Empirical spectral processes for locally stationary time series

Dahlhaus, Rainer; Polonik, Wolfgang

doi:10.3150/08-bej137

Cited by 91 publications

(125 citation statements)

References 21 publications

(30 reference statements)

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“…For example, Paparoditis (2009) and Paparoditis (2010) compare nonparametric estimators of the spectral density of the stationary and locally stationary process, and as a consequence, the resulting statistical analysis depends sensitively on the choice of a smoothing parameter which is required for the density estimation. An alternative approach in this context is the application of the empirical spectral measure for inference in locally stationary time series [see Dahlhaus and Polonik (2009)]. In particular Dahlhaus (2009) proposed a test for stationarity by comparing estimates of the integrated time frequency spectral density under the null hypothesis of stationarity and the alternative of local stationarity.…”

Section: Introductionmentioning

confidence: 99%

A Measure of Stationarity in Locally Stationary Processes With Applications to Testing

Dette

Preuß

Vetter

2011

Journal of the American Statistical Association

131

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July 28, 2010 AbstractIn this paper we investigate the problem of measuring deviations from stationarity in locally stationary time series. Our approach is based on a direct estimate of the L 2 -distance between the spectral density of the locally stationary process and its best approximation by a spectral density of a stationary process. An explicit expression of the minimal distance is derived, which depends only on integrals of the spectral density of the stationary process and its square. These integrals can be estimated directly without estimating the spectral density, and as a consequence, the estimation of the measure of stationarity does not require the specification of smoothing parameters. We show weak convergence of an appropriately standardized version of the statistic to a standard normal distribution. The results are used to construct confidence intervals for the measure of stationarity and to develop a new test for the hypothesis of stationarity which does not require regularization. Finally, we investigate the finite sample properties of the resulting confidence intervals and tests by means of a small simulation study and illustrate the methodology in three data examples.

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Section: Introductionmentioning

confidence: 99%

A Measure of Stationarity in Locally Stationary Processes With Applications to Testing

Dette

Preuß

Vetter

2011

Journal of the American Statistical Association

131

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“…with zero mean and unit variance, where the {a t,n } sequence satisfies a number of technical conditions, see also Dahlhaus and Polonik (2009), and t = 1, . .…”

Section: Introductionmentioning

confidence: 99%

Costationarity of Locally Stationary Time Series

Cardinali

Nason²

2011

Journal of Time Series Econometrics

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“…These models replace the time invariant term with an expression that explicitly depends on time, e.g. (see for example Priestley (1983), Dahlhaus (1997); Dahlhaus and Polonik (2006) or Dahlhaus and Polonik (2009)). The localized autocovariances, , are computed following Nason et al (2000):…”

Section: Identifying Time-varying Dynamics: Localized Autocorrelationmentioning

confidence: 99%

Time-varying convergence in European electricity spot markets and their association with carbon and fuel prices

2016

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Long-run dynamics of electricity prices are expected to reflect fuel price developments, since fuels generally account for a large share in the cost of generation. As an integrated European market for electricity develops, wholesale electricity prices should be converging as a result of market coupling and increased interconnectivity. Electricity mixes are also changing, spurred by a drive to significantly increase the share of renewables. Consequently, the electricity wholesale price dynamics are evolving, and the fuel-electricity price nexus that has been described in the literature is likely to reflect this evolution. This study investigates associations between spot prices from the British, French and Nordpool markets with those in connected electricity markets and fuel input prices, from December 2005 to October 2013. In order to assess the timevarying dynamics of electricity spot price series, localized autocorrelation functions are used. Electricity spot prices in the three markets are found to have stationary and non-stationary periods. When a trend in spot prices is observed, it is likely to reflect the trend in fuel prices. Cointegration analysis is then used to assess co-movement between electricity spot prices and fuel inputs to generation. The results show that British electricity spot prices are associated with fuel prices and not with price developments in connected markets, while the opposite is observed in the French and Nordpool day-ahead markets.

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Empirical spectral processes for locally stationary time series

Cited by 91 publications

References 21 publications

A Measure of Stationarity in Locally Stationary Processes With Applications to Testing

A Measure of Stationarity in Locally Stationary Processes With Applications to Testing

Costationarity of Locally Stationary Time Series

Time-varying convergence in European electricity spot markets and their association with carbon and fuel prices

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