Testing time series linearity via goodness-of-fit methods |
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| Institution: | 1. Research Department, The Bank of Korea, South Korea;2. Department of Economics, Boston University, 270 Bay State Road, Boston, MA 02215, United States;1. Obstetrics and Gynecology Department (Drs. Uccella, Ferrari, and Zorzato), Ospedale degli Infermi, Biella, Italy;2. Department of Woman and Child Health (Drs. Uccella, Capozzi, Perrone, Ergasti, Cianci, Alletti, and Scambia), Fondazione Policlinico Gemelli, IRCCS, Rome, Italy;3. Obstetrics and Gynecology Department (Drs. Capozzi and Berretta), University of Parma, Parma, Italy;4. Service for Health and Safety on the Workplaces (Dr. Ricco’), AUSL - I.R.C.C.S. di Reggio Emilia, Italy;5. Minimally Invasive Gynecological Surgery Unit (Drs. Zanello and Seracchioli), Sant''Orsola-Malpighi Hospital, Bologna, Italy;6. Department of Obstetrics and Gynecology (Drs. Cromi, Serati, and Ghezzi), University of Insubria, Del Ponte Hospital, Varese, Italy;7. Department of Medicine and Aging Sciences (Dr. Fanfani), University “Gabriele d''Annunzio” of Chieti-Pescara, Italy;8. Endoscopica Malzoni-Center for Advanced Endoscopic Gynecological Surgery (Dr. Malzoni), Avellino, Italy;9. Department of Oncological Surgery, Gynecologic Oncologic Unit (Dr. Vizza), “Regina Elena” National Cancer Institute, IRCCS, Rome, Italy;10. Division of Gynaecology, Department of Obstetrics and Gynaecology (Drs. Guido and Legge), “F. Miulli” General Hospital, Acquaviva delle Fonti, Bari, Italy;11. Department of Obstetrics and Gynecology (Dr. Ciravolo), Spedali Civili di Brescia, Brescia, Italy;12. Gynecology Department (Dr. Candiani), IRCCS San Raffaele Scientific Institute, Milan, Italy. |
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| Abstract: | We consider the problem of testing time series linearity. Existing time domain and spectral domain tests are discussed. A new approach relying on spectral domain properties of a time series under the null hypothesis of linearity is suggested. Under linearity, the normalized bispectral density function Z is a constant. Under the null hypothesis of linearity, properly constructed estimators of 2|Z|2 have a non-central chi-squared distribution with two degrees of freedom and constant non-centrality parameter 2|Z|2. If the null hypothesis is false, the non-centrality parameter is non-constant. This suggests goodness-of-fit tests might be effective in diagnosing non-linearity. Several approaches are introduced. |
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