Bootstrap prediction intervals for ARCH models

Reeves, Jonathan J.

doi:10.1016/j.ijforecast.2004.09.005

Cited by 38 publications

(28 citation statements)

References 18 publications

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“…A series of papers on using the bootstrap to compute prediction intervals for an AR model has appeared beginning with Masarotto (1990), and including McCullough (1994McCullough ( , 1996, Grigoletto (1998), Clements & Taylor (2001) and Kim (2004b). Similar procedures for other models have also been considered including ARIMA models (Pascual et al, 2001(Pascual et al, , 2004(Pascual et al, , 2005, Wall & Stoffer (2002), VAR (Kim, 1999(Kim, , 2004a, ARCH (Reeves, 2005) and regression (Lam & Veall, 2002). It seems likely that such bootstrap methods will become more widely used as computing speeds increase due to their better coverage properties.…”

Section: Prediction Intervals and Densitiesmentioning

confidence: 99%

25 years of time series forecasting

Gooijer

Hyndman

2006

International Journal of Forecasting

1,295

632

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During this period, over one third of all papers published in these journals concerned time series forecasting. We also review highly influential works on time series forecasting that have been published elsewhere during this period. Enormous progress has been made in many areas, but we find that there are a large number of topics in need of further development. We conclude with comments on possible future research directions in this field.

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Section: Prediction Intervals and Densitiesmentioning

confidence: 99%

25 years of time series forecasting

Gooijer

Hyndman

2006

International Journal of Forecasting

1,295

632

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“…Recent research has considered how bootstrap procedures can be used to include parameter uncertainty in density forecasts generated from GARCH models (Reeves 2005;Pascual et al 2006). However, such procedures are highly computational as they require repeated maximum likelihood estimation.…”

Section: Bivariate Varma-garch Model For Wind Speed and Directionmentioning

confidence: 99%

Using Conditional Kernel Density Estimation for Wind Power Density Forecasting

Jeon

Taylor

2012

Journal of the American Statistical Association

187

124

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Of the various renewable energy resources, wind power is widely recognized as one of the most promising. The management of wind farms and electricity systems can benefit greatly from the availability of estimates of the probability distribution of wind power generation. However, most research has focused on point forecasting of wind power. In this paper, we develop an approach to producing density forecasts for the wind power generated at individual wind farms. Our interest is in intraday data and prediction from 1 to 72 hours ahead. We model wind power in terms of wind speed and wind direction. In this framework, there are two key uncertainties. First, there is the inherent uncertainty in wind speed and direction, and we model this using a bivariate VARMA-GARCH model, with a Student t distribution, in the Cartesian space of wind speed and direction. Second, there is the stochastic nature of the relationship of wind power to wind speed (described by the power curve), and to wind direction. We model this using conditional kernel density (CKD) estimation, which enables a nonparametric modeling of the conditional density of wind power. Using Monte Carlo simulation of the VARMA-GARCH model and CKD estimation, density forecasts of wind speed and direction are converted to wind power density forecasts. Our work is novel in several respects: previous wind power studies have not modeled a stochastic power curve; to accommodate time evolution in the power curve, we incorporate a time decay factor within the CKD method; and the CKD method is conditional on a density, rather than a single value. The new approach is evaluated using datasets from four Greek wind farms.

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“…The asymptotic validity of the forward bootstrap procedure has been established above for linear VAR models. However, given that the bootstrap procedure considered in this paper does not rely on the BR, it can be extended to deal with conditionally heteroscedastic models; see Pascual, Romo, and Ruiz (2006) and Reeves (2005) for bootstrap procedures in the context of forecasting univariate GARCH models. In this section, we show how to use the forward bootstrap procedure to obtain forecast intervals and regions for returns, volatilities and correlations in the context of the Dynamic Conditional Correlation (DCC) model proposed by Engle (2002).…”

Section: Bootstrap Forecasts Of Returns Volatilities and Correlationmentioning

confidence: 99%

Bootstrap multi-step forecasts of non-Gaussian VAR models

Fresoli

Ruiz

Pascual

2015

International Journal of Forecasting

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a b s t r a c tIn this paper, we establish the asymptotic validity and analyse the finite sample performance of a simple bootstrap procedure for constructing multi-step multivariate forecast densities in the context of non-Gaussian unrestricted VAR models. This bootstrap procedure avoids the backward representation, and, as a consequence, can be used to obtain multivariate forecast densities in, for example, VARMA or VAR-GARCH models. In the context of bivariate stationary VAR(p) models, we show that its finite sample properties are comparable to those of alternatives based on the backward representation. The bootstrap procedure is also implemented in a VAR-DCC model which lacks a backward representation. Finally, joint forecast densities of US quarterly inflation, unemployment and GDP growth are obtained.

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Bootstrap prediction intervals for ARCH models

Cited by 38 publications

References 18 publications

25 years of time series forecasting

25 years of time series forecasting

Using Conditional Kernel Density Estimation for Wind Power Density Forecasting

Bootstrap multi-step forecasts of non-Gaussian VAR models

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