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An additive model would be used when the variations around the trend do not vary with the level of the time series whereas a multiplicative model would be appropriate if the trend is proportional to the level of the time series. Sometimes the trend and cyclical components are grouped into one, called the trend-cycle component.
Curve fitting [1] [2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [3] possibly subject to constraints. [4] [5] Curve fitting can involve either interpolation, [6] [7] where an exact fit to the data is required, or smoothing, [8] [9] in which a "smooth" function is ...
In stochastic processes, chaos theory and time series analysis, detrended fluctuation analysis ( DFA) is a method for determining the statistical self-affinity of a signal. It is useful for analysing time series that appear to be long-memory processes (diverging correlation time, e.g. power-law decaying autocorrelation function) or 1/f noise .
In statistics, a moving average ( rolling average or running average or moving mean [1] or rolling mean) is a calculation to analyze data points by creating a series of averages of different selections of the full data set. Variations include: simple, cumulative, or weighted forms. Mathematically, a moving average is a type of convolution.
Linear trend estimation. Linear trend estimation is a statistical technique used to analyze data patterns. Data patterns, or trends, occur when the information gathered "tends" to increase or decrease over time. Linear trend estimation essentially creates a straight line on a graph of data that models the general direction that the data is heading.
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 closing value of ...
Box–Jenkins method. In time series analysis, the Box–Jenkins method, [1] named after the statisticians George Box and Gwilym Jenkins, applies autoregressive moving average (ARMA) or autoregressive integrated moving average (ARIMA) models to find the best fit of a time-series model to past values of a time series .
As defined by Theil (1950), the Theil–Sen estimator of a set of two-dimensional points (xi, yi) is the median m of the slopes (yj − yi)/ (xj − xi) determined by all pairs of sample points. Sen (1968) extended this definition to handle the case in which two data points have the same x coordinate. In Sen's definition, one takes the median ...