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

Chapter 6
Time Series
The autocovariance function is given by the following:
k
asz
g ( k)=
, k= 012 , , ¼, hence
2
( 1-a
)
g k
k
rk
= ( ) a
g 0
( ) = 2
model.
Figure 6-4 shows a time series and its autocorrelation plot of the AR
Figure 6-4. A time series and AR model
Estimating Parameters of an AR Process
A process is called weakly stationary if its mean is constant and the
autocovariance function depends only on time lag. There is no weakly
stationary process, but it is imposed on time-series data to do some
stochastic analysis. Suppose Z(t) is a weak stationary process with mean 0
and constant variance. Then X(t) is an autoregressive process of order p if
you have the following:
X(t) = a1 x X(t-1) + a2 x X(t-2) + … + ap x X(t-p) +Z(t), where a ∊ R and p ∊ I
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