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We present 22 new times of mid-transit that confirm the existence of transit timing variations, and are well fitted by a quadratic ephemeris with period decay dP\/dt\u00a0= \u22129.2\u00a0\u00b1\u00a01.1\u2009ms\u2009yr\u22121. We rule out instrumental issues, stellar activity, and the Applegate mechanism as possible causes. The light-time effect is also not favoured due to the non-detection of changes in the systemic velocity. Orbital decay and apsidal precession are plausible but unproven. WASP-4\u2009b is only the third hot Jupiter known to show transit timing variations to high confidence. We discuss a variety of observations of this and other planetary systems that would be useful in improving our understanding of WASP-4 in particular and orbital decay in general.<\/jats:p>","DOI":"10.1093\/mnras\/stz2602","type":"journal-article","created":{"date-parts":[[2019,9,18]],"date-time":"2019-09-18T07:36:37Z","timestamp":1568792197000},"page":"4230-4236","source":"Crossref","is-referenced-by-count":35,"title":["Transit timing variations in the WASP-4 planetary system"],"prefix":"10.1093","volume":"490","author":[{"given":"John","family":"Southworth","sequence":"first","affiliation":[{"name":"Astrophysics Group, Keele University, Staffordshire ST5 5BG, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3202-0343","authenticated-orcid":false,"given":"M","family":"Dominik","sequence":"additional","affiliation":[{"name":"Centre for Exoplanet Science, SUPA, School of Physics\u00a0& Astronomy, University of St Andrews, North Haugh, St Andrews KY16 9SS, UK"}]},{"given":"U G","family":"J\u00f8rgensen","sequence":"additional","affiliation":[{"name":"Niels Bohr Institute\u00a0& Centre for Star and Planet Formation, University of Copenhagen, \u00d8ster Voldgade 5, DK-1350 Copenhagen, Denmark"}]},{"given":"M I","family":"Andersen","sequence":"additional","affiliation":[{"name":"Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen, Denmark"}]},{"given":"V","family":"Bozza","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica \u2018E.R. 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