Last Update: June 20, 2022
Time Series Decomposition: Classical Method in Python can be done using
seasonal_decompose function found within its
statsmodels.tsa.api module for estimating time series trend-cycle, seasonal and remainder components. Main parameters within
seasonal_decompose function are
x with time series data,
model with seasonal component type and
two_sided with moving average method used in filtering.
As example, we can do training range univariate time series classical additive seasonal decomposition by moving averages using data included within
datasets R package
AirPassengers object .
First, we import packages
pandas for data frames,
statsmodels for data downloading and time series decomposition and
matplotlib for training range and time series decomposition charts .
In : import pandas as pd import statsmodels.api as sm import statsmodels.tsa.api as ts import matplotlib.pyplot as plt
Second, we create
mdata model data object using
get_rdataset function, convert
mdata object into a data frame using
DataFrame function and display first five months of data using
head data frame method to view time series structure.
In : mdata = sm.datasets.get_rdataset(dataname="AirPassengers", package="datasets", cache=True).data mdata = pd.DataFrame(data=mdata["value"]).set_index( pd.date_range(start="1949", end="1961", freq="M")) print(mdata.head())
Out : value 1949-01-31 112 1949-02-28 118 1949-03-31 132 1949-04-30 129 1949-05-31 121
Third, we delimit training range for model fitting as first ten years of data and store outcome within
tdata object. Then, we delimit testing range for model forecasting as last two years of data and store outcome within
fdata object. Notice that training and testing ranges delimiting was only included as an educational example which can be modified according to your needs.
In : tdata = mdata[:"1958-12-31"] fdata = mdata["1959-01-01":]
Fourth, we view training range data with
xlabel functions. Within
plot function, training range data object is included. Within
xlabel functions, vertical axis label and horizontal axis label strings are included.
In : plt.plot(tdata) plt.ylabel("Air Passengers") plt.xlabel("Year") plt.show()
Fifth, we do training range time series classical additive seasonal decomposition by moving averages with
seasonal_decompose function and store results within
tsdec object. Within
seasonal_decompose function, parameters
x=tdata includes training range data object,
model="additive" includes additive seasonal component and
two_sided=True includes centered seasonal simple moving average estimation. Notice that we have to evaluate whether time series classical additive or multiplicative seasonal decomposition is needed. Also, notice that
seasonal_decompose function parameters were only included as educational examples which can be modified according to your needs. Then we do time series decomposition chart with
In : tsdec = ts.seasonal_decompose(x=tdata, model="additive", two_sided=True) tsdec.plot() plt.show()
 Data Description: Monthly international airline passenger numbers in thousands from 1949 to 1960.
Original Source: Box, G. E. P., Jenkins, G. M. and Reinsel, G. C. (1976). “Time Series Analysis, Forecasting and Control”. Third Edition. Holden-Day. Series G.
Source: datasets R Package AirPassengers Object. R Core Team (2021). “R: A language and environment for statistical computing”. R Foundation for Statistical Computing, Vienna, Austria.
 pandas Python package: Wes McKinney. (2010). Data Structures for Statistical Computing in Python, Proceedings of the 9th Python in Science Conference, 51-56.
statsmodels Python package: Seabold, Skipper, and Josef Perktold. (2010). “statsmodels: Econometric and statistical modeling with python”. Proceedings of the 9th Python in Science Conference.
matplotlib Python package: John D. Hunter. (2007). Matplotlib: A 2D Graphics Environment. Computing in Science & Engineering, 9, 90-95.