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The Analysis of Seasonal Long Memory: The Case of Spanish Inflation

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  • Josu Arteche

Abstract

This paper describes semiparametric techniques recently proposed for the analysis of seasonal or cyclical long memory and applies them to a monthly Spanish inflation series. One of the conclusions is that this series has long memory not only at the origin but also at some but not all seasonal frequencies, suggesting that the fractional difference operator (1−L12)d should be avoided. Moreover, different persistent cycles are observed before and after the first oil crisis. Whereas the cycles seem stationary in the former period, we find evidence of a unit root after 1973, which implies that a shock has a permanent effect. Finally, it is shown how to compute the exact impulse responses and the coefficients in the autoregressive expansion of parametric seasonal long memory models. These two quantities are important to assess the impact of aleatory shocks such as those produced by a change of economic policy and for forecasting purposes, respectively.

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  • Josu Arteche, 2007. "The Analysis of Seasonal Long Memory: The Case of Spanish Inflation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 69(6), pages 749-772, December.
    • Handle: RePEc:bla:obuest:v:69:y:2007:i:6:p:749-772
    DOI: 10.1111/j.1468-0084.2007.00478.x
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    Cited by:

    1. Josu Arteche, 2012. "Standard and seasonal long memory in volatility: an application to Spanish inflation," Empirical Economics, Springer, vol. 42(3), pages 693-712, June.
    2. Voges, Michelle & Sibbertsen, Philipp, 2021. "Cyclical fractional cointegration," Econometrics and Statistics, Elsevier, vol. 19(C), pages 114-129.
    3. Richard Hunt & Shelton Peiris & Neville Weber, 2022. "Estimation methods for stationary Gegenbauer processes," Statistical Papers, Springer, vol. 63(6), pages 1707-1741, December.
    4. Luis Gil-Alana, 2010. "A seasonal fractional multivariate model. A testing procedure and impulse responses for the analysis of GDP and unemployment dynamics," Empirical Economics, Springer, vol. 38(2), pages 471-501, April.
    5. García Enríquez, Javier & Arteche González, Jesús María & Murillas Maza, Arantza, 2010. "Fractional Integration Analysis and its Implications on Profitability: the Case of the Mackerel Market in the Basque Country," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    6. Guglielmo Maria Caporale & Luis Alberiko Gil-Alana & Carlos Poza & Alvaro Baños Izquierdo, 2023. "Persistence and Seasonality in the US Industrial Production Index," CESifo Working Paper Series 10756, CESifo.
    7. Leschinski, Christian & Sibbertsen, Philipp, 2019. "Model order selection in periodic long memory models," Econometrics and Statistics, Elsevier, vol. 9(C), pages 78-94.
    8. Stéphane Goutte & David Guerreiro & Bilel Sanhaji & Sophie Saglio & Julien Chevallier, 2019. "International Financial Markets," Post-Print halshs-02183053, HAL.

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