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A Random Walk Test for Functional Time Series

Author

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  • Mingotti, Nicola
  • Lillo Rodríguez, Rosa Elvira
  • Romo, Juan

Abstract

In this paper we introduce a Random Walk test for Functional Autoregressive Processes of Order One. The test is non parametric, based on Bootstrap and Functional Principal Components. The power of the test is shown through an extensive Montecarlo simulation. We apply the test to two real dataset, Bitcoin prices and electrical energy consumption in France.

Suggested Citation

  • Mingotti, Nicola & Lillo Rodríguez, Rosa Elvira & Romo, Juan, 2015. "A Random Walk Test for Functional Time Series," DES - Working Papers. Statistics and Econometrics. WS ws1506, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws1506
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    References listed on IDEAS

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    1. Battaglia, Francesco, 2005. "Outliers in functional autoregressive time series," Statistics & Probability Letters, Elsevier, vol. 72(4), pages 323-332, May.
    2. Haeran Cho & Yannig Goude & Xavier Brossat & Qiwei Yao, 2013. "Modeling and Forecasting Daily Electricity Load Curves: A Hybrid Approach," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 7-21, March.
    3. Philippe C. Besse & Herve Cardot & David B. Stephenson, 2000. "Autoregressive Forecasting of Some Functional Climatic Variations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 673-687, December.
    4. Piotr Kokoszka & Matthew Reimherr, 2013. "Determining the order of the functional autoregressive model," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 116-129, January.
    5. Gabrys, Robertas & Horváth, Lajos & Kokoszka, Piotr, 2010. "Tests for Error Correlation in the Functional Linear Model," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1113-1125.
    6. Meese, Richard A. & Rogoff, Kenneth, 1983. "Empirical exchange rate models of the seventies : Do they fit out of sample?," Journal of International Economics, Elsevier, vol. 14(1-2), pages 3-24, February.
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