Serial dependence
Encyclopedia
In statistics
and signal processing
, random variables in a time series
have serial dependence if the value at some time t in the series is statistically dependent
on the value at another time s. A series is serially independent if there is no dependence between any pair.
Similarly, a time series has serial correlation if the condition holds that some pair of values are correlated, rather than the condition of statistical dependence: see autocorrelation
.
If a time series {Xt} is stationary
, then statistical dependence between the pair (Xt , Xs) would imply that there is statistical dependence between all pairs of values at the same lag s−t.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
and signal processing
Signal processing
Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...
, random variables in a time series
Time series
In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the...
have serial dependence if the value at some time t in the series is statistically dependent
Statistical independence
In probability theory, to say that two events are independent intuitively means that the occurrence of one event makes it neither more nor less probable that the other occurs...
on the value at another time s. A series is serially independent if there is no dependence between any pair.
Similarly, a time series has serial correlation if the condition holds that some pair of values are correlated, rather than the condition of statistical dependence: see autocorrelation
Autocorrelation
Autocorrelation is the cross-correlation of a signal with itself. Informally, it is the similarity between observations as a function of the time separation between them...
.
If a time series {Xt} is stationary
Stationary process
In the mathematical sciences, a stationary process is a stochastic process whose joint probability distribution does not change when shifted in time or space...
, then statistical dependence between the pair (Xt , Xs) would imply that there is statistical dependence between all pairs of values at the same lag s−t.
External links
- serial-dependence at www.quantiphile.com