Advanced Data Analytics Using Python_ With Machine Learning, Deep Learning and NLP Examples ( 2023)

Chapter 6
Time Series
Irregular Fluctuations
A time series without trends and cyclic variations can be realized as a
weekly stationary time series. In the next section, you will examine various
probabilistic models to realize weekly time series.
Stationary Time Series
Normally, a time series is said to be stationary if there is no systematic
change in mean and variance and if strictly periodic variations have
been done away with. In real life, there are no stationary time series.
Whatever data you receive by using transformations, you may try to make
it somehow nearer to a stationary series.
Stationary Process
A time series is strictly stationary if the joint distribution of X(t 1 ),...,X(t k ) is
the same as the joint distribution of X(t 1 + τ),...,X(t k + τ) for all t 1 ,…,t k ,τ. If k
=1, strict stationary implies that the distribution of X(t) is the same for all t,
so provided the first two moments are finite, you have the following:
μ(t) = μ
σ 2 (t) = σ 2
They are both constants, which do not depend on the value of t.
A weekly stationary time series is a stochastic process where the mean
is constant and autocovariance is a function of time lag.
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