PARMA Models with Applications in R

Dudek, Anna E.; Hurd, Harry L.; Wójtowicz, Wioletta

doi:10.1007/978-3-319-16330-7_7

Cited by 10 publications

(8 citation statements)

References 20 publications

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“…0 is rejected for some h ≠ 0, we conclude that the sequence is not cyclostationary white noise; see Dudek et al (2015). This is the case for the considered series {y t , t = 1, … , n} as the hypothesis H (h) 0 is rejected for each h ≠ 0.…”

Section: Identifying Periodic Correlation In Ghi Seriesmentioning

confidence: 65%

“…for different h ≠ 0. Here, if H(h) 0 is rejected for some h ≠ 0, then we cannot decline that the sequence comes from a proper cyclostationary process; see Dudek et al (2015). For the series {y t , t = 1, … , n}, the hypothesis H(h) 0 also gets rejected for all h ≠ 0 indicating that the observed data are not generated by an amplitude-modulated stationary process.…”

Section: Identifying Periodic Correlation In Ghi Seriesmentioning

confidence: 97%

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A cyclostationary model for temporal forecasting and simulation of solar global horizontal irradiance

et al. 2021

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As part of Saudi Vision 2030, a major strategic framework developed by the Council of Economic and Development Affairs of Saudi Arabia, the country aims to reduce its dependency on oil and promote renewable energy for domestic power generation. Among the sustainable energy resources, solar energy is one of the leading resources because of the endowment of Saudi Arabia with plentiful sunlight exposure and year-round clear skies. This essentializes to forecast and simulate solar irradiance, in particular global horizontal irradiance (GHI), as accurately as possible, mainly to be utilized by the power system operators among many others. Motivated by a dataset of hourly solar GHIs, this article proposes a model for short-term point forecast and simulation of GHIs. Two key points, that make our model competent, are: (1) the consideration of the strong dependency of GHIs on aerosol optical depths and (2) the identification of the periodic correlation structure or cyclostationarity of GHIs. The proposed model is shown to produce better forecasts and more realistic simulations than a classical model, which fails to recognize the GHI data as cyclostationary. Further, simulated samples from both the models as well as the original GHI data are used to calculate the corresponding photovoltaic power outputs to provide a comprehensive comparison among them.

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Section: Identifying Periodic Correlation In Ghi Seriesmentioning

confidence: 65%

Section: Identifying Periodic Correlation In Ghi Seriesmentioning

confidence: 97%

A cyclostationary model for temporal forecasting and simulation of solar global horizontal irradiance

et al. 2021

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“…We consider the series containing hourly observations from volumes of energy traded on the Nord Pool Spot exchange collected between 6 July and 31 August 2010. The detailed description of the series can be found in Dudek et al (2015). Moreover, in the mentioned paper periodic ARMA model is fitted to these data.…”

Section: Real Data Examplementioning

confidence: 99%

“…and simultaneously we get (12). Since to obtain the consistency of µ * ECBB it is enough to follow the proof presented in Dudek et al (2014a), we decided to omit technical details.…”

Section: Proof Of Theorem 21mentioning

confidence: 99%

Block bootstrap for periodic characteristics of periodically correlated time series

Dudek

2017

Journal of Nonparametric Statistics

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This research is dedicated to the study of periodic characteristics of periodically correlated time series such as seasonal means, seasonal variances and autocovariance functions. Two bootstrap methods are used: the extension of the usual Moving Block Bootstrap (EMBB) and the Generalized Seasonal Block Bootstrap (GSBB). The first approach is proposed, because the usual MBB does not preserve the periodic structure contained in the data and cannot be applied for the considered problems. For the aforementioned periodic characteristics the bootstrap estimators are introduced and consistency of the EMBB in all cases is obtained. Moreover, the GSBB consistency results for seasonal variances and autocovariance function are presented. Additionally, the bootstrap consistency of both considered techniques for smooth functions of the parameters of interest is obtained. Finally, the simultaneous bootstrap confidence intervals are constructed. A simulation study to compare their actual coverage probabilities is provided. A real data example is presented.

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“…For a PC time series with period , it is expected that the sample spectral coherence statistic has a significant value on pairs (P, Q) for |P − Q| = kn/ , k = 0, • • • , − 1. The plot of the support of the sample spectral coherence statistic can be used to identify the type of model and analysis of the time series X 0 , X 1 , • • • , X n−1 , see [6]:…”

Section: Consider Positive Real Numbersmentioning

confidence: 99%

Semi-Levy driven continuous-time GARCH process

Mohammadi

Rezakhah

Modarresi

2018

Preprint

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In this paper, we study the class of semi-Lévy driven continuous-time GARCH, denoted by SLD-COGARCH, process. The statistical properties of this process are characterized. We show that the state process of such process can be described by a random recurrence equation with the periodic random coefficients. We establish sufficient conditions for the existence of a strictly periodically stationary solution of the state process which causes the volatility process to be strictly periodically stationary. Furthermore, it is shown that the increments with constant length of such SLD-COGARCH process are themselves a discrete-time periodically correlated (PC) process. We apply some tests to verify the PC behavior of these increments by the simulation studies. Finally, we show that how well this model fits a set of high-frequency financial data.

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PARMA Models with Applications in R

Cited by 10 publications

References 20 publications

A cyclostationary model for temporal forecasting and simulation of solar global horizontal irradiance

A cyclostationary model for temporal forecasting and simulation of solar global horizontal irradiance

Block bootstrap for periodic characteristics of periodically correlated time series

Semi-Levy driven continuous-time GARCH process

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