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

Chapter 6 Time Series
Here, b1, often referred to as the permanent component, is the initial
weight of the seasonality; b2 represents the trend, which is linear in this
case.
However, there is no standard implementation of the Holt-Winters
model in Python. It is available in R (see Chapter 1 for how R’s Holt-
Winters model can be called from Python code).
Removing Seasonality from a Time Series
There are two ways of removing seasonality from a time series.
• By filtering
• By differencing
By Filtering
The series {x t } is converted into another called {y t } with the linear operation
shown here, where {a r } is a set of weights:
Y t = ∑ +s r=-qa r x t+r
To smooth out local fluctuations and estimate the local mean, you
should clearly choose the weights so that ∑ a r = 1; then the operation is
often referred to as a moving average. They are often symmetric with
s = q and a j = a -j . The simplest example of a symmetric smoothing filter is
the simple moving average, for which a r = 1 / (2q+1) for r = -q, …, + q.
The smoothed value of x t is given by the following:
1
Sm(x t ) =
2q + 1
∑+q r=-qx t+r
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