PDF Печать E-mail

DOI: https://doi.org/10.15407/techned2019.02.038


Journal Tekhnichna elektrodynamika
Publisher Institute of Electrodynamics National Academy of Science of Ukraine
ISSN 1607-7970 (print), 2218-1903 (online)
Issue No 2, 2019 (March/April)
Pages 38 – 47

M. Fryz1*, L. Scherbak2**

1 – Ternopil Ivan Puluj National Technical University,
str. Ruska, 56, Ternopil, 46001, Ukraine,
e-mail: Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript
2 – Kyiv International University,
str. Lvivska, 49, Kyiv, 03179, Ukraine,
e-mail: Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript
* ORCID ID : http://orcid.org/0000-0002-8720-6479
** ORCID ID : http://orcid.org/0000-0002-1536-4806


А conditional linear random process (CLRP) has been defined as the stochastic integral of a random function with respect to a process with independent increments. When the process with independent increments is Poisson then CLRP represents the signal as a sum of a large amount of stochastically dependent impulses whose times of occurrence are the times of a Poisson process. For example, the electricity loads of the electrical power systems, also the processes of gas and water consumption, electrophysiological signals et al. can be modelled using CLRP. Moreover, the stochastic periodicity of the signals can be taken into account. A random coefficient autoregressive model has been shown to be a member of the class of discrete-time CLRP and suitable for estimation purposes. The main goal of the paper is to develop the procedure for the parameter estimation of random coefficient periodic autoregressive (RCPAR) model. The model has periodic parameters and consequently periodic probability distribution. The estimations have been obtained as a result of applying the least squares method to the set of L (where L is a period) stationary and jointly stationary subsequences of RCPAR model. The simulation results have been presented which confirm the consistency of the developed estimations, that is, the precision of the estimates increases with the increase in the sample size. The results of short-term electricity consumption forecasting of the enterprise (which belongs to the class of small and medium-sized) have been presented and analyzed using RCPAR model. References 16, figures 4, tables 2.


Key words: mathematical model, conditional linear random process, period, random coefficient autoregression, parameter estimation, computer simulation, forecasting, electricity consumption.


Received:    03.04.2017
Accepted:    28.01.2019
Published:  19.02.2019


1. Babak S.V., Myslovich M.V., Sysak R.M. Electrotechnical equipment statistical diagnostics: monograph. Kyiv: Institut elektrodinamiki NAN Ukrainy, 2015. 456 p. (Rus)
2. Zvarych V.M. Diagnostics systems of power engineering equipment on the linear autoregressive models basis: author's abstract of Dr. tech. sci. diss.: 05.13.05. Instytut elektrodynamiky NAN Ukrainy. Kyiv. 2013. 35 p. (Ukr)
3. Marchenko B.G., Scherbak L.N. Linear random processes and their applications. Кyiv: Naukova dumka, 1975. 143 p. (Rus)
4. Mlynko B.B., Fryz M.Ye., Scherbak L.M. Methodology of stochastic signal mathematical modelling using conditional linear random processes. Modeliuvannia ta informatsiini tekhnologii. Zbirnyk naukovykh prats. Кyiv: Instytut problem modeliuvannia v enerhetytsi im. G.Ye. Pukhova NAN Ukrainy, 2016. Issue 77. Pp. 20–25. (Ukr)
5. Fryz M.Ye. Properties of conditional linear processes and their application in the problems of stochastic signal mathematical modelling. Matematychne ta kompiuterne modeliuvannia. Seria: Tekhnichni nauky: zbirnyk naukovykh prats. 2012. Issue 6. Pp. 228–238. (Ukr)
6. Pierre P.A. Central limit theorems for conditionally linear random processes. SIAM Journal of Applied Mathematics. 1971. Volume 20. Issue 3. Pp. 449–461. DOI: https://doi.org/10.1137/0120048
7. Gardner W.A., Napolitano A., Paura L. Cyclostationarity: Half a century of research. Signal Processing. Elsevier, 2006. No 86 (4). Pp. 639–697. DOI: https://doi.org/10.1016/j.sigpro.2005.06.016
8. Nicholls D.F., Quinn B.G. Random Coefficient Autoregressive Models: an Introduction. Lecture Notes in Statistics, 11. New York: Springer Verlag, 1983. 154 p.
9. Aknouche A., Guerbyenne H. Periodic stationarity of random coefficient periodic autoregressions. Statistics and Probability Letters. 2009. Volume 79. Issue 7. Pp. 990–996. DOI: https://doi.org/10.1016/j.spl.2008.12.012
10. Franses P.H., Paap R. Random-coefficient periodic autoregressions. Statistica Neerlandica. 2011. Volume 65. Nо 1. Pp. 101–115. DOI: https://doi.org/10.1111/j.1467-9574.2010.00477.x

11. Humeau S., Wijaya T.K., Vasirani M., Aberer K. Electricity load forecasting for residential customers: Exploiting aggregation and correlation between households. Sustainable Internet and ICT for Sustainability (SustainIT). Palermo, Italy, 30-31 October 2013. Pp. 1–6. DOI: https://doi.org/10.1109/SustainIT.2013.6685208

12. Fryz M.Ye. Conditional linear random sequences. Zbirnyk naukovykh prats Instytutu problem modeliuvannia v enerhetytsi im. G.Ye. Pukhova NAN Ukrainy. 2011. Issue 60. Pp. 41–45. (Ukr)
13. Magnus J.R., Neudecker H. The elimination matrix: Some lemmas and applications. SIAM Journal on Algebraic and Discrete Methods. 1980. Volume 1. Issue 4. Pp. 422–449. DOI: https://doi.org/10.1137/0601049
14. Chernenko P.O., Martyniuk O.V., Miroshnyk V.O. Modeling and short-term forecasting of technology component of electrical load of the regional electric power system. Tekhnichna Elektrodynamika. 2016. No 4. Pp. 68–70. (Ukr) DOI: https://doi.org/10.15407/techned2016.04.068
15. Sevlian R., Rajagopal R. A scaling law for short term load forecasting on varying levels of aggregation. Electrical Power and Energy Systems. 2018. Volume 98. Pp. 350 – 361. DOI: https://doi.org/10.1016/j.ijepes.2017.10.032
16. Rodrigues F., Cardeira C., Calado J.M.F. The Daily and Hourly Energy Consumption and Load Forecas-ting Using Artificial Neural Network Method: A Case Study Using a Set of 93 Households in Portugal. Energy Procedia. 2014. Volume 62. Pp. 220–229. DOI: https://doi.org/10.1016/j.egypro.2014.12.383