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It is shown that the \u201ctrend free\u201d moving average difference series formed by the difference between the terms of the original series and the moving average is always liable to be oscillatory whether or not the original series contains oscillatory components. The expression for the serial correlation coefficients and variance of the moving average difference series is derived in terms of the serial correlation coefficients and variance of the original series. It is shown that for typical examples of auto-correlated non-oscillatory time series the method of moving averages is liable to introduce oscillations of considerable magnitude.<\/jats:p>","DOI":"10.2307\/2983574","type":"journal-article","created":{"date-parts":[[2006,6,18]],"date-time":"2006-06-18T05:10:37Z","timestamp":1150607437000},"page":"104-113","source":"Crossref","is-referenced-by-count":1,"title":["The Oscillatory Properties of the Moving Average"],"prefix":"10.1093","volume":"9","author":[{"given":"J. L.","family":"Spencer-Smith","sequence":"first","affiliation":[{"name":"Linen Industry Research Association"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"key":"2024051016103351100_cit1","doi-asserted-by":"crossref","first-page":"43","DOI":"10.2307\/2980258","article-title":"The effect of the elimination of trend on oscillations in time series","volume":"104","author":"Kendall","year":"1941","journal-title":"J. Roy. Stat. 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Soc."},{"key":"2024051016103351100_cit6","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1093\/biomet\/33.2.105","article-title":"On auto regressive time series","volume":"33","author":"Kendall","year":"1944","journal-title":"Biometrika"},{"key":"2024051016103351100_cit7","first-page":"267","article-title":"On a method of investigating periodicities in disturbed series with special reference to Wolfer\u2019s sunspot numbers","volume":"226a","author":"Yule","year":"1927","journal-title":"Phil. Trans."},{"key":"2024051016103351100_cit8","first-page":"518","article-title":"On periodicity in related terms","volume":"131a","author":"Walker","year":"1931","journal-title":"Proc. Roy. Soc."},{"key":"2024051016103351100_cit9","volume-title":"Symposium on Serial Correlation","author":"","year":"1946"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/9\/1\/104\/49093513\/jrsssb_9_1_104.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/9\/1\/104\/49093513\/jrsssb_9_1_104.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,10]],"date-time":"2024-05-10T16:12:22Z","timestamp":1715357542000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/9\/1\/104\/7026524"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1947,1,1]]},"references-count":9,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,12,5]]},"published-print":{"date-parts":[[1947,1,1]]}},"URL":"https:\/\/doi.org\/10.2307\/2983574","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[1947,1]]},"published":{"date-parts":[[1947,1,1]]}}}