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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 ...
In the statistical analysis of time series, autoregressive–moving-average (ARMA) models are a way to describe a (weakly) stationary stochastic process using autoregression (AR) and a moving average (MA), each with a polynomial. They are a tool for understanding a series and predicting future values.
Cobweb plot of the Gauss map for = and =.This shows an 8-cycle. In mathematics, the Gauss map (also known as Gaussian map [1] or mouse map), is a nonlinear iterated map of the reals into a real interval given by the Gaussian function:
Together with the moving-average (MA) model, it is a special case and key component of the more general autoregressive–moving-average (ARMA) and autoregressive integrated moving average (ARIMA) models of time series, which have a more complicated stochastic structure; it is also a special case of the vector autoregressive model (VAR), which ...
If each of and is a scalar random variable which is realized repeatedly in a time series, then the correlations of the various temporal instances of are known as autocorrelations of , and the cross-correlations of with across time are temporal cross-correlations. In probability and statistics, the definition of correlation always includes a ...
where Δt is the time interval between two co-local events (i.e. happening at the same place) for an observer in some inertial frame (e.g. ticks on their clock), known as the proper time, Δt′ is the time interval between those same events, as measured by another observer, inertially moving with velocity v with respect to the former observer ...
Panel data is the general class, a multidimensional data set, whereas a time series data set is a one-dimensional panel (as is a cross-sectional dataset). A data set may exhibit characteristics of both panel data and time series data. One way to tell is to ask what makes one data record unique from the other records.
Ideally, unevenly spaced time series are analyzed in their unaltered form. However, most of the basic theory for time series analysis was developed at a time when limitations in computing resources favored an analysis of equally spaced data, since in this case efficient linear algebra routines can be used and many problems have an explicit ...