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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.
Two simulated time series processes, one stationary and the other non-stationary, are shown above. The augmented Dickey–Fuller (ADF) test statistic is reported for each process; non-stationarity cannot be rejected for the second process at a 5% significance level. White noise is the simplest example of a stationary process.
For example, time series are usually decomposed into: , the trend component at time t, which reflects the long-term progression of the series (secular variation). A trend exists when there is a persistent increasing or decreasing direction in the data. The trend component does not have to be linear. [1]
Time series datasets can also have fewer relationships between data entries in different tables and don't require indefinite storage of entries. [6] The unique properties of time series datasets mean that time series databases can provide significant improvements in storage space and performance over general purpose databases. [6]
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.
It is common practice in some disciplines (e.g. statistics and time series analysis) to normalize the autocovariance function to get a time-dependent Pearson correlation coefficient. However, in other disciplines (e.g. engineering) the normalization is usually dropped and the terms "autocorrelation" and "autocovariance" are used interchangeably.
Ideally, unevenly spaced time series are analyzed in their unaltered form. However, most of the basic theory for time series analysis was developed at a time when limitations in computing resources favored an analysis of equally spaced data, since in this case efficient linear algebra routines can be used and many problems have an explicit ...
For example, repeated throws of loaded dice will produce a sequence that is i.i.d., despite the outcomes being biased. In signal processing and image processing, the notion of transformation to i.i.d. implies two specifications, the "i.d." part and the "i." part: i.d. – The signal level must be balanced on the time axis. i.