"key":"S0266466612000102_ref15","doi-asserted-by":"publisher","DOI":"10.2307\/2999632"},{"key":"S0266466612000102_ref3","volume-title":"Convergence of Probability Measures","author":"Billingsley","year":"1968"},{"key":"S0266466612000102_ref5","unstructured":"Brownlees, C.T. , Cipollini, F. , & Gallo, G.M. 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