Share / Export Citation / Email / Print / Text size:

Statistics in Transition New Series

Polish Statistical Association

Central Statistical Office of Poland

Subject: Economics , Statistics & Probability


ISSN: 1234-7655
eISSN: 2450-0291





Volume / Issue / page

Related articles

VOLUME 19 , ISSUE 2 (June 2018) > List of articles


Daniel Kosiorowski / Dominik Mielczarek / Jerzy P. Rydlewski / Małgorzata Snarska

Keywords : functional time series, hierarchical time series, forecast reconciliation, depth for functional data.

Citation Information : Statistics in Transition New Series. Volume 19, Issue 2, Pages 331-350, DOI:

License : (CC BY-NC-ND 4.0)

Published Online: 28-July-2018



Shang and Hyndman (2017) proposed a grouped functional time series forecasting approach as a combination of individual forecasts obtained using the generalized least squares method. We modify their methodology using a generalized exponential smoothing technique for the most disaggregated functional time series in order to obtain a more robust predictor. We discuss some properties of our proposals based on the results obtained via simulation studies and analysis of real data related to the prediction of demand for electricity in Australia in 2016.

Content not available PDF Share



AUE, A., DUBABART NORINHO, D., HO¨ RMANN, S., (2015). On the prediction of stationary functional time series, Journal of the American Statistical Association, 110 (509), pp. 378–392.


BESSE, P. C., CARDOT, H., STEPHENSON, D. B., (2000). Autoregressive forecasting of some functional climatic variations, Scandinavian Journal of Statistics, 27 (4), pp. 673–687.


BOSQ, D. (2000). Linear processes in function spaces. Springer.


DIDERICKSEN, D., KOKOSZKA, P., ZHANG, X. (2012). Empirical properties of forecasts with the functional autoregressive model, Computational Statistics, 27 (2), pp. 285–298.


FEBRERO-BANDE, M. O., DE LA FUENTE, M., (2012). Statistical computing in functional data analysis: the R package fda.usc, Journal of Statistical Software, 51 (4), pp. 1–28.


HORVATH, L., KOKOSZKA, P., (2012). Inference for functional data with applications, Springer-Verlag.


HORMANN S., KOKOSZKA, P., (2012). Functional Time Series, in Handbook of Statistics: Time Series Analysis – Methods and Applications, 30, pp. 157–186.


HYNDMAN, R. J., AHMED R. A., ATHANASOPOULOS, G., SHANG, H. L., (2011). Optimal combination forecasts for hierarchical time series, Computational Statistics & Data Analysis, 55 (9), pp. 2579–2589.


HYNDMAN, R.J., KOEHLER, A.B., ORD, J. K., SNYDER, R. D., (2008). Forecasting with exponential smoothing – the state space approach, Springer-Verlag.


HYNDMAN, R. J., SHANG, H., L., (2009). Forecasting functional time series, Journal of the Korean Statistical Society, 38 (3), pp. 199–221.


HYNDMAN, R. J., ULLAH, M., (2007). Robust forecasting of mortality and fertility rates: A functional data approach, Computational Statistics & Data Analysis, 51 (10), pp. 4942–4956.


HYNDMAN, R. J., KOEHLER, A. B., SNYDER, R.D., GROSE, S., (2002). A state space framework for automatic forecasting using exponential smoothing methods, International Journal of Forecasting, 18 (3), pp. 439–454.


KAHN, K. B., (1998). Revisiting top-down versus bottom-up forecasting, The Journal of Business Forecasting Methods & Systems, 17 (2), pp. 14–19.


KOHN, R., (1982). When is an aggregate of a time series efficiently forecast by its past, Journal of Econometrics, 18 (3), pp. 337–349.


KOSIOROWSKI, D., ZAWADZKI, Z., (2018). DepthProc: An R package for robust exploration of multidimensional economic phenomena, arXiv: 1408.4542.


KOSIOROWSKI, D., (2014). Functional regression in short term prediction of economic time series, Statistics in Transition, 15 (4), pp. 611–626.


KOSIOROWSKI, D. (2016). Dilemmas of robust analysis of economic data streams, Journal of Mathematical Sciences (Springer), 218 (2), pp. 167–181.


KOSIOROWSKI, D., RYDLEWSKI, J. P., SNARSKA, M., (2017a). Detecting a structural change in functional time series using local Wilcoxon statistic, Statistical Papers, pp. 1–22, URL s00362-017-0891-y.


KOSIOROWSKI, D., MIELCZAREK, D., RYDLEWSKI, J. P., (2017b). Double functional median in robust prediction of hierarchical functional time series – an application to forecasting of the Internet service users behaviour, available at: arXiv:1710.02669v1.


KOSIOROWSKI, D., RYDLEWSKI, J.P., ZAWADZKI Z., (2018a). Functional outliers detection by the example of air quality monitoring, Statistical Review (in Polish, forthcoming).


KOSIOROWSKI, D., MIELCZAREK, D., RYDLEWSKI, J. P., (2018b). Forecasting of a Hierarchical Functional Time Series on Example of Macromodel for the Day and Night Air Pollution in Silesia Region - A Critical Overview, Central European Journal of Economic Modelling and Econometrics, 10 (1), pp. 53–73.


KOSIOROWSKI, D., MIELCZAREK, D., RYDLEWSKI, J. P., (2018c). Outliers in Functional Time Series – Challenges for Theory and Applications of Robust Statistics, In M. Papiez & S. Smiech (eds.), The 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, Conference Proceedings, Cracow: Foundation of the Cracow University of Economics, pp. 209–218.


KRZYSKO, M., DEREGOWSKI, K., GORECKI, T., WOŁYNSKI, W., (2013). Kernel and functional principal component analysis, Multivariate Statistical Analysis 2013 Conference, plenary lecture.


LOPEZ-PINTADO, S., ROMO, J., (2009). On the concept of depth for functional data, Journal of the American Statistical Association, 104, pp. 718–734.


LOPEZ-PINTADO, S., JO¨ RNSTEN, R., (2007). Functional analysis via extensions of the band depth, IMS Lecture Notes–Monograph Series Complex Datasets and Inverse Problems: Tomography, Networks and Beyond, Vol. 54, pp. 103–120, Institute of Mathematical Statistics.


NAGY, S., GIJBELS, I., OMELKA, M., HLUBINKA, D., (2016). Integrated depth for functional data: Statistical properties and consistency, ESIAM Probability and Statistics, 20, pp. 95–130.


NAGY, S. GIJBELS, I., HLUBINKA, D., (2017). Depth-Based Recognition of Shape Outlying Functions, Journal of Computational and Graphical Statistics, DOI: 10.1080/10618600.2017.1336445.


NIETO-REYES, A., BATTEY, H., (2016). A topologically valid definition of depth for functional data, Statistical Science 31 (1), pp. 61–79.


PAINDAVEINE, D., G. VAN BEVER, G., (2013). From depth to local depth: a focus on centrality, Journal of the American Statistical Asssociation, Vol. 108, No. 503, Theory and Methods, pp. 1105–1119.


RAMSAY, J.O., G. HOOKER, G., GRAVES, S., (2009). Functional data analysis with R and Matlab, Springer-Verlag.


SGUERA, C., GALEANO, P., LILLO, R. E., (2016). Global and local functional depths, arXiv 1607.05042v1.


SHANG, H., L., HYNDMAN, R. J., (2017). Grouped functional time series forecasting: an application to age-specific mortality rates, Journal of Computational and Graphical Statistics, 26(2), pp. 330–343.


SHANG, H., L., (2018). Bootstrap methods for stationary functional time series, Statistics and Computing, 28(1), pp. 1–10.


WEALE, M., (1988). The reconciliation of values, volumes and prices in the national accounts, Journal of the Royal Statistical Society A, 151(1),pp. 211–221.


VAKILI, K., SCHMITT, E., (2014). Finding multivariate outliers with FastPCS, Computational Statistics & Data Analysis, 69, pp. 54–66.


VINOD, H.D., LO´ PEZ-DE-LACALLE, J. L., (2009). Maximum entropy bootstrap for time series: the meboot R package, Journal of Statistical Software, 29 (5).


ZUO, Y., SERFLING, R., (2000). Structural properties and convergence results for contours of sample statistical depth functions, Annals of Statistics, 28 (2), pp. 483–499.


Australian Energy Market Operator,