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We also provide a frontier for the subset of these tests for which the fixed\u2010<jats:italic>b<\/jats:italic>distribution is<jats:italic>t<\/jats:italic>or<jats:italic>F<\/jats:italic>. These frontiers are respectively achieved by the QS kernel and equal\u2010weighted periodogram. The frontiers have simple closed\u2010form expressions, which show that the price paid for restricting attention to tests with<jats:italic>t<\/jats:italic>and<jats:italic>F<\/jats:italic>critical values is small. The frontiers are derived for the Gaussian multivariate location model, but simulations suggest the qualitative findings extend to stochastic regressors.<\/jats:p>","DOI":"10.3982\/ecta15404","type":"journal-article","created":{"date-parts":[[2021,9,16]],"date-time":"2021-09-16T06:55:56Z","timestamp":1631775356000},"page":"2497-2516","source":"Crossref","is-referenced-by-count":32,"title":["The Size\u2010Power Tradeoff in HAR Inference"],"prefix":"10.3982","volume":"89","author":[{"given":"Eben","family":"Lazarus","sequence":"first","affiliation":[{"name":"Sloan School of Management, Massachusetts Institute of Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniel J.","family":"Lewis","sequence":"additional","affiliation":[{"name":"Federal Reserve Bank of New York"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James H.","family":"Stock","sequence":"additional","affiliation":[{"name":"Department of Economics, Harvard University"},{"name":"NBER"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2021]]},"reference":[{"key":"ecta200306-bib-0001","doi-asserted-by":"crossref","first-page":"817","DOI":"10.2307\/2938229","volume":"59","author":"Andrews","year":"1991","journal-title":"Econometrica"},{"key":"ecta200306-bib-0002","volume-title":"Time Series: Data Analysis and Theory","author":"Brillinger","year":"1975"},{"key":"ecta200306-bib-0003","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/j.jeconom.2006.05.023","volume":"138","author":"Clark","year":"2007","journal-title":"Journal of Econometrics"},{"key":"ecta200306-bib-0004","first-page":"291","volume":"15","author":"den Haan","year":"1997","journal-title":"Handbook of Statistics"},{"key":"ecta200306-bib-0005","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1137\/1114019","volume":"14","author":"Epanechnikov","year":"1969","journal-title":"Theory of Probability & Its Applications"},{"key":"ecta200306-bib-0006","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1017\/S0266466610000496","volume":"27","author":"Gon\u00e7alves","year":"2011","journal-title":"Econometric Theory"},{"key":"ecta200306-bib-0007","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1007\/BF02591360","volume":"1","author":"Grenander","year":"1951","journal-title":"Arkiv F\u00f6r Matematik"},{"key":"ecta200306-bib-0008","doi-asserted-by":"crossref","DOI":"10.1063\/1.3060405","volume-title":"Statistical Analysis of Stationary Time Series","author":"Grenander","year":"1957"},{"key":"ecta200306-bib-0009","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1111\/j.2517-6161.1958.tb00297.x","volume":"20","author":"Hannan","year":"1958","journal-title":"Journal of the Royal Statistical Society. 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