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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 ...
The usefulness of the Wold Theorem is that it allows the dynamic evolution of a variable to be approximated by a linear model. If the innovations are independent, then the linear model is the only possible representation relating the observed value of to its past evolution. However, when is merely an uncorrelated but not independent sequence ...
Cointegration. Cointegration is a statistical property of a collection (X1, X2, ..., Xk) of time series variables. First, all of the series must be integrated of order d (see Order of integration ). Next, if a linear combination of this collection is integrated of order less than d, then the collection is said to be co-integrated.
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 ...
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 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 ...
In statistics, autoregressive fractionally integrated moving average models are time series models that generalize ARIMA ( autoregressive integrated moving average) models by allowing non-integer values of the differencing parameter. These models are useful in modeling time series with long memory —that is, in which deviations from the long ...
The trend component does not have to be linear., the cyclical component at time t, which reflects repeated but non-periodic fluctuations. The duration of these fluctuations depend on the nature of the time series., the seasonal component at time t, reflecting seasonality (seasonal variation). A seasonal pattern exists when a time series is ...