Search results
Results from the WOW.Com Content Network
Time series. In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily ...
Plot with random data showing homoscedasticity: at each value of x, the y -value of the dots has about the same variance. Plot with random data showing heteroscedasticity: The variance of the y -values of the dots increases with increasing values of x. In statistics, a sequence of random variables is homoscedastic (/ ˌhoʊmoʊskəˈdæstɪk ...
Stationary process. In mathematics and statistics, a stationary process (or a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional joint probability distribution does not change when shifted in time. Consequently, parameters such as mean and variance also do not change over time.
In the statistical analysis of time series, autoregressive–moving-average (ARMA) models provide a parsimonious description of a (weakly) stationary stochastic process in terms of two polynomials, one for the autoregression (AR) and the second for the moving average (MA). The general ARMA model was described in the 1951 thesis of Peter Whittle ...
Unit root. In probability theory and statistics, a unit root is a feature of some stochastic processes (such as random walks) that can cause problems in statistical inference involving time series models. A linear stochastic process has a unit root if 1 is a root of the process's characteristic equation. Such a process is non-stationary but ...
Moving-average model. In time series analysis, the moving-average model (MA model), also known as moving-average process, is a common approach for modeling univariate time series. [1][2] The moving-average model specifies that the output variable is cross-correlated with a non-identical to itself random-variable.
The (potentially time-dependent) autocorrelation matrix (also called second moment) of a (potentially time-dependent) random vector is an matrix containing as elements the autocorrelations of all pairs of elements of the random vector . The autocorrelation matrix is used in various digital signal processing algorithms.
For example, time series are usually decomposed into: , the trend component at time t, which reflects the long-term progression of the series (secular variation). A trend exists when there is a persistent increasing or decreasing direction in the data. The trend component does not have to be linear. [1]