Costationarity of Locally Stationary Time Series

Cardinali, A.; Nason, Guy P.

doi:10.2202/1941-1928.1074

Cited by 30 publications

(39 citation statements)

References 66 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The conservatism of the single-hypothesis test, relative to the multiple hypothesis test, broadly aligns with observations by Cardinali and Nason (2010) and Taylor et al (2014).…”

Section: Stationarity Resultsmentioning

confidence: 52%

The locally stationary dual-tree complex wavelet model

et al. 2017

View full text Add to dashboard Cite

We here harmonise two significant contributions to the field of wavelet analysis in the past two decades, namely the locally stationary wavelet process and the family of dualtree complex wavelets. By combining these two components, we furnish a statistical model that can simultaneously access benefits from these two constructions. On the one hand, our model borrows the debiased spectrum and auto-covariance estimator from the locally stationary wavelet model. On the other hand, the enhanced directional selectivity is obtained from the dual-tree complex wavelets over the regular lattice. The resulting model allows for the description and identification of wavelet fields with significantly more directional fidelity than was previously possible. The corresponding estimation theory is established for the new model, and some stationarity detection experiments illustrate its practicality.

show abstract

“…The conservatism of the single-hypothesis test, relative to the multiple hypothesis test, broadly aligns with observations by Cardinali and Nason (2010) and Taylor et al (2014).…”

Section: Stationarity Resultsmentioning

confidence: 52%

The locally stationary dual-tree complex wavelet model

et al. 2017

View full text Add to dashboard Cite

show abstract

“…, where ∑ , is the autocorrelation wavelet of the discrete non-decimated wavelet , and , is the autocovariance of at lag and at rescaled time / for time points t=1, ….T where T is the length of the time series (Cardinali and Nason, 2013). The LACF estimates are computed with the costat package available in R (Nason, 2013).…”

Section: Identifying Time-varying Dynamics: Localized Autocorrelationmentioning

confidence: 99%

“…A more detailed description of the generation mix is provided in section 1.2.1. For assessing long-run dynamics, a two-stage analysis is developed: (1) stationary and non-stationary periods of electricity spot prices are identified via local autocorrelation functions (Cardinali and Nason, 2013), (2) convergence with fuel, carbon and other electricity markets is assessed in a cointegration analysis (Johansen, 1988(Johansen, , 1991.…”

Section: Introductionmentioning

confidence: 99%

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

2016

View full text Add to dashboard Cite

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.

show abstract

“…This article describes the (new) test of stationarity introduced in Cardinali and Nason (2010) and presented in the costat package: this is described in Section 3.…”

Section: Introduction: Locally Stationary Time Seriesmentioning

confidence: 99%

“…Again, Sanderson et al (2010) is a notable exception. This article considers the implementation of the costationary methods introduced by Cardinali and Nason (2010) in Section 5. Given two locally stationary time series the goal of costationarity determination is to investigate whether there are two sequences α t , β t that can be found such that Z t is a classically (second-order) stationary time series where…”

Section: Introduction: Locally Stationary Time Seriesmentioning

confidence: 99%

Costationarity of Locally Stationary Time Series Usingcostat

Cardinali¹,

Nason²

2013

J. Stat. Soft.

Self Cite

View full text Add to dashboard Cite

This article describes the R package costat. This package enables a user to (i) perform a test for time series stationarity; (ii) compute and plot time-localized autocovariances, and (iii) to determine and explore any costationary relationship between two locally stationary time series. Two locally stationary time series are said to be costationary if there exists two time-varying combination functions such that the linear combination of the two series with the functions produces another time series which is stationary. Costationarity existing between two time series indicates a relationship between the series that might be usefully exploited in a number of ways. Sometimes the relationship itself is of interest, sometimes the derived stationary series is of interest and useful as a substitute for either of the original stationary series in some applications.Keywords: local stationarity, costationary time series, local autocovariance, costat. SummaryThe costat package, available from the Comprehensive R Archive Network at http://CRAN. R-project.org/package=costat, is designed for the analysis of locally stationary time series, particularly locally stationary wavelet time series. The package includes functionality for computing tests of stationarity, BootTOS; computing localized autocovariances, lacv; discovering costationarity between two time series, findstysols Several method functions exist that print, summarize or plot the various outputs of these functions. 2 Costationarity of Locally Stationary Time Series Using costat Introduction: Locally stationary time seriesThis article concerns the analysis of discrete time series, X t . That is, a sequence of observations taken through time where t could be an integer or some other regular spacing. Many are familiar with the concept of a stationary time series: that is, loosely speaking, a series whose statistical properties do not change over time. In much of classical time series analysis stationary means second-order stationary where the mean and variance of a series, X t , do not depend on time and the autocovariance:only depends on the lag τ between two different variates X t and X t+τ , but not the time point t = 1, . . . , T . There are several excellent books dealing with (stationary) time series analysis, for example, Brockwell and Davis (1991), Chatfield (2003), Hamilton (1994), Hannan (1960, Priestley (1983) or Shumway and Stoffer (2006).Mathematical theory demands that a stationary time series X t possesses the following representation:where A(ω) is an amplitude function, {e itω } is the usual system of harmonic complex exponentials and dz(ω) is an orthonormal increments process. The amplitude function controls the second-order properties of the time series. The usual spectrum f (ω) = |A(ω)| 2 and the spectrum and autocovariance are a Fourier transform pair. The amplitude, spectrum and autocovariance here reflect the time-invariant nature of the time series X t : none of them depend on time, t.However, many actual time series, arising in many disc...

show abstract

Costationarity of Locally Stationary Time Series

Cited by 30 publications

References 66 publications

The locally stationary dual-tree complex wavelet model

The locally stationary dual-tree complex wavelet model

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

Costationarity of Locally Stationary Time Series Usingcostat

Contact Info

Product

Resources

About