The quantilogram: with an application to evaluating directional predictability. We propose a new diagnostic tool for time series called the quantilogram. The tool can be used formally and we provide the inference tools to do this under general conditions, and it can also be used as a simple graphical device. We apply our method to measure directional predictability and to test the hypothesis that a given time series has no directional predictability. The test is based on comparing the correlogram of quantile hits to a pointwise confidence interval or on comparing the cumulated squared autocorrelations with the corresponding critical value. We provide the distribution theory needed to conduct inference, propose some model free upper bound critical values, and apply our methods to S&P500 stock index return data. The empirical results suggest some directional predictability in returns. The evidence is strongest in mid range quantiles like 5--10% and for daily data. The evidence for predictability at the median is of comparable strength to the evidence around the mean, and is strongest at the daily frequency.

References in zbMATH (referenced in 24 articles , 1 standard article )

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  1. Ando, Tomohiro; Bai, Jushan: Quantile co-movement in financial markets: a panel quantile model with unobserved heterogeneity (2020)
  2. Ćmiel, Bogdan; Ledwina, Teresa: Validation of association (2020)
  3. Frongillo, Rafael; Nobel, Andrew: Memoryless sequences for general losses (2020)
  4. Lee, Ji Hyung; Linton, Oliver; Whang, Yoon-Jae: Quantilograms under strong dependence (2020)
  5. Meziani, Aymen; Medkour, Tarek; Djouani, Karim: Penalised quantile periodogram for spectral estimation (2020)
  6. Chen, Cathy Yi-Hsuan; Härdle, Wolfgang Karl; Okhrin, Yarema: Tail event driven networks of SIFIs (2019)
  7. Hué, Sullivan; Lucotte, Yannick; Tokpavi, Sessi: Measuring network systemic risk contributions: a leave-one-out approach (2019)
  8. Jiang, Huayun; Todorova, Neda; Roca, Eduardo; Su, Jen-Je: Agricultural commodity futures trading based on cross-country rolling quantile return signals (2019)
  9. Lee, Ji Hyung: Martingale decomposition and approximations for nonlinearly dependent processes (2019)
  10. Davis, Richard A.; Drees, Holger; Segers, Johan; Warchoł, Michał: Inference on the tail process with application to financial time series modeling (2018)
  11. Vilar, José A.; Lafuente-Rego, Borja; D’Urso, Pierpaolo: Quantile autocovariances: a powerful tool for hard and soft partitional clustering of time series (2018)
  12. Ćmiel, Bogdan; Ledwina, Teresa: Validation of positive expectation dependence (2017)
  13. Montes-Rojas, Gabriel: Reduced form vector directional quantiles (2017)
  14. Han, Heejoon; Linton, Oliver; Oka, Tatsushi; Whang, Yoon-Jae: The cross-quantilogram: measuring quantile dependence and testing directional predictability between time series (2016)
  15. Kley, Tobias; Volgushev, Stanislav; Dette, Holger; Hallin, Marc: Quantile spectral processes: asymptotic analysis and inference (2016)
  16. Lafuente-Rego, Borja; Vilar, José A.: Clustering of time series using quantile autocovariances (2016)
  17. Lee, Ji Hyung: Predictive quantile regression with persistent covariates: IVX-QR approach (2016)
  18. Dette, Holger; Hallin, Marc; Kley, Tobias; Volgushev, Stanislav: Of copulas, quantiles, ranks and spectra: an (L_1)-approach to spectral analysis (2015)
  19. Schmitt, Thilo A.; Schäfer, Rudi; Dette, Holger; Guhr, Thomas: Quantile correlations: uncovering temporal dependencies in financial time series (2015)
  20. Park, Joon Y.; Whang, Yoon-Jae: Random walk or chaos: a formal test on the Lyapunov exponent (2012)

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