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Time series: random data plus trend, with best-fit line and different applied filters. In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time.
In time series data, seasonality refers to the trends that occur at specific regular intervals less than a year, such as weekly, monthly, or quarterly. Seasonality may be caused by various factors, such as weather, vacation, and holidays [1] and consists of periodic, repetitive, and generally regular and predictable patterns in the levels [2] of a time series.
, the irregular component (or "noise") at time t, which describes random, irregular influences. It represents the residuals or remainder of the time series after the other components have been removed. Hence a time series using an additive model can be thought of as = + + +,
The secular variation of a time series is its long-term, non-periodic variation (see Decomposition of time series).Whether a variation is perceived as secular or not depends on the available timescale: a variation that is secular over a timescale of centuries may be a segment of what is, over a timescale of millions of years, a periodic variation.
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Time series datasets are relatively large and uniform compared to other datasets―usually being composed of a timestamp and associated data. [6] Time series datasets can also have fewer relationships between data entries in different tables and don't require indefinite storage of entries. [6]
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.
A Satellite Image Time Series (SITS) is a set of satellite images taken from the same scene at different times. A SITS makes use of different satellite sources to obtain a larger data series with short time interval between two images. In this case, it is fundamental to observe the spatial resolution and registration constraints.