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This is an important technique for all types of time series analysis, especially for seasonal adjustment. [2] It seeks to construct, from an observed time series, a number of component series (that could be used to reconstruct the original by additions or multiplications) where each of these has a certain characteristic or type of behavior.
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.
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.
Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function.Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time.
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.
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 ...
Partial autocorrelation function of Lake Huron's depth with confidence interval (in blue, plotted around 0). In time series analysis, the partial autocorrelation function (PACF) gives the partial correlation of a stationary time series with its own lagged values, regressed the values of the time series at all shorter lags.
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.