Whittle likelihood
E695659
The Whittle likelihood is an approximate likelihood function used in time series analysis that simplifies inference for stationary stochastic processes by working in the frequency domain.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
approximate likelihood
ⓘ
likelihood function ⓘ statistical method ⓘ time series analysis method ⓘ |
| advantage |
computational efficiency for long time series
ⓘ
diagonalization of covariance structure in frequency domain ⓘ |
| appliesTo |
stationary stochastic processes
ⓘ
stationary time series ⓘ |
| approximates | Gaussian likelihood for time series ⓘ |
| approximationType | frequency domain approximation to exact likelihood ⓘ |
| assumes |
asymptotic independence of Fourier frequencies
ⓘ
large sample size ⓘ second-order stationarity ⓘ |
| basedOn |
periodogram
ⓘ
spectral density ⓘ |
| domain |
probability theory
ⓘ
signal processing ⓘ statistics ⓘ |
| implementedIn |
MATLAB time series toolboxes
NERFINISHED
ⓘ
Python time series libraries ⓘ R time series packages ⓘ |
| introducedBy | Peter Whittle NERFINISHED ⓘ |
| introducedIn | 1950s ⓘ |
| minimizedAs | Whittle contrast function ⓘ |
| namedAfter | Peter Whittle NERFINISHED ⓘ |
| relatedConcept |
Fourier transform
NERFINISHED
ⓘ
Toeplitz covariance matrices NERFINISHED ⓘ exact Gaussian likelihood ⓘ spectral factorization ⓘ |
| relatedTo |
Gaussian time series models
ⓘ
periodogram likelihood ⓘ |
| requires |
discrete Fourier transform of the data
ⓘ
estimation of spectral density ⓘ |
| simplifies | likelihood computation for long time series ⓘ |
| usedFor |
approximate Bayesian computation in spectral domain
ⓘ
approximate maximum likelihood estimation ⓘ fitting ARMA models ⓘ fitting fractional ARIMA models ⓘ fitting long-memory models ⓘ fitting state-space spectral models ⓘ inference for stationary stochastic processes ⓘ parameter estimation in time series models ⓘ |
| usedIn |
Bayesian time series analysis
ⓘ
frequency domain analysis ⓘ spectral analysis ⓘ time series analysis ⓘ |
| worksIn | frequency domain ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.