Statistical analysis of autoregressive fractionally integrated moving average models in R

Renewable energy generation has been constantly increasing during recent years. Wind and solar have had the most significant growths among all renewable resources. Wind and solar resources are highly intermittent and dependent on meteorological parameters and climatic conditions. The power output of wind turbines is subject to various meteorological parameters, such as wind speed, wind direction, air temperature, relative humidity, etc., among which the wind speed is the most direct and influential factor in wind power generation. Solar photovoltaic (PV) power is a function of solar radiation. Wind speed and solar radiation time series data exhibit unique features which complicate their prediction. This makes wind and solar power forecasting challenging. Accurate wind and solar forecasting enhances the value of renewable energy by improving the reliability and economic feasibility of these resources. It also supports integrating solar and wind power into electric grids by reducing the integration and operation costs associated with these intermittent generation sources. This chapter provides an overview of the time series methods that can be used for more accurate wind and solar forecasting.

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“…ARFIMA generalizes ARIMA by allowing the differencing to take fractional values. An ARFIMA model is given by [5]:…”

Section: Autoregressive Fractionally Integrated Moving Average (Arfima)mentioning

confidence: 99%

Time Series and Renewable Energy Forecasting

Ghofrani¹,

Alolayan²

2018

Time Series Analysis and Applications

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“…Meanwhile, however, the fractional order d is closely related to the Hurst parameter in Equations (10) and (11). There are more than ten methods to estimate Hurst parameters, R/S method, aggregated variance method, absolute value method, periodogram method, whittle method, Higuchi's method, etc.…”

Section: Fractional Order Difference Filtermentioning

confidence: 99%

“…Contreras-Reyes and Palma developed the statistical tools afmtools package in R for analyzing ARFIMA models. In addition, the implemented methods are illustrated with applications to some numerical examples and tree ring data base [10]. Baillie and Chung considered the estimation of both univariate and multivariate trend-stationary ARFIMA models, which generated a long memory autocorrelated process around a deterministic time trend.…”

Section: Introductionmentioning

confidence: 99%

An Evaluation of ARFIMA (Autoregressive Fractional Integral Moving Average) Programs

Liu

Chen

Zhang

2017

Axioms

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Strong coupling between values at different times that exhibit properties of long range dependence, non-stationary, spiky signals cannot be processed by the conventional time series analysis. The autoregressive fractional integral moving average (ARFIMA) model, a fractional order signal processing technique, is the generalization of the conventional integer order models-autoregressive integral moving average (ARIMA) and autoregressive moving average (ARMA) model. Therefore, it has much wider applications since it could capture both short-range dependence and long range dependence. For now, several software programs have been developed to deal with ARFIMA processes. However, it is unfortunate to see that using different numerical tools for time series analysis usually gives quite different and sometimes radically different results. Users are often puzzled about which tool is suitable for a specific application. We performed a comprehensive survey and evaluation of available ARFIMA tools in the literature in the hope of benefiting researchers with different academic backgrounds. In this paper, four aspects of ARFIMA programs concerning simulation, fractional order difference filter, estimation and forecast are compared and evaluated, respectively, in various software platforms. Our informative comments can serve as useful selection guidelines.

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“…Contreras-Reyes and Palma developed the statistical tools "afmtools" package in R for analyzing ARFIMA models. In addition, the implemented methods are illustrated with applications to some numerical examples and tree ring data base [6]. Baillie and Chung considered the estimation of both univariate and multivariate trend-stationary ARFIMA models, which generated a long memory autocorrelated process around a deterministic time trend.…”

Section: Detc2017-67483mentioning

confidence: 99%

An Evaluation of ARFIMA Programs

Liu

Zhang

Chen

2017

Volume 9: 13th ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications

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Strong coupling between values at different time that exhibit properties of long range dependence, non-stationary, spiky signals cannot be processed by the conventional time series analysis. The ARFIMA model, which employs the fractional order signal processing techniques, is the generalization of the conventional integer order models — ARIMA and ARMA model. Therefore, it has much wider applications since it could capture both short-range dependence and long range dependence. For now, several software have developed functions dealing with ARFIMA processes. However, it could be a big difference, if using different numerical tools for time series analysis. Time to time, being asked about which tool is suitable for a specific application, the authors decide to carry out this survey to present recapitulative information of the available tools in the literature, in hope of benefiting researchers with different academic backgrounds. In this paper, 4 primary functions concerning simulation, fractional order difference filter, estimation and forecast are compared and evaluated respectively in the different software and informative comments are also provided for selection.

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Statistical analysis of autoregressive fractionally integrated moving average models in R

Cited by 38 publications

References 28 publications

Time Series and Renewable Energy Forecasting

Time Series and Renewable Energy Forecasting

An Evaluation of ARFIMA (Autoregressive Fractional Integral Moving Average) Programs

An Evaluation of ARFIMA Programs

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