Nonparametric quasi-maximum likelihood estimation for Gaussian locally stationary processes

In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive (point) estimation, the construction of adaptive confidence regions is severely limited (cf. Li, 1989). The present paper sheds new light on this gap. We develop exact and adaptive confidence regions for the best approximating model in terms of risk. One of our constructions is based on a multiscale procedure and a particular coupling argument. Utilizing exponential inequalities for noncentral χ 2 -distributions, we show that the risk and quadratic loss of all models within our confidence region are uniformly bounded by the minimal risk times a factor close to one.AMS 2000 subject classifications: 62G15, 62G20.

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“…It extends inequalities of Dahlhaus and Polonik (2006) for quadratic forms and is of independent interest. Proposition 6.…”

Section: Exponential Inequalitiesmentioning

confidence: 91%

“…Since F |J| (T n (J) | δ 2 ) is strictly decreasing in δ 2 with limit 0 as δ 2 → ∞, (10) entails the simultaneous (1 − α)-confidence intervals δ2 n,α,l (J),δ 2 n,α,u (J) for all parameters δ 2 n (J) as follows: We setδ 2 n,α,l (∅) :=δ 2 n,α,u (∅) := 0, while for nonvoid…”

Section: Confidence Sets In Case Of Larger Families Of Candidatesmentioning

confidence: 99%

Statistical inference for the optimal approximating model

Rohde

Dümbgen

2012

Probab. Theory Relat. Fields

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“…Recently, Dahlhaus and Polonik (2006) introduced a general infinite order time-varying moving average (MA) representation for LS processes:…”

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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Nonparametric quasi-maximum likelihood estimation for Gaussian locally stationary processes

Cited by 67 publications

References 21 publications

Statistical inference for the optimal approximating model

Statistical inference for the optimal approximating model

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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