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Long-range dependence (LRD), also called long memory or long-range persistence, is a phenomenon that may arise in the analysis of spatial or time series data. It relates to the rate of decay of statistical dependence of two points with increasing time interval or spatial distance between the points.
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 ...
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. Generally, time series data is modelled as a stochastic process.
The time series refers to the data over the period, while the interruption is the intervention, which is a controlled external influence or set of influences. [1] [2] Effects of the intervention are evaluated by changes in the level and slope of the time series and statistical significance of the intervention parameters. [3]
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], the cyclical component at time t, which reflects repeated but non-periodic fluctuations. The duration of these fluctuations depend on the nature of the time series.
Given a time series of data x t, the STAR model is a tool for understanding and, perhaps, predicting future values in this series, assuming that the behaviour of the series changes depending on the value of the transition variable. The transition might depend on the past values of the x series (similar to the SETAR models), or exogenous variables.
In order to still use the Box–Jenkins approach, one could difference the series and then estimate models such as ARIMA, given that many commonly used time series (e.g. in economics) appear to be stationary in first differences. Forecasts from such a model will still reflect cycles and seasonality that are present in the data.
High frequency data employs the collection of a large sum of data over a time series, and as such the frequency of single data collection tends to be spaced out in irregular patterns over time. This is especially clear in financial market analysis, where transactions may occur in sequence, or after a prolonged period of inactivity.