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The perturbation term in the updating equation of the state covariance matrix is weighted by the estimate of the measurement error variance. This avoids the calibration of a design parameter as the perturbation term is scaled by the amount of uncertainty in the data. It is shown by Monte Carlo simulations that this perturbation method is associated with a good tracking of the dynamics of the parameters compared to other online algorithms and to classical and Bayesian methods. The standardized self\u2010perturbed Kalman filter is adopted to forecast the equity premium on the S&amp;P 500 index under several model specifications, and determines the extent to which realized variance can be used to predict excess returns. Copyright \u00a9 2016 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/jae.2522","type":"journal-article","created":{"date-parts":[[2016,4,30]],"date-time":"2016-04-30T09:36:27Z","timestamp":1462008987000},"page":"318-341","source":"Crossref","is-referenced-by-count":14,"title":["Forecasting With the Standardized Self\u2010Perturbed Kalman Filter"],"prefix":"10.1002","volume":"32","author":[{"given":"Stefano","family":"Grassi","sequence":"first","affiliation":[{"name":"School of Economics University of Kent Canterbury UK"},{"name":"CREATES Aarhus University Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nima","family":"Nonejad","sequence":"additional","affiliation":[{"name":"CREATES Aarhus University Denmark"},{"name":"Department of Mathematical Sciences Aalborg University Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Paolo Santucci","family":"De Magistris","sequence":"additional","affiliation":[{"name":"CREATES Aarhus University Denmark"},{"name":"Department of Economics and Business Econometrics Aarhus University Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2016,4,28]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.2307\/2527343"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1198\/016214501750332965"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/hhl021"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/jae.691"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1198\/07350010152596718"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(86)90063-1"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1093\/jjfinec\/nbj014"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-2966.2008.00453.x"},{"key":"e_1_2_8_10_1","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/hhm046"},{"key":"e_1_2_8_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.red.2004.10.009"},{"key":"e_1_2_8_12_1","doi-asserted-by":"publisher","DOI":"10.1257\/mac.2.1.43"},{"key":"e_1_2_8_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfineco.2012.04.003"},{"key":"e_1_2_8_14_1","volume-title":"Time Series Analysis by State Space Methods","author":"Durbin J","year":"2001"},{"key":"e_1_2_8_15_1","doi-asserted-by":"publisher","DOI":"10.2307\/1912773"},{"key":"e_1_2_8_16_1","unstructured":"FaginS.1964.Recursive linear regression theory optimal filter theory and error analysis of optimal systems IEEE International Convention Record Vol.2:New York;216\u2013240."},{"key":"e_1_2_8_17_1","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.49.5.639.15149"},{"key":"e_1_2_8_18_1","doi-asserted-by":"publisher","DOI":"10.2202\/1941-1928.1050"},{"key":"e_1_2_8_19_1","series-title":"Advanced Texts in Econometrics","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780199278657.001.0001","volume-title":"Readings in Unobserved Components Models","author":"Harvey AC","year":"2005"},{"key":"e_1_2_8_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfineco.2010.09.008"},{"key":"e_1_2_8_21_1","volume-title":"Stochastic Processes and Filtering Theory","author":"Jazwinsky A","year":"1970"},{"key":"e_1_2_8_22_1","doi-asserted-by":"crossref","unstructured":"JensenMJ MaheuJM.2013.Risk return and volatility feedback: a Bayesian nonparametric analysis. 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