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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.
For example, a seasonal decomposition of time series by Loess (STL) [4] plot decomposes a time series into seasonal, trend and irregular components using loess and plots the components separately, whereby the cyclical component (if present in the data) is included in the "trend" component plot.
Seasonal sub-series plots are formed by [3] Vertical axis: response variable; Horizontal axis: time of year; for example, with monthly data, all the January values are plotted (in chronological order), then all the February values, and so on. The horizontal line displays the mean value for each month over the time series.
Transformations such as logarithms can help to stabilize the variance of a time series. One of the ways for identifying non-stationary times series is the ACF plot. Sometimes, patterns will be more visible in the ACF plot than in the original time series; however, this is not always the case. [6]
For example, the plot can show if the trajectory is strictly periodic with period , then all such pairs of times will be separated by a multiple of and visible as diagonal lines. Typical examples of recurrence plots (top row: time series (plotted over
The original model uses an iterative three-stage modeling approach: Model identification and model selection: making sure that the variables are stationary, identifying seasonality in the dependent series (seasonally differencing it if necessary), and using plots of the autocorrelation (ACF) and partial autocorrelation (PACF) functions of the dependent time series to decide which (if any ...
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 ...
A Poincaré plot, named after Henri Poincaré, is a graphical representation used to visualize the relationship between consecutive data points in time series to detect patterns and irregularities in the time series, revealing information about the stability of dynamical systems, providing insights into periodic orbits, chaotic motions, and bifurcations.