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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 ...
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. Together with the autoregressive (AR) model, the ...
H is directly related to fractal dimension, D, and is a measure of a data series' "mild" or "wild" randomness. [4] The Hurst exponent is referred to as the "index of dependence" or "index of long-range dependence". It quantifies the relative tendency of a time series either to regress strongly to the mean or to cluster in a direction. [5]
The general ARMA model was described in the 1951 thesis of Peter Whittle, Hypothesis testing in time series analysis, and it was popularized in the 1970 book by George E. P. Box and Gwilym Jenkins. Given a time series of data , the ARMA model is a tool for understanding and, perhaps, predicting future values in this series. The AR part involves ...
Periodogram. In signal processing, a periodogram is an estimate of the spectral density of a signal. The term was coined by Arthur Schuster in 1898. [ 1] Today, the periodogram is a component of more sophisticated methods (see spectral estimation ). It is the most common tool for examining the amplitude vs frequency characteristics of FIR ...
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 ...
Autoregressive integrated moving average. In statistics and econometrics, and in particular in time series analysis, an autoregressive integrated moving average ( ARIMA) model is a generalization of an autoregressive moving average (ARMA) model. To better comprehend the data or to forecast upcoming series points, both of these models are fitted ...
In time series analysis, dynamic time warping ( DTW) is an algorithm for measuring similarity between two temporal sequences, which may vary in speed. For instance, similarities in walking could be detected using DTW, even if one person was walking faster than the other, or if there were accelerations and decelerations during the course of an ...