Identification and validation of periodic autoregressive model with additive noise: finite-variance case

Żuławiński, Wojciech; Grzesiek, Aleksandra; Zimroz, Radosław; Wyłomańska, Agnieszka

doi:10.1016/j.cam.2023.115131

Cited by 3 publications

(6 citation statements)

References 31 publications

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“…Let (ξ 1−p (ω), ..., ξ 0 (ω), ξ 1 (ω), ..., ξ qL (ω)) be the sample (sample size is equal to qL + p) of sequence (7) observations, where q ∈ N (number of cycles) and period L are considered to be known.…”

Section: Random Coefficient Periodic Autoregressive Modelmentioning

confidence: 99%

“…The obtained estimations are consistent and asymptotically normal. The approach for statistical estimating the coefficients of the RCPAR model has been developed in [8], it is based on the above results, but takes into account the cyclostationarity properties of the sequence (7).…”

Section: Random Coefficient Periodic Autoregressive Modelmentioning

confidence: 99%

“…We should emphasize the difference between the RCPAR-based computer simulation model of electricity consumption and other close established constructive models such as periodic autoregressive (PAR) model [6,7] (or more general periodic moving average (PARMA) model [6]) and seasonal autoregressive moving average (SARMA) model [18]. All these models can be used both for computer simulation of electricity consumption, as well as for its forecasting.…”

Section: Hourly Electricity Consumption Simulationmentioning

confidence: 99%

“…Mathematical models represented as continuous-time or discrete-time linear random processes (LRP) are very useful for solving the above problems in energy engineering [6,7]. In the mentioned above application domains, the different implementations of linear periodic random processes [6,7] are also very useful, which allows taking into consideration the cyclostationarity of the studied signals or processes, caused, for example, by the rhythmic daily (weekly, yearly, etc.) behaviour of electricity, gas, or water consumers, vibrations of the bearings of energy facilities, and other energy objects that are subject to monitoring and diagnosis.…”

Section: Introductionmentioning

confidence: 99%

“…For the problems of statistical monitoring, forecasting, diagnostics, and computer simulation, discrete-time LRP is mostly used in the form of an autoregressive sequence, and for cyclostationary processes as periodic autoregression [6,7,9]. Similarly, the random coefficient autoregressive (RCA) model [8,10] is an effective tool for the statistical analysis of CLRP.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Electricity consumption simulation using random coefficient periodic autoregressive model

Scherbak,

Fryz,

Hotovych

2023

IOP Conf. Ser.: Earth Environ. Sci.

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The concept of a continuous-time conditional linear random process involves a random kernel being integrated stochastically by a process with independent increments, which is often called a “generative process”. In cases where the “generative process” is Poisson, the resulting model represents an investigated signal as a sum of numerous stochastically dependent random impulses each of which occurs according to some inhomogeneous Poisson arrival process. This model can be applied to represent various processes related to energy consumption, such as electricity loads of electrical power systems, gas and water consumption, and other energy resources, while also considering the signals’ cyclostationarity, which is usually caused by the rhythmic nature of consumer behaviour. A member of the discretetime conditional linear cyclostationary random processes class is the random coefficient periodic autoregressive (RCPAR) model, which is appropriate for use in energy informatics, including estimation, forecasting, and computer simulation purposes. The primary objective of the paper is to establish a procedure for simulating the hourly electricity consumption of small and medium-sized enterprises using the RCPAR model, which has periodic parameters and creates cyclostationary properties while also accounting for the investigated process conditional heteroscedasticity. The statistical estimation step of the proposed procedure uses the general methodology for estimating the parameters of the RCPAR model and the methods of statistical analysis of cyclostationary signals. This step is used to identify the simulation characteristics. The simulation step is based on the methods of cyclostationary white noise generation and its transformation by a digital linear filter with random parameters. The last ones are obtained using the Gaussian random vectors computer simulation methods, taking into account the cyclostaionarity property.

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Section: Random Coefficient Periodic Autoregressive Modelmentioning

confidence: 99%

Section: Random Coefficient Periodic Autoregressive Modelmentioning

confidence: 99%

Section: Hourly Electricity Consumption Simulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Electricity consumption simulation using random coefficient periodic autoregressive model

Scherbak,

Fryz,

Hotovych

2023

IOP Conf. Ser.: Earth Environ. Sci.

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Empirical study of periodic autoregressive models with additive noise – estimation and testing

Żuławiński,

Wyłomańska

2023

Communications in Statistics - Simulation and Computation

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Robust coherent and incoherent statistics for detection of hidden periodicity in models with non-Gaussian additive noise

Żuławiński,

Antoni,

Zimroz

et al. 2024

EURASIP J. Adv. Signal Process.

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We address the issue of detecting hidden periodicity when the signal exhibits periodic correlation, but is additionally affected by non-Gaussian noise with unknown characteristics. This scenario is common in various applications. The conventional approach for identifying periodically correlated (PC) behavior involves the frequency domain-based analysis. In our investigation, we also employ such an approach; however, we use a robust version of the discrete Fourier transform incorporating the Huber function-based M-estimation, unlike the classical algorithm. Building upon this approach, we propose robust coherent and incoherent statistics originally designed to identify hidden periodicity in pure PC models. The novelty of this paper lies in introducing robust coherent and incoherent statistics through the application of the robust discrete Fourier transform in classical algorithms and proposing a new technique for period estimation based on the proposed methodology. We explore two types of PC models and two types of additive noise, resulting in PC signals disturbed by non-Gaussian additive noise. Detecting hidden periodicity in such cases proves to be significantly more challenging than in classical scenarios. Through Monte Carlo simulations, we demonstrate the effectiveness of the proposed robust approaches and their superiority over classical. To further substantiate our findings, we analyze three datasets in which hidden periodicity had previously been confirmed in the literature. Among them, two datasets correspond to the condition monitoring area, being a main motivation of our research.

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Identification and validation of periodic autoregressive model with additive noise: finite-variance case

Cited by 3 publications

References 31 publications

Electricity consumption simulation using random coefficient periodic autoregressive model

Electricity consumption simulation using random coefficient periodic autoregressive model

Empirical study of periodic autoregressive models with additive noise – estimation and testing

Robust coherent and incoherent statistics for detection of hidden periodicity in models with non-Gaussian additive noise

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