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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 ...
Decomposition of time series. The decomposition of time series is a statistical task that deconstructs a time series into several components, each representing one of the underlying categories of patterns. [1] There are two principal types of decomposition, which are outlined below.
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 time series analysis, the partial autocorrelation function (PACF) gives the partial correlation of a stationary time series with its own lagged values, regressed the values of the time series at all shorter lags. It contrasts with the autocorrelation function, which does not control for other lags. This function plays an important role in ...
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.
Autoregressive model. In statistics, econometrics, and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it can be used to describe certain time-varying processes in nature, economics, behavior, etc. The autoregressive model specifies that the output variable depends linearly on its own ...
Seasonal subseries plot. Seasonal subseries plots are a graphical tool to visualize and detect seasonality in a time series. [1] Seasonal subseries plots involves the extraction of the seasons from a time series into a subseries. Based on a selected periodicity, it is an alternative plot that emphasizes the seasonal patterns are where the data ...
Tent map. Graph of tent map function. Example of iterating the initial condition x0 = 0.4 over the tent map with μ = 1.9. In mathematics, the tent map with parameter μ is the real -valued function fμ defined by. the name being due to the tent -like shape of the graph of fμ. For the values of the parameter μ within 0 and 2, fμ maps the ...