Aggregation of Seasonal Long-Memory Processes

del Barrio Castro, Tomás and Rachinger, Heiko (2020): Aggregation of Seasonal Long-Memory Processes. Forthcoming in: Econometrics and Statistics

Abstract

To understand the impact of temporal aggregation on the properties of a seasonal long-memory process, the effects of skip and cumulation sampling on both stationary and nonstationary processes with poles at several potential frequencies are analyzed. By allowing for several poles in the disaggregated process, their interaction in the aggregated series is investigated. Further, by definning the process according to the truncated Type II definition, the proposed approach encompasses both stationary and nonstationary processes without requiring prior knowledge of the case. The frequencies in the aggregated series to which the poles in the disaggregated series are mapped can be directly deduced. Specifically, unlike cumulation sampling, skip sampling can impact on non-seasonal memory properties. Moreover, with cumulation sampling, seasonal long-memory can vanish in some cases. Using simulations, the mapping of the frequencies implied by temporal aggregation is illustrated and the estimation of the memory at the different frequencies is analyzed

• Item Type: MPRA Paper
• Language: English
• Keywords: Aggregation, cumulation sampling, skip sampling, seasonal long memory.
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes

References

[1] Arteche, J. (2020), Multiple Exact Local Whittle estimation in Long Memory Time Series. Econometric Theory, In Press.

[2] Arteche, J. and Orbe (2017) A strategy for optimal bandwidth selection in Local Whittle estimation. Econometrics and Statistics 4, 3 ñ17. doi: https://doi.org/10.1016/j.ecosta.2016.10.003.

[3] Beran, J. (1994), Statistics for long memory processes. New York [u.a.] : Chapman & Hall. ISBN 0-412-04901-5

[4] Barrio Castro, T. d., Rodrigues, P. M. and Taylor, R. A. M. (2019), Temporal Aggregation of Seasonally Near-Integrated Processes. J. Time Ser. Anal.. doi:10.1111/jtsa.12453

[5] Chung, C-F. (1996), Estimating A Generalized Long Memory Process, Journal of Econometrics, 73(1), 237-259.

[6] Giraitis, L., Leipus, R. (1995), A generalized fractionally di§erencing approach in long-memory modeling. Lith Math J 35: 53.

[7] Gray, H.L., Zhang, N., Woodward, W.A. (1989), On Generalized fractional processes. J. Time Ser. Anal., 10, 233ñ257.

[8] Gregoir, S. (1999), Multivariate time series with various hidden unit roots: Part I : Integral operator algebra and representation theory. Econometric Theory 15, 435ñ468.

[9] Gregoir, S. (2006), E¢ cient tests for the presence of a pair of complex conjugate unit roots in real time series. Journal of Econometrics 130, 45ñ100.

[10] Gregoir, S. (2010), Fully modiÖed estimation of seasonally cointegrated processes. Econometric Theory 26, 1491ñ1528.

[11] Hassler, U. (2011), Estimation of fractional integration under temporal aggregation. Journal of Econometrics, Elsevier, vol. 162(2), pages 240-247, June.

[12] Hassler, U. (2013) E§ect of temporal aggregation on multiple time series in the frequency domain, Journal of Time Series Analysis, 34, 5, 562-573.

[13] Hassler, U. (2019), Time Series Analysis with Long Memory in View, Wiley.

[14] Hidalgo, J., Soulier, P. (2004), Estimation of the location and exponent of the spectral singularity of a long memory process. Journal of Time Series Analysis, 25: 55-81 16

[15] Hosking, J. R.M. (1981), Fractional Di§erencing. Biometrika 68(1), 165-176

[16] Marinucci, D., Robinson, P.M. (1999), Alternative forms of fractional Brownian motion. Journal of Statistical Planning and Inference 80, 111-122

[17] Pons, G. (2006), Testing monthly seasonal unit roots with monthly and quarterly information. Journal of Time Series Analysis 27, 191ñ209.

[18] Shimotsu, K., Phillips, P. C. B. (2005), Exact local Whittle estimation of fractional integration. Ann. Statist. 33, no. 4, 1890ñ1933.

[19] Sun, J., Shi, W. (2014), Aggregation of the generalized fractional processes. Economics Letters, Elsevier, vol. 124(2), pages 258-262.

[20] Silvestrini, A. and D. Veredas (2008), Temporal aggregation of univariate and multivariate timeseries models: A survey. Journal of Economic Surveys 22, 458-497.

[21] Tsai, H., Chan, K.S. (2005), Temporal aggregation of stationary and nonstationary discretetime processes. Journal of Time Series Analysis. 26 613-624

[22] Wei, W.S.W. (2006) Time Series Analysis, Univariate and Multivariate Methods (Second Edition). Pearson Addison Wesley.