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Estimating the turning point location in shifted exponential model of time series

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  • Camillo Cammarota

Abstract

We consider the distribution of the turning point location of time series modeled as the sum of deterministic trend plus random noise. If the variables are modeled by shifted exponentials, whose location parameters define the trend, we provide a formula for computing the distribution of the turning point location and consequently to estimate a confidence interval for the location. We test this formula in simulated data series having a trend with asymmetric minimum, investigating the coverage rate as a function of a bandwidth parameter. The method is applied to estimate the confidence interval of the minimum location of two types of real-time series: the RT intervals extracted from the electrocardiogram recorded during the exercise test and an economic indicator, the current account balance. We discuss the connection with stochastic ordering.

Suggested Citation

  • Camillo Cammarota, 2017. "Estimating the turning point location in shifted exponential model of time series," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(7), pages 1269-1281, May.
    • Handle: RePEc:taf:japsta:v:44:y:2017:i:7:p:1269-1281
    DOI: 10.1080/02664763.2016.1201797
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    References listed on IDEAS

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    1. Klaus Frick & Axel Munk & Hannes Sieling, 2014. "Multiscale change point inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(3), pages 495-580, June.
    2. Camillo Cammarota, 2011. "The difference-sign runs length distribution in testing for serial independence," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 1033-1043, February.
    3. Ram Mudambi, 1997. "Estimating turning points using polynomial regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 24(6), pages 723-732.
    4. Florenz Plassmann & Neha Khanna, 2007. "Assessing the Precision of Turning Point Estimates in Polynomial Regression Functions," Econometric Reviews, Taylor & Francis Journals, vol. 26(5), pages 503-528.
    5. E. Andersson & D. Bock & M. Frisen, 2006. "Some statistical aspects of methods for detection of turning points in business cycles," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(3), pages 257-278.
    6. Vasyl Golosnoy & Jens Hogrefe, 2013. "Signaling NBER turning points: a sequential approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(2), pages 438-448, February.
    7. Venkata Jandhyala & Stergios Fotopoulos & Ian MacNeill & Pengyu Liu, 2013. "Inference for single and multiple change-points in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 423-446, July.
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