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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 general ARMA model was described in the 1951 thesis of Peter Whittle, Hypothesis testing in time series analysis, and it was popularized in the 1970 book by George E. P. Box and Gwilym Jenkins. Given a time series of data , the ARMA model is a tool for understanding and, perhaps, predicting future values in this series. The AR part involves ...
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 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 ...
Bayesian structural time series. Bayesian structural time series ( BSTS) model is a statistical technique used for feature selection, time series forecasting, nowcasting, inferring causal impact and other applications. The model is designed to work with time series data. The model has also promising application in the field of analytical marketing.
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. It contrasts with the autocorrelation function, which does not control for other lags. This function plays an important role in ...
Correlogram. A plot showing 100 random numbers with a "hidden" sine function, and an autocorrelation (correlogram) of the series on the bottom. In the analysis of data, a correlogram is a chart of correlation statistics. For example, in time series analysis, a plot of the sample autocorrelations versus (the time lags) is an autocorrelogram.
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 ...