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The general ARMA model was described in the 1951 thesis of Peter Whittle, who used mathematical analysis (Laurent series and Fourier analysis) and statistical inference. [ 12 ] [ 13 ] ARMA models were popularized by a 1970 book by George E. P. Box and Jenkins, who expounded an iterative ( Box–Jenkins ) method for choosing and estimating them.
Time series analysis comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series forecasting is the use of a model to predict future values based on previously observed values.
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.
In time series analysis used in statistics and econometrics, autoregressive integrated moving average (ARIMA) and seasonal ARIMA (SARIMA) models are generalizations of the autoregressive moving average (ARMA) model to non-stationary series and periodic variation, respectively.
A First Course on Time Series Analysis – an open source book on time series analysis with SAS (Chapter 7) Box–Jenkins models in the Engineering Statistics Handbook of NIST; Box–Jenkins modelling by Rob J Hyndman; The Box–Jenkins methodology for time series models by Theresa Hoang Diem Ngo
In time series analysis, singular spectrum analysis (SSA) is a nonparametric spectral estimation method. It combines elements of classical time series analysis, multivariate statistics , multivariate geometry, dynamical systems and signal processing .
A time series is the sequence of a variable's value over equally spaced periods, such as years or quarters in business applications. [11] To accomplish this, the data must be smoothed, or the random variance of the data must be removed in order to reveal trends in the data.
For example, in time series analysis, a plot of the sample autocorrelations versus (the time lags) is an autocorrelogram. If cross-correlation is plotted, the result is called a cross-correlogram. The correlogram is a commonly used tool for checking randomness in a data set. If random, autocorrelations should be near zero for any and all time ...