Examples¶

Four end-to-end worked examples ship with the toolbox. Each is available as both a Python script (VS Code / Spyder # %% cell format) and a Jupyter notebook.

Running the examples¶

cd TimeSeriesSRC/Examples/PyFiles
python 01_ARMA_Model.py

Or open the notebooks in TimeSeriesSRC/Examples/NoteBooks/.

Example 1 — ARMA model (Series A)¶

Dataset: Chemical-plant concentration, 197 observations.

Goal: Identify the best ARMA(\(n_c, n_d\)) order and fit the model.

Script: Examples/PyFiles/01_ARMA_Model.py

Notebook: Examples/NoteBooks/01_ARMA_Model.ipynb

Key steps:

y = Series_A_Chemical_Concentration   (197 obs)

uniAnal(y)          # ACF, PACF, GPAC → order hints
selpmod(...)        # grid search → best AIC/BIC order
estimate(pm, y)     # LM estimation
uniChi(e, ...)      # residual whiteness test
pmoddisp(pm, stat)  # confidence intervals

Example 2 — ARIMA model (Series C)¶

Dataset: Chemical-plant temperature, 226 observations (non-stationary trend).

Goal: Apply regular differencing to achieve stationarity, then fit ARMA.

Script: Examples/PyFiles/02_ARIMA_Model.py

Notebook: Examples/NoteBooks/02_ARIMA_Model.ipynb

Key steps:

y = Series_C_Chemical_Temperature   (226 obs)

uniAnal(y, diff=[1])          # differenced series analysis
pmodel(..., diff=[1])         # ARIMA structure
estimate(pm, y)

Example 3 — Seasonal ARIMA (Series G)¶

Dataset: International airline passengers, 144 monthly observations.

Goal: Identify and fit a seasonal ARIMA model with period \(s = 12\).

Script: Examples/PyFiles/03_Seasonal_ARIMA_Model.py

Notebook: Examples/NoteBooks/03_Seasonal_ARIMA_Model.ipynb

Key steps:

y = Series_G_Airline_Passengers   (144 monthly obs, s=12)

uniAnal(y, diff=[1,1], per=[0,12])   # seasonal differencing
pmodel(..., diff=[1,1], per=[0,12])  # seasonal ARIMA structure
estimate(pm, y)

Example 4 — BJTF / ARMAX / ARX (Series J)¶

Dataset: Box-Jenkins gas-furnace, 296 observations (input: CH4 flow, output: CO2).

Goal: Compare ARX, ARMAX, and BJTF model classes on the same dataset.

Script: Examples/PyFiles/04_BJTF_Model.py

Notebook: Examples/NoteBooks/04_BJTF_Model.ipynb

Key steps:

y, u = Series_J_Gas_Furnace   (296 obs, MISO)

multiAnal(y, u)                     # impulse response, cross-correlation
pmodel("arx",   na=[2],nb=[2], delay=[3])
pmodel("armax", na=[2],nb=[2],nc=[1], delay=[3])
pmodel("bjtf",  nb=[2],nc=[1],nd=[1],nf=[2], delay=[3])
estimate(pm, y, u=u)
multiChi(e, u)                      # residual/input independence test

Benchmark datasets¶

All datasets are in TimeSeriesSRC/TestData/ and can be loaded with:

import pathlib, pandas as pd
import TimeSeriesSRC as ts

data_dir = pathlib.Path(ts.__file__).parent / "TestData"
y = pd.read_csv(data_dir / "Series_A_Chemical_Concentration.csv").values.flatten()

File	Description	Length	Type
Series_A_Chemical_Concentration.csv	Chemical process concentration	197	Univariate
Series_B_IBM_Stock.csv	IBM weekly stock price	369	Univariate
Series_C_Chemical_Temperature.csv	Chemical process temperature	226	Univariate
Series_D_Chemical_Viscosity.csv	Chemical process viscosity	—	Univariate
Series_E_Sunspot_Numbers.csv	Annual sunspot numbers	—	Univariate
Series_F_Chemical_Yields.csv	Chemical process yields	—	Univariate
Series_G_Airline_Passengers.csv	Monthly airline passengers	144	Univariate (seasonal)
Series_J_Gas_Furnace.csv	Gas furnace (CH4 in, CO2 out)	296	Bivariate