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  2. Stationary process - Wikipedia

    en.wikipedia.org/wiki/Stationary_process

    An example of a discrete-time stationary process where the sample space is also discrete (so that the random variable may take one of N possible values) is a Bernoulli scheme. Other examples of a discrete-time stationary process with continuous sample space include some autoregressive and moving average processes which are both subsets of the ...

  3. Autoregressive integrated moving average - Wikipedia

    en.wikipedia.org/wiki/Autoregressive_integrated...

    According to Wold's decomposition theorem, [4] [5] [6] the ARMA model is sufficient to describe a regular (a.k.a. purely nondeterministic [6]) wide-sense stationary time series, so we are motivated to make such a non-stationary time series stationary, e.g., by using differencing, before we can use ARMA. [7]

  4. Trend-stationary process - Wikipedia

    en.wikipedia.org/wiki/Trend-stationary_process

    In both unit root and trend-stationary processes, the mean can be growing or decreasing over time; however, in the presence of a shock, trend-stationary processes are mean-reverting (i.e. transitory, the time series will converge again towards the growing mean, which was not affected by the shock) while unit-root processes have a permanent ...

  5. Autoregressive moving-average model - Wikipedia

    en.wikipedia.org/wiki/Autoregressive_moving...

    The CRAN task view on Time Series contains links to most of these. Mathematica has a complete library of time series functions including ARMA. [11] MATLAB includes functions such as arma, ar and arx to estimate autoregressive, exogenous autoregressive and ARMAX models. See System Identification Toolbox and Econometrics Toolbox for details.

  6. Moving-average model - Wikipedia

    en.wikipedia.org/wiki/Moving-average_model

    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.

  7. Time series - Wikipedia

    en.wikipedia.org/wiki/Time_series

    In addition, time-series analysis can be applied where the series are seasonally stationary or non-stationary. Situations where the amplitudes of frequency components change with time can be dealt with in time-frequency analysis which makes use of a time–frequency representation of a time-series or signal.

  8. List of stochastic processes topics - Wikipedia

    en.wikipedia.org/wiki/List_of_stochastic...

    In practical applications, the domain over which the function is defined is a time interval (time series) or a region of space (random field). Familiar examples of time series include stock market and exchange rate fluctuations, signals such as speech, audio and video; medical data such as a patient's EKG , EEG , blood pressure or temperature ...

  9. Unit root - Wikipedia

    en.wikipedia.org/wiki/Unit_root

    In both unit root and trend-stationary processes, the mean can be growing or decreasing over time; however, in the presence of a shock, trend-stationary processes are mean-reverting (i.e. transitory, the time series will converge again towards the growing mean, which was not affected by the shock) while unit-root processes have a permanent ...