December 2018
Intermediate to advanced
318 pages
8h 28m
English
Content preview from Hands-On Machine Learning for Cybersecurity
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Strictly stationary process
A strictly stationary process is a process with a random probability distribution, such that its joint probability distribution is independent of time.
Strong sense stationarity: A time series T is called strongly or strictly stationary if two or more random vectors have equal joint distribution for all indices and integers, for example:
Random vector 1 = { Xt1, Xt2, Xt3, ..., Xtn}
Random vector 2 = { Xt1 +s, Xt2 + s, Xt3+s, ..., Xtn +s}
- s is all integers
- t1..tn is all indices
Weak or wide sense stationarity: A time series T is called weakly stationary if it has a shift invariance for the first and second moments of the process.
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