Maximum entropy spectral estimationMaximum entropy spectral estimation is a method of spectral density estimation. The goal is to improve the spectral quality based on the principle of maximum entropy. The method is based on choosing the spectrum which corresponds to the most random or the most unpredictable time series whose autocorrelation function agrees with the known values. This assumption, which corresponds to the concept of maximum entropy as used in both statistical mechanics and information theory, is maximally non-committal with regard to the unknown values of the autocorrelation function of the time series.
Trend-stationary processIn the statistical analysis of time series, a trend-stationary process is a stochastic process from which an underlying trend (function solely of time) can be removed, leaving a stationary process. The trend does not have to be linear. Conversely, if the process requires differencing to be made stationary, then it is called difference stationary and possesses one or more unit roots. Those two concepts may sometimes be confused, but while they share many properties, they are different in many aspects.
CUSUMIn statistical quality control, the CUsUM (or cumulative sum control chart) is a sequential analysis technique developed by E. S. Page of the University of Cambridge. It is typically used for monitoring change detection. CUSUM was announced in Biometrika, in 1954, a few years after the publication of Wald's sequential probability ratio test (SPRT). E. S. Page referred to a "quality number" , by which he meant a parameter of the probability distribution; for example, the mean.
Singular spectrum analysisIn time series analysis, singular spectrum analysis (SSA) is a nonparametric spectral estimation method. It combines elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems and signal processing. Its roots lie in the classical Karhunen (1946)–Loève (1945, 1978) spectral decomposition of time series and random fields and in the Mañé (1981)–Takens (1981) embedding theorem. SSA can be an aid in the decomposition of time series into a sum of components, each having a meaningful interpretation.
Sinusoidal modelIn statistics, signal processing, and time series analysis, a sinusoidal model is used to approximate a sequence Yi to a sine function: where C is constant defining a mean level, α is an amplitude for the sine, ω is the angular frequency, Ti is a time variable, φ is the phase-shift, and Ei is the error sequence. This sinusoidal model can be fit using nonlinear least squares; to obtain a good fit, routines may require good starting values for the unknown parameters.
Causalité au sens de GrangerLa causalité a été introduite dans l'analyse économétrique par Wiener (1956) et Granger (1969). À l'origine, on retrouve la formalisation de la notion de causalité en physique, notamment dans les travaux d'Isaac Newton sur la force motrice (cause) et le changement de mouvement (effet). Dans ce cas, la notion de causalité traduit un principe d’après lequel si un phénomène est la cause d’un autre phénomène, nommé « effet », alors ce dernier ne peut pas précéder la cause.
Domaine temporelLe domaine temporel se rapporte à l'analyse de fonctions mathématiques ou de signaux physiques modélisant une variation quelconque au cours du temps. En domaine temporel, la valeur de la fonction ou du signal est connue, soit en quelques points discrets de la durée d'analyse, ou éventuellement, pour tous les nombres réels. L'oscilloscope est parmi les outils usuels permettant de visualiser les signaux physiques du domaine temporel. Domaine fréquentiel Temps (physique) Catégorie:Analyse du signal Catégorie:
Modèle de cointégrationLa cointégration est une propriété statistique des séries temporelles introduite dans l'analyse économique, notamment par Engle et Newbold (1974). En des termes simples, la cointégration permet de détecter la relation de long terme entre deux ou plusieurs séries temporelles. Sa formalisation rigoureuse est due à Granger (1981), et Johansen (1991, 1995). Techniquement, la notion de cointégration implique implicitement celle d'intégration.
SeasonalityIn time series data, seasonality is the presence of variations that occur at specific regular intervals less than a year, such as weekly, monthly, or quarterly. Seasonality may be caused by various factors, such as weather, vacation, and holidays and consists of periodic, repetitive, and generally regular and predictable patterns in the levels of a time series. Seasonal fluctuations in a time series can be contrasted with cyclical patterns. The latter occur when the data exhibits rises and falls that are not of a fixed period.
Cross-covarianceIn probability and statistics, given two stochastic processes and , the cross-covariance is a function that gives the covariance of one process with the other at pairs of time points. With the usual notation for the expectation operator, if the processes have the mean functions and , then the cross-covariance is given by Cross-covariance is related to the more commonly used cross-correlation of the processes in question.
