PyCaret Time Series – Passenger Forecast Dublin Airport¶

Roberto Tavares de Oliveira Neto | Student ID: 2025444¶

Module: Strategic Thinking – Higher Diploma in Data Analytics
CCT College Dublin | 2025–2026

Use of AI Tools: I have not used any AI tools or technologies in the preparation of this assessment.

Overview¶

Two experimental setups are compared:

  • Setup A (exp1) – Full series including COVID period (reference only)
  • Setup B (exp2) – COVID period excluded, drift imputation (primary setup)

Pipeline per setup:

  1. check_stats – stationarity, seasonality and white noise validation
  2. compare_models – automated benchmarking
  3. create_model – train selected models
  4. tune_model – hyperparameter optimisation (native TS models only)
  5. blend_models – ensemble of top models
  6. stack_models – stacked ensemble with meta-learner
  7. plot_model – decomposition, ACF, diagnostics, in-sample, forecast with CI
  8. finalize_model + predict_model – forecasts stored in dictionary for comparison
  9. get_config('dataset_transformed') – inspect drift imputation applied to COVID gap

Environment Configuration¶

Component Version
Python 3.9.6 (Clang 21.0.0, macOS-26.4.1-arm64)
PyCaret 3.3.2
sktime 0.26.0
scikit-learn 1.4.2
statsmodels 0.14.6
pandas 2.1.4
numpy 1.26.4
jupyter_core 5.8.1
ipykernel 6.30.1

Note: Results may vary on different environments. PyCaret 3.3.2 with sktime 0.26.0 is the validated configuration for this notebook.

1. Libraries and Data Loading¶

In [1]:
import subprocess
import sys

# Install pyjstat if not available
subprocess.check_call([sys.executable, '-m', 'pip', 'install', 'pyjstat', '-q'])

import warnings
warnings.filterwarnings('ignore')

import pandas as pd
import numpy as np
from collections import OrderedDict
import matplotlib.pyplot as plt
import requests
from pyjstat import pyjstat

WARNING: You are using pip version 21.2.4; however, version 26.0.1 is available.
You should consider upgrading via the '/Library/Developer/CommandLineTools/usr/bin/python3 -m pip install --upgrade pip' command.
In [2]:
url = "https://ws.cso.ie/public/api.restful/PxStat.Data.Cube_API.ReadDataset/ASM01/JSON-stat/2.0/en"
r = requests.get(url)
r.raise_for_status()
json_stat_obj = r.json(object_pairs_hook=OrderedDict)
df_list = pyjstat.from_json_stat(json_stat_obj)
df = pd.DataFrame(df_list[0])

# delete non necessary columns and filter for air arrivals only
df = df.drop(columns=['STATISTIC'])
df = df[df['Mode'] == 'Air'].drop(columns=['Mode'])
df['Date'] = pd.to_datetime(df['Month'])
df = df.set_index('Date').sort_index().drop(columns=['Month'])

# fix to Dublin airport arrivals only (83% of total air arrivals)
df['Dublin_airport'] = df['value'] * 0.83
df = df.drop(columns=['value'])
df = df[df['Direction'] == 'Arrivals'].drop(columns=['Direction'])

print(f"Dataset: {df.shape[0]} observations | {df.index[0].date()} to {df.index[-1].date()}")
df.tail(14)

Dataset: 195 observations | 2010-01-01 to 2026-03-01
Out[2]:
Dublin_airport
Date
2025-02-01 1059.578
2025-03-01 1286.998
2025-04-01 1519.066
2025-05-01 1657.095
2025-06-01 1720.507
2025-07-01 1877.294
2025-08-01 1924.106
2025-09-01 1661.162
2025-10-01 1593.932
2025-11-01 1279.279
2025-12-01 1276.540
2026-01-01 1197.109
2026-02-01 1152.538
2026-03-01 1402.866

2. Setup A – Full Series Including COVID¶

Reference only. Included to demonstrate the impact of the pandemic structural break on model performance.

In [3]:
from pycaret.time_series import *

df_A = df.copy()
df_A.index = df_A.index.to_period('M')
print(f"Setup A: {df_A.shape[0]} observations")
df_A

Setup A: 195 observations
Out[3]:
Dublin_airport
Date
2010-01 604.572
2010-02 628.476
2010-03 752.478
2010-04 610.714
2010-05 803.855
... ...
2025-11 1279.279
2025-12 1276.540
2026-01 1197.109
2026-02 1152.538
2026-03 1402.866

195 rows × 1 columns

In [4]:
exp1 = TSForecastingExperiment()
exp1.setup(
    data=df_A,
    target='Dublin_airport',
    session_id=100,
    fh=12,
    fold=3,
    fold_strategy='expanding',
    seasonal_period=12,
    coverage=0.90,
    verbose=True
)
  Description Value
0 session_id 100
1 Target Dublin_airport
2 Approach Univariate
3 Exogenous Variables Not Present
4 Original data shape (195, 1)
5 Transformed data shape (195, 1)
6 Transformed train set shape (183, 1)
7 Transformed test set shape (12, 1)
8 Rows with missing values 0.0%
9 Fold Generator ExpandingWindowSplitter
10 Fold Number 3
11 Enforce Prediction Interval False
12 Splits used for hyperparameters all
13 User Defined Seasonal Period(s) 12
14 Ignore Seasonality Test False
15 Seasonality Detection Algo user_defined
16 Max Period to Consider 60
17 Seasonal Period(s) Tested [12]
18 Significant Seasonal Period(s) [12]
19 Significant Seasonal Period(s) without Harmonics [12]
20 Remove Harmonics False
21 Harmonics Order Method harmonic_max
22 Num Seasonalities to Use 1
23 All Seasonalities to Use [12]
24 Primary Seasonality 12
25 Seasonality Present True
26 Seasonality Type mul
27 Target Strictly Positive True
28 Target White Noise No
29 Recommended d 1
30 Recommended Seasonal D 0
31 Preprocess False
32 CPU Jobs -1
33 Use GPU False
34 Log Experiment False
35 Experiment Name ts-default-name
36 USI 937f
Out[4]:
<pycaret.time_series.forecasting.oop.TSForecastingExperiment at 0x12acc8700>

2.1 Statistical Validation (Setup A)¶

check_stats() runs formal tests for stationarity (ADF, KPSS), seasonality, and white noise before any model is trained.

In [5]:
exp1.check_stats()
Out[5]:
Test Test Name Data Property Setting Value
0 Summary Statistics Transformed Length 195.0
1 Summary Statistics Transformed # Missing Values 0.0
2 Summary Statistics Transformed Mean 1005.049554
3 Summary Statistics Transformed Median 1026.71
4 Summary Statistics Transformed Standard Deviation 416.164152
5 Summary Statistics Transformed Variance 173192.601164
6 Summary Statistics Transformed Kurtosis 0.025503
7 Summary Statistics Transformed Skewness -0.394332
8 Summary Statistics Transformed # Distinct Values 194.0
9 White Noise Ljung-Box Transformed Test Statictic {'alpha': 0.05, 'K': 24} 865.945938
10 White Noise Ljung-Box Transformed Test Statictic {'alpha': 0.05, 'K': 48} 1208.888895
11 White Noise Ljung-Box Transformed p-value {'alpha': 0.05, 'K': 24} 0.0
12 White Noise Ljung-Box Transformed p-value {'alpha': 0.05, 'K': 48} 0.0
13 White Noise Ljung-Box Transformed White Noise {'alpha': 0.05, 'K': 24} 0.0
14 White Noise Ljung-Box Transformed White Noise {'alpha': 0.05, 'K': 48} 0.0
15 Stationarity ADF Transformed Stationarity {'alpha': 0.05} True
16 Stationarity ADF Transformed p-value {'alpha': 0.05} 0.028922
17 Stationarity ADF Transformed Test Statistic {'alpha': 0.05} -3.069149
18 Stationarity ADF Transformed Critical Value 1% {'alpha': 0.05} -3.467211
19 Stationarity ADF Transformed Critical Value 5% {'alpha': 0.05} -2.877735
20 Stationarity ADF Transformed Critical Value 10% {'alpha': 0.05} -2.575403
21 Stationarity KPSS Transformed Trend Stationarity {'alpha': 0.05} True
22 Stationarity KPSS Transformed p-value {'alpha': 0.05} 0.081382
23 Stationarity KPSS Transformed Test Statistic {'alpha': 0.05} 0.129054
24 Stationarity KPSS Transformed Critical Value 10% {'alpha': 0.05} 0.119
25 Stationarity KPSS Transformed Critical Value 5% {'alpha': 0.05} 0.146
26 Stationarity KPSS Transformed Critical Value 2.5% {'alpha': 0.05} 0.176
27 Stationarity KPSS Transformed Critical Value 1% {'alpha': 0.05} 0.216
28 Normality Shapiro Transformed Normality {'alpha': 0.05} False
29 Normality Shapiro Transformed p-value {'alpha': 0.05} 0.001567
In [6]:
exp1.plot_model(plot='cv')
exp1.plot_model(plot='train_test_split')
In [7]:
best_A = exp1.compare_models(sort='SMAPE', n_select=3)
results_A = exp1.pull()  # called immediately after compare_models
  Model MASE RMSSE MAE RMSE MAPE SMAPE R2 TT (Sec)
ets ETS 0.5264 0.2817 107.6606 114.5154 0.0862 0.0910 0.4690 0.0267
arima ARIMA 0.5388 0.3325 109.8586 134.3540 0.0865 0.0928 0.0874 0.6033
lasso_cds_dt Lasso w/ Cond. Deseasonalize & Detrending 0.5675 0.3372 128.3293 144.4958 0.0944 0.1008 0.4976 0.1033
lr_cds_dt Linear w/ Cond. Deseasonalize & Detrending 0.5680 0.3374 128.4184 144.5756 0.0945 0.1009 0.4971 0.1300
en_cds_dt Elastic Net w/ Cond. Deseasonalize & Detrending 0.5677 0.3373 128.3709 144.5352 0.0945 0.1009 0.4973 0.1067
ridge_cds_dt Ridge w/ Cond. Deseasonalize & Detrending 0.5680 0.3374 128.4184 144.5756 0.0945 0.1009 0.4971 0.1067
llar_cds_dt Lasso Least Angular Regressor w/ Cond. Deseasonalize & Detrending 0.5676 0.3373 128.3355 144.5035 0.0944 0.1009 0.4975 0.0467
br_cds_dt Bayesian Ridge w/ Cond. Deseasonalize & Detrending 0.5706 0.3423 129.4126 146.7938 0.0945 0.1013 0.4815 0.0467
exp_smooth Exponential Smoothing 0.5910 0.3687 120.1458 148.5408 0.0938 0.1040 -0.1009 0.0233
theta Theta Forecaster 0.6646 0.3769 140.7851 156.0420 0.1084 0.1128 0.3272 0.0100
huber_cds_dt Huber w/ Cond. Deseasonalize & Detrending 0.7032 0.3942 147.4265 163.2344 0.1118 0.1217 0.1222 0.1200
auto_arima Auto ARIMA 0.7463 0.4124 160.0231 172.1743 0.1217 0.1319 0.1977 3.5367
rf_cds_dt Random Forest w/ Cond. Deseasonalize & Detrending 0.8412 0.4471 170.2034 180.9643 0.1351 0.1541 -0.5760 0.1233
ada_cds_dt AdaBoost w/ Cond. Deseasonalize & Detrending 0.9034 0.4952 189.6974 204.8522 0.1454 0.1604 -0.3554 0.0600
et_cds_dt Extra Trees w/ Cond. Deseasonalize & Detrending 0.8680 0.4681 175.3988 189.6681 0.1399 0.1616 -0.7129 0.1167
omp_cds_dt Orthogonal Matching Pursuit w/ Cond. Deseasonalize & Detrending 0.9295 0.5341 199.5970 224.2139 0.1475 0.1646 -0.4640 0.1167
gbr_cds_dt Gradient Boosting w/ Cond. Deseasonalize & Detrending 0.8932 0.5333 183.8293 218.6532 0.1485 0.1714 -0.5899 0.0567
lightgbm_cds_dt Light Gradient Boosting w/ Cond. Deseasonalize & Detrending 1.0435 0.5889 217.8155 242.5443 0.1669 0.1890 -0.7832 0.1033
dt_cds_dt Decision Tree w/ Cond. Deseasonalize & Detrending 1.0174 0.5333 203.5298 214.4032 0.1631 0.1965 -1.5193 0.0467
knn_cds_dt K Neighbors w/ Cond. Deseasonalize & Detrending 1.1000 0.5921 222.3731 239.8312 0.1773 0.2119 -1.6969 0.1033
naive Naive Forecaster 1.2969 0.7693 278.2114 320.5331 0.2005 0.2259 -1.6132 1.1633
stlf STLF 1.2359 0.6751 245.9252 270.0803 0.1947 0.2526 -3.5322 0.6533
polytrend Polynomial Trend Forecaster 1.9047 1.1193 415.1086 470.5673 0.2942 0.3574 -4.0191 0.6100
grand_means Grand Means Forecaster 1.9050 1.1213 420.9558 473.8693 0.2957 0.3584 -3.7682 0.5800
snaive Seasonal Naive Forecaster 1.5853 0.8716 315.3723 348.6414 0.2459 0.3663 -6.7446 0.5867
croston Croston 2.1742 1.2115 455.8357 500.0620 0.3388 0.4433 -6.8855 0.0100

2.2 Create and Tune Models (Setup A)¶

In [8]:
models_A = ['exp_smooth', 'arima', 'ets', 'lasso_cds_dt', 'lr_cds_dt']
tune_A   = ['exp_smooth', 'arima', 'ets', 'lasso_cds_dt', 'lr_cds_dt']  # only native TS models support tune_model

resultados_A   = {}
resultados_t_A = {}

for model_name in models_A:
    print(f'Creating: {model_name}')
    resultados_A[model_name] = exp1.create_model(model_name)

for model_name in tune_A:
    print(f'Tuning: {model_name}')
    resultados_t_A[model_name] = exp1.tune_model(resultados_A[model_name])

Creating: exp_smooth
  cutoff MASE RMSSE MAE RMSE MAPE SMAPE R2
0 2022-03 1.2619 0.7870 241.5628 307.5916 0.1930 0.2261 -2.1239
1 2023-03 0.1382 0.0944 32.8447 41.8083 0.0242 0.0243 0.9654
2 2024-03 0.3728 0.2246 86.0299 96.2226 0.0642 0.0617 0.8558
Mean NaT 0.5910 0.3687 120.1458 148.5408 0.0938 0.1040 -0.1009
SD NaT 0.4840 0.3005 88.5578 114.6388 0.0720 0.0876 1.4312 
Creating: arima
  cutoff MASE RMSSE MAE RMSE MAPE SMAPE R2
0 2022-03 1.1545 0.7159 221.0189 279.8213 0.1735 0.1951 -1.5853
1 2023-03 0.2908 0.1765 69.1127 78.1979 0.0559 0.0537 0.8791
2 2024-03 0.1709 0.1052 39.4443 45.0427 0.0302 0.0296 0.9684
Mean NaT 0.5388 0.3325 109.8586 134.3540 0.0865 0.0928 0.0874
SD NaT 0.4382 0.2727 79.5299 103.7477 0.0624 0.0730 1.1833 
Creating: ets
  cutoff MASE RMSSE MAE RMSE MAPE SMAPE R2
0 2022-03 1.0770 0.5305 206.1783 207.3455 0.1718 0.1885 -0.4195
1 2023-03 0.1366 0.0942 32.4681 41.7288 0.0239 0.0240 0.9656
2 2024-03 0.3654 0.2205 84.3355 94.4720 0.0629 0.0604 0.8610
Mean NaT 0.5264 0.2817 107.6606 114.5154 0.0862 0.0910 0.4690
SD NaT 0.4004 0.1833 72.8096 69.0822 0.0626 0.0705 0.6297 
Creating: lasso_cds_dt
  cutoff MASE RMSSE MAE RMSE MAPE SMAPE R2
0 2022-03 0.3554 0.2036 68.0448 79.5626 0.0569 0.0581 0.7910
1 2023-03 0.8838 0.5246 210.0203 232.4646 0.1494 0.1634 -0.0686
2 2024-03 0.4633 0.2835 106.9229 121.4603 0.0770 0.0810 0.7703
Mean NaT 0.5675 0.3372 128.3293 144.4958 0.0944 0.1008 0.4976
SD NaT 0.2280 0.1365 59.9052 64.5122 0.0397 0.0452 0.4004 
Creating: lr_cds_dt
  cutoff MASE RMSSE MAE RMSE MAPE SMAPE R2
0 2022-03 0.3561 0.2039 68.1786 79.6925 0.0570 0.0582 0.7903
1 2023-03 0.8841 0.5247 210.0740 232.5020 0.1494 0.1635 -0.0690
2 2024-03 0.4637 0.2837 107.0026 121.5323 0.0771 0.0811 0.7700
Mean NaT 0.5680 0.3374 128.4184 144.5756 0.0945 0.1009 0.4971
SD NaT 0.2278 0.1364 59.8752 64.4770 0.0397 0.0452 0.4004 
Tuning: exp_smooth
  cutoff MASE RMSSE MAE RMSE MAPE SMAPE R2
0 2022-03 1.0578 0.5213 202.5059 203.7724 0.1688 0.1848 -0.3710
1 2023-03 0.1389 0.0920 32.9991 40.7578 0.0242 0.0243 0.9672
2 2024-03 0.3765 0.2264 86.8834 96.9969 0.0647 0.0621 0.8535
Mean NaT 0.5244 0.2799 107.4628 113.8424 0.0859 0.0904 0.4832
SD NaT 0.3895 0.1793 70.7143 67.6080 0.0609 0.0685 0.6058 
Fitting 3 folds for each of 10 candidates, totalling 30 fits

[Parallel(n_jobs=-1)]: Using backend LokyBackend with 10 concurrent workers.
[Parallel(n_jobs=-1)]: Done  30 out of  30 | elapsed:    0.4s finished

Tuning: arima
  cutoff MASE RMSSE MAE RMSE MAPE SMAPE R2
0 2022-03 0.6543 0.3536 125.2491 138.1992 0.0989 0.1050 0.3694
1 2023-03 0.3446 0.2075 81.8936 91.9285 0.0638 0.0628 0.8329
2 2024-03 0.4903 0.3403 113.1434 145.7729 0.0947 0.0873 0.6691
Mean NaT 0.4964 0.3004 106.7620 125.3002 0.0858 0.0850 0.6238
SD NaT 0.1265 0.0660 18.2659 23.7991 0.0157 0.0173 0.1919 
Fitting 3 folds for each of 10 candidates, totalling 30 fits

[Parallel(n_jobs=-1)]: Using backend LokyBackend with 10 concurrent workers.
[Parallel(n_jobs=-1)]: Done  30 out of  30 | elapsed:    2.0s finished

Tuning: ets
  cutoff MASE RMSSE MAE RMSE MAPE SMAPE R2
0 2022-03 1.0770 0.5305 206.1783 207.3455 0.1718 0.1885 -0.4195
1 2023-03 0.1366 0.0942 32.4681 41.7288 0.0239 0.0240 0.9656
2 2024-03 0.3654 0.2205 84.3355 94.4720 0.0629 0.0604 0.8610
Mean NaT 0.5264 0.2817 107.6606 114.5154 0.0862 0.0910 0.4690
SD NaT 0.4004 0.1833 72.8096 69.0822 0.0626 0.0705 0.6297 
Fitting 3 folds for each of 10 candidates, totalling 30 fits

[Parallel(n_jobs=-1)]: Using backend LokyBackend with 10 concurrent workers.
[Parallel(n_jobs=-1)]: Done  30 out of  30 | elapsed:    0.5s finished

Tuning: lasso_cds_dt
  cutoff MASE RMSSE MAE RMSE MAPE SMAPE R2
0 2022-03 0.4612 0.2792 88.2830 109.1143 0.0695 0.0697 0.6069
1 2023-03 0.8838 0.5246 210.0158 232.4614 0.1494 0.1634 -0.0686
2 2024-03 0.3151 0.2279 72.7194 97.6240 0.0543 0.0573 0.8516
Mean NaT 0.5534 0.3439 123.6727 146.3999 0.0911 0.0968 0.4633
SD NaT 0.2412 0.1295 61.3835 61.0352 0.0417 0.0474 0.3892 
Fitting 3 folds for each of 10 candidates, totalling 30 fits

[Parallel(n_jobs=-1)]: Using backend LokyBackend with 10 concurrent workers.
[Parallel(n_jobs=-1)]: Done  30 out of  30 | elapsed:    0.8s finished

Tuning: lr_cds_dt
  cutoff MASE RMSSE MAE RMSE MAPE SMAPE R2
0 2022-03 0.3561 0.2039 68.1786 79.6925 0.0570 0.0582 0.7903
1 2023-03 0.8841 0.5247 210.0740 232.5020 0.1494 0.1635 -0.0690
2 2024-03 0.4637 0.2837 107.0026 121.5323 0.0771 0.0811 0.7700
Mean NaT 0.5680 0.3374 128.4184 144.5756 0.0945 0.1009 0.4971
SD NaT 0.2278 0.1364 59.8752 64.4770 0.0397 0.0452 0.4004 
Fitting 3 folds for each of 10 candidates, totalling 30 fits

[Parallel(n_jobs=-1)]: Using backend LokyBackend with 10 concurrent workers.
[Parallel(n_jobs=-1)]: Done  30 out of  30 | elapsed:    0.9s finished

2.3 Blend and Stack (Setup A)¶

In [9]:
# Blend – weighted average of the top 3 models from compare_models
blended_A = exp1.blend_models(best_A)
print("Blended model created – Setup A")
  cutoff MASE RMSSE MAE RMSE MAPE SMAPE R2
0 2022-03 0.6292 0.3998 120.4427 156.2658 0.0932 0.1010 0.1937
1 2023-03 0.2302 0.1442 54.6971 63.8840 0.0381 0.0390 0.9193
2 2024-03 0.1205 0.0724 27.8157 31.0275 0.0197 0.0196 0.9850
Mean NaT 0.3266 0.2055 67.6519 83.7258 0.0503 0.0532 0.6993
SD NaT 0.2186 0.1405 38.9085 53.0184 0.0312 0.0347 0.3585 
Blended model created – Setup A

2.4 Diagnostics and Plots (Setup A)¶

In [10]:
# Seasonal decomposition and ACF for the best individual model
exp1.plot_model(resultados_t_A['exp_smooth'], plot='decomp')
exp1.plot_model(resultados_t_A['exp_smooth'], plot='acf')
In [11]:
for model_name in tune_A:
    print(f'Diagnostics: {model_name}')
    exp1.plot_model(estimator=resultados_t_A[model_name], plot='diagnostics')

Diagnostics: exp_smooth

Diagnostics: arima

Diagnostics: ets

Diagnostics: lasso_cds_dt
In sample predictions has not been implemented for this estimator of type 'BaseCdsDtForecaster' in `sktime`. When this is implemented, it will be enabled by default in pycaret.
In sample predictions has not been implemented for this estimator of type 'BaseCdsDtForecaster' in `sktime`. When this is implemented, it will be enabled by default in pycaret.
Diagnostics: lr_cds_dt
In sample predictions has not been implemented for this estimator of type 'BaseCdsDtForecaster' in `sktime`. When this is implemented, it will be enabled by default in pycaret.
In sample predictions has not been implemented for this estimator of type 'BaseCdsDtForecaster' in `sktime`. When this is implemented, it will be enabled by default in pycaret.
In [12]:
for model_name in tune_A:
    print(f'In-sample: {model_name}')
    exp1.plot_model(resultados_t_A[model_name], plot='insample')

In-sample: exp_smooth

In-sample: arima

In-sample: ets

In-sample: lasso_cds_dt
In sample predictions has not been implemented for this estimator of type 'BaseCdsDtForecaster' in `sktime`. When this is implemented, it will be enabled by default in pycaret.
In-sample: lr_cds_dt
In sample predictions has not been implemented for this estimator of type 'BaseCdsDtForecaster' in `sktime`. When this is implemented, it will be enabled by default in pycaret.

2.5 Finalize and Store Forecasts (Setup A)¶

In [13]:
forecasts_A        = {}
resultados_final_A = {}

# stack_models not supported in this PyCaret version for time series
# blend_models is used as the ensemble method
all_models_A = {**resultados_A, 'blend': blended_A}

for model_name, model_obj in all_models_A.items():
    source      = resultados_t_A.get(model_name, model_obj)
    final_model = exp1.finalize_model(source)
    pred        = exp1.predict_model(final_model, fh=12)
    forecasts_A[model_name]        = pred['y_pred']
    resultados_final_A[model_name] = final_model
    print(f'Forecast – {model_name}:')
    display(pred)
    exp1.plot_model(final_model, plot='forecast', data_kwargs={'fh': 12})
    print()

Forecast – exp_smooth:
y_pred
2026-04 1581.6608
2026-05 1720.6196
2026-06 1832.7146
2026-07 2041.7404
2026-08 2069.9425
2026-09 1794.0123
2026-10 1706.0981
2026-11 1370.2635
2026-12 1339.9335
2027-01 1254.7507
2027-02 1254.1143
2027-03 1465.3596 
Forecast – arima:
y_pred
2026-04 1549.5826
2026-05 1657.3518
2026-06 1736.2438
2026-07 1882.2799
2026-08 1925.8036
2026-09 1755.0969
2026-10 1700.8654
2026-11 1489.3823
2026-12 1467.4014
2027-01 1409.8464
2027-02 1411.5449
2027-03 1545.9635 
Forecast – ets:
y_pred
2026-04 1573.6837
2026-05 1711.4875
2026-06 1822.9991
2026-07 2032.1108
2026-08 2060.7454
2026-09 1784.9221
2026-10 1696.5987
2026-11 1360.3668
2026-12 1326.9046
2027-01 1239.1107
2027-02 1237.3567
2027-03 1443.5386 
Forecast – lasso_cds_dt:
y_pred
2026-04 1542.0120
2026-05 1628.6971
2026-06 1704.8745
2026-07 1932.0375
2026-08 2057.1938
2026-09 1793.3397
2026-10 1680.6175
2026-11 1320.3128
2026-12 1285.1271
2027-01 1148.7629
2027-02 1123.8197
2027-03 1268.6165 
Forecast – lr_cds_dt:
y_pred
2026-04 1557.6938
2026-05 1640.9832
2026-06 1708.6036
2026-07 1840.1089
2026-08 1832.0089
2026-09 1624.9880
2026-10 1530.8852
2026-11 1288.6661
2026-12 1243.2458
2027-01 1158.4668
2027-02 1160.6390
2027-03 1290.4236 
Forecast – blend:
y_pred
2026-04 1586.7699
2026-05 1704.5554
2026-06 1783.6016
2026-07 1947.6311
2026-08 1968.4477
2026-09 1718.2799
2026-10 1633.5293
2026-11 1334.4188
2026-12 1305.8150
2027-01 1220.5191
2027-02 1204.5537
2027-03 1398.7796 


























3. Setup B – COVID Excluded (Primary Setup)¶
The COVID period (Jan 2020 – Feb 2022) is removed and the index rebuilt with NaN in the gap. PyCaret imputes these using drift interpolation — a linear bridge between pre- and post-pandemic levels that preserves the seasonal structure.


















In [14]:






df_B = df[(df.index < '2020-01-01') | (df.index > '2022-02-01')].copy()
df_B = df_B[['Dublin_airport']].dropna()
df_B.index = df_B.index.to_period('M')

idx_full = pd.period_range(min(df_B.index), max(df_B.index), freq='M')
df_B = df_B.reindex(idx_full, fill_value=np.nan)

print(f"Setup B: {df_B.shape[0]} observations")
print(f"  Period   : {df_B.index[0]} to {df_B.index[-1]}")
print(f"  NaN count: {df_B['Dublin_airport'].isna().sum()} months (COVID gap)")
df_B

























Setup B: 195 observations
  Period   : 2010-01 to 2026-03
  NaN count: 26 months (COVID gap)









Out[14]:












Dublin_airport






2010-01
604.572




2010-02
628.476




2010-03
752.478




2010-04
610.714




2010-05
803.855




...
...




2025-11
1279.279




2025-12
1276.540




2026-01
1197.109




2026-02
1152.538




2026-03
1402.866






195 rows × 1 columns






















In [15]:






exp2 = TSForecastingExperiment()
exp2.setup(
    data=df_B,
    target='Dublin_airport',
    session_id=42,
    fh=12,
    fold=3,
    fold_strategy='expanding',
    seasonal_period=12,
    coverage=0.90,
    numeric_imputation_target='drift',
    verbose=True
)






























 
Description
Value






0
session_id
42




1
Target
Dublin_airport




2
Approach
Univariate




3
Exogenous Variables
Not Present




4
Original data shape
(195, 1)




5
Transformed data shape
(195, 1)




6
Transformed train set shape
(183, 1)




7
Transformed test set shape
(12, 1)




8
Rows with missing values
13.3%




9
Fold Generator
ExpandingWindowSplitter




10
Fold Number
3




11
Enforce Prediction Interval
False




12
Splits used for hyperparameters
all




13
User Defined Seasonal Period(s)
12




14
Ignore Seasonality Test
False




15
Seasonality Detection Algo
user_defined




16
Max Period to Consider
60




17
Seasonal Period(s) Tested
[12]




18
Significant Seasonal Period(s)
[12]




19
Significant Seasonal Period(s) without Harmonics
[12]




20
Remove Harmonics
False




21
Harmonics Order Method
harmonic_max




22
Num Seasonalities to Use
1




23
All Seasonalities to Use
[12]




24
Primary Seasonality
12




25
Seasonality Present
True




26
Seasonality Type
mul




27
Target Strictly Positive
True




28
Target White Noise
No




29
Recommended d
1




30
Recommended Seasonal D
0




31
Preprocess
True




32
Numerical Imputation (Target)
drift




33
Transformation (Target)
None




34
Scaling (Target)
None




35
Feature Engineering (Target) - Reduced Regression
False




36
CPU Jobs
-1




37
Use GPU
False




38
Log Experiment
False




39
Experiment Name
ts-default-name




40
USI
bc48












Out[15]:




<pycaret.time_series.forecasting.oop.TSForecastingExperiment at 0x14d1635e0>
























3.1 Statistical Validation (Setup B)¶


















In [16]:






exp2.check_stats()





















Out[16]:












Test
Test Name
Data
Property
Setting
Value






0
Summary
Statistics
Transformed
Length

195.0




1
Summary
Statistics
Transformed
# Missing Values

0.0




2
Summary
Statistics
Transformed
Mean

1126.863943




3
Summary
Statistics
Transformed
Median

1138.428




4
Summary
Statistics
Transformed
Standard Deviation

300.028783




5
Summary
Statistics
Transformed
Variance

90017.270496




6
Summary
Statistics
Transformed
Kurtosis

-0.394798




7
Summary
Statistics
Transformed
Skewness

0.155182




8
Summary
Statistics
Transformed
# Distinct Values

194.0




9
White Noise
Ljung-Box
Transformed
Test Statictic
{'alpha': 0.05, 'K': 24}
1286.307799




10
White Noise
Ljung-Box
Transformed
Test Statictic
{'alpha': 0.05, 'K': 48}
1720.25752




11
White Noise
Ljung-Box
Transformed
p-value
{'alpha': 0.05, 'K': 24}
0.0




12
White Noise
Ljung-Box
Transformed
p-value
{'alpha': 0.05, 'K': 48}
0.0




13
White Noise
Ljung-Box
Transformed
White Noise
{'alpha': 0.05, 'K': 24}
0.0




14
White Noise
Ljung-Box
Transformed
White Noise
{'alpha': 0.05, 'K': 48}
0.0




15
Stationarity
ADF
Transformed
Stationarity
{'alpha': 0.05}
False




16
Stationarity
ADF
Transformed
p-value
{'alpha': 0.05}
0.945526




17
Stationarity
ADF
Transformed
Test Statistic
{'alpha': 0.05}
-0.137938




18
Stationarity
ADF
Transformed
Critical Value 1%
{'alpha': 0.05}
-3.467005




19
Stationarity
ADF
Transformed
Critical Value 5%
{'alpha': 0.05}
-2.877644




20
Stationarity
ADF
Transformed
Critical Value 10%
{'alpha': 0.05}
-2.575355




21
Stationarity
KPSS
Transformed
Trend Stationarity
{'alpha': 0.05}
True




22
Stationarity
KPSS
Transformed
p-value
{'alpha': 0.05}
0.1




23
Stationarity
KPSS
Transformed
Test Statistic
{'alpha': 0.05}
0.10397




24
Stationarity
KPSS
Transformed
Critical Value 10%
{'alpha': 0.05}
0.119




25
Stationarity
KPSS
Transformed
Critical Value 5%
{'alpha': 0.05}
0.146




26
Stationarity
KPSS
Transformed
Critical Value 2.5%
{'alpha': 0.05}
0.176




27
Stationarity
KPSS
Transformed
Critical Value 1%
{'alpha': 0.05}
0.216




28
Normality
Shapiro
Transformed
Normality
{'alpha': 0.05}
False




29
Normality
Shapiro
Transformed
p-value
{'alpha': 0.05}
0.049615






























3.2 Inspect Drift Imputation Applied to COVID Gap¶


















In [17]:






# Visualise how drift imputation filled the 26 missing months
df_transformed = exp2.get_config('dataset_transformed')

fig, ax = plt.subplots(figsize=(16, 5))
df_transformed['Dublin_airport'].plot(ax=ax, color='steelblue', lw=1.5, label='After imputation')
ax.axvspan(
    df_transformed.index.asof(pd.Period('2020-01', 'M')),
    df_transformed.index.asof(pd.Period('2022-02', 'M')),
    alpha=0.15, color='red', label='COVID gap (drift filled)'
)
ax.set_title('Dataset After Drift Imputation – COVID Gap Highlighted')
ax.set_ylabel('Passengers (thousands)')
ax.legend()
ax.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()
























No description has been provided for this image



















In [18]:






exp2.plot_model(plot='cv')
exp2.plot_model(plot='train_test_split')













































In [19]:






best_B   = exp2.compare_models(sort='SMAPE', n_select=3)
results_B = exp2.pull()  # called immediately after compare_models








































 
Model
MASE
RMSSE
MAE
RMSE
MAPE
SMAPE
R2
TT (Sec)






exp_smooth
Exponential Smoothing
0.8150
0.7053
68.3717
81.6027
0.0543
0.0548
0.8293
0.0300




et_cds_dt
Extra Trees w/ Cond. Deseasonalize & Detrending
0.9256
0.7908
76.7661
90.8576
0.0601
0.0594
0.7638
0.1333




omp_cds_dt
Orthogonal Matching Pursuit w/ Cond. Deseasonalize & Detrending
0.9179
0.7500
77.9127
87.8537
0.0627
0.0614
0.8346
0.0567




gbr_cds_dt
Gradient Boosting w/ Cond. Deseasonalize & Detrending
1.0126
0.8466
83.8836
97.0198
0.0652
0.0645
0.7165
0.0767




rf_cds_dt
Random Forest w/ Cond. Deseasonalize & Detrending
1.0271
0.8798
85.3169
101.0986
0.0674
0.0663
0.7094
0.1433




dt_cds_dt
Decision Tree w/ Cond. Deseasonalize & Detrending
1.0579
0.9629
90.0574
112.4471
0.0641
0.0664
0.7111
0.0533




knn_cds_dt
K Neighbors w/ Cond. Deseasonalize & Detrending
1.0946
0.9350
91.6093
107.6575
0.0716
0.0695
0.6763
0.1233




lightgbm_cds_dt
Light Gradient Boosting w/ Cond. Deseasonalize & Detrending
1.1015
0.9255
90.8624
105.7087
0.0721
0.0701
0.6397
0.1133




ada_cds_dt
AdaBoost w/ Cond. Deseasonalize & Detrending
1.1980
1.0012
99.0010
114.6962
0.0797
0.0774
0.6009
0.0667




arima
ARIMA
1.3680
1.0628
109.8095
118.8804
0.0865
0.0897
0.2589
0.0300




snaive
Seasonal Naive Forecaster
1.4778
1.2156
121.5364
138.8985
0.0931
0.0951
0.3747
0.0367




theta
Theta Forecaster
1.3855
1.0569
111.6768
118.8350
0.0904
0.0976
0.3182
0.0333




huber_cds_dt
Huber w/ Cond. Deseasonalize & Detrending
1.4851
1.2577
120.8226
142.1904
0.0933
0.0987
0.1714
0.0667




ets
ETS
1.4810
1.1344
120.0975
128.1750
0.0966
0.1031
0.2951
0.0300




br_cds_dt
Bayesian Ridge w/ Cond. Deseasonalize & Detrending
1.5906
1.2852
129.0605
145.0602
0.1016
0.1050
0.0976
0.0600




auto_arima
Auto ARIMA
1.6152
1.2883
131.1861
145.4063
0.1043
0.1086
0.0849
2.3433




en_cds_dt
Elastic Net w/ Cond. Deseasonalize & Detrending
1.7032
1.3734
137.8067
154.6299
0.1087
0.1134
-0.0901
0.0567




lasso_cds_dt
Lasso w/ Cond. Deseasonalize & Detrending
1.7032
1.3734
137.8044
154.6274
0.1087
0.1134
-0.0901
0.0667




llar_cds_dt
Lasso Least Angular Regressor w/ Cond. Deseasonalize & Detrending
1.7032
1.3734
137.8036
154.6269
0.1087
0.1134
-0.0901
0.0600




lr_cds_dt
Linear w/ Cond. Deseasonalize & Detrending
1.7039
1.3740
137.8607
154.6899
0.1088
0.1135
-0.0913
0.0567




ridge_cds_dt
Ridge w/ Cond. Deseasonalize & Detrending
1.7039
1.3740
137.8603
154.6895
0.1088
0.1135
-0.0913
0.0733




stlf
STLF
1.8791
1.5711
155.9059
180.9973
0.1162
0.1215
0.0298
0.0433




polytrend
Polynomial Trend Forecaster
2.5179
2.0991
213.2533
244.8161
0.1715
0.1603
-0.3413
0.0167




croston
Croston
2.5137
2.1289
214.7543
250.5319
0.1532
0.1623
-0.3177
0.0200




grand_means
Grand Means Forecaster
3.3003
2.9833
282.2588
351.1370
0.1895
0.2206
-1.5736
0.0167




naive
Naive Forecaster
3.3298
2.7725
278.2114
320.5331
0.2005
0.2259
-1.6132
0.0200






































3.3 Create and Tune Models (Setup B)¶


















In [20]:






models_B = ['exp_smooth', 'arima', 'et_cds_dt', 'omp_cds_dt', 'gbr_cds_dt']
tune_B   = ['exp_smooth', 'arima', 'et_cds_dt', 'omp_cds_dt', 'gbr_cds_dt']

resultados_B   = {}
resultados_t_B = {}

for model_name in models_B:
    print(f'Creating: {model_name}')
    resultados_B[model_name] = exp2.create_model(model_name)

for model_name in tune_B:
    print(f'Tuning: {model_name}')
    resultados_t_B[model_name] = exp2.tune_model(resultados_B[model_name])

























Creating: exp_smooth




























 
cutoff
MASE
RMSSE
MAE
RMSE
MAPE
SMAPE
R2






0
2022-03
1.0243
0.9165
79.7430
99.7027
0.0648
0.0683
0.6718




1
2023-03
0.6694
0.5116
57.4432
60.8166
0.0426
0.0430
0.9269




2
2024-03
0.7512
0.6876
67.9290
84.2886
0.0556
0.0530
0.8894




Mean
NaT
0.8150
0.7053
68.3717
81.6027
0.0543
0.0548
0.8293




SD
NaT
0.1517
0.1658
9.1092
15.9884
0.0091
0.0104
0.1125


























Creating: arima




























 
cutoff
MASE
RMSSE
MAE
RMSE
MAPE
SMAPE
R2






0
2022-03
3.0688
2.3258
238.9059
253.0125
0.1953
0.2043
-1.1137




1
2023-03
0.6672
0.5628
57.2550
66.8977
0.0394
0.0405
0.9115




2
2024-03
0.3679
0.2997
33.2678
36.7311
0.0247
0.0244
0.9790




Mean
NaT
1.3680
1.0628
109.8095
118.8804
0.0865
0.0897
0.2589




SD
NaT
1.2088
0.8996
91.8087
95.6419
0.0772
0.0813
0.9710


























Creating: et_cds_dt




























 
cutoff
MASE
RMSSE
MAE
RMSE
MAPE
SMAPE
R2






0
2022-03
1.2907
1.1048
100.4847
120.1832
0.0856
0.0826
0.5231




1
2023-03
0.9880
0.8068
84.7826
95.9076
0.0586
0.0603
0.8181




2
2024-03
0.4980
0.4608
45.0310
56.4819
0.0362
0.0352
0.9503




Mean
NaT
0.9256
0.7908
76.7661
90.8576
0.0601
0.0594
0.7638




SD
NaT
0.3266
0.2632
23.3378
26.2500
0.0202
0.0194
0.1786


























Creating: omp_cds_dt




























 
cutoff
MASE
RMSSE
MAE
RMSE
MAPE
SMAPE
R2






0
2022-03
0.8654
0.6910
67.3718
75.1735
0.0593
0.0583
0.8134




1
2023-03
0.9486
0.7317
81.4045
86.9760
0.0624
0.0617
0.8504




2
2024-03
0.9396
0.8273
84.9619
101.4115
0.0665
0.0642
0.8399




Mean
NaT
0.9179
0.7500
77.9127
87.8537
0.0627
0.0614
0.8346




SD
NaT
0.0373
0.0571
7.5938
10.7296
0.0029
0.0024
0.0156


























Creating: gbr_cds_dt




























 
cutoff
MASE
RMSSE
MAE
RMSE
MAPE
SMAPE
R2






0
2022-03
1.4489
1.2430
112.7988
135.2171
0.0958
0.0930
0.3963




1
2023-03
1.0486
0.8428
89.9845
100.1785
0.0626
0.0644
0.8015




2
2024-03
0.5404
0.4541
48.8675
55.6638
0.0370
0.0363
0.9518




Mean
NaT
1.0126
0.8466
83.8836
97.0198
0.0652
0.0645
0.7165




SD
NaT
0.3717
0.3221
26.4540
32.5542
0.0241
0.0231
0.2346


























Tuning: exp_smooth




























 
cutoff
MASE
RMSSE
MAE
RMSE
MAPE
SMAPE
R2






0
2022-03
0.7210
0.6546
56.1295
71.2073
0.0458
0.0471
0.8326




1
2023-03
0.5332
0.4535
45.7605
53.9062
0.0345
0.0349
0.9425




2
2024-03
0.7777
0.6945
70.3248
85.1325
0.0560
0.0536
0.8872




Mean
NaT
0.6773
0.6009
57.4049
70.0820
0.0454
0.0452
0.8874




SD
NaT
0.1045
0.1055
10.0688
12.7729
0.0088
0.0078
0.0449


























Fitting 3 folds for each of 10 candidates, totalling 30 fits













[Parallel(n_jobs=-1)]: Using backend LokyBackend with 10 concurrent workers.
[Parallel(n_jobs=-1)]: Done  30 out of  30 | elapsed:    0.6s finished













Tuning: arima




























 
cutoff
MASE
RMSSE
MAE
RMSE
MAPE
SMAPE
R2






0
2022-03
2.2248
1.8587
173.2023
202.1963
0.1507
0.1451
-0.3499




1
2023-03
1.3013
1.1206
111.6712
133.2062
0.0757
0.0798
0.6491




2
2024-03
0.3656
0.3009
33.0603
36.8801
0.0240
0.0239
0.9788




Mean
NaT
1.2972
1.0934
105.9779
124.0942
0.0834
0.0829
0.4260




SD
NaT
0.7590
0.6363
57.3542
67.7969
0.0520
0.0495
0.5649


























Fitting 3 folds for each of 10 candidates, totalling 30 fits













[Parallel(n_jobs=-1)]: Using backend LokyBackend with 10 concurrent workers.
[Parallel(n_jobs=-1)]: Done  30 out of  30 | elapsed:    0.8s finished













Tuning: et_cds_dt




























 
cutoff
MASE
RMSSE
MAE
RMSE
MAPE
SMAPE
R2






0
2022-03
1.4945
1.3302
116.3518
144.7052
0.1048
0.0969
0.3086




1
2023-03
0.7065
0.5791
60.6265
68.8395
0.0436
0.0446
0.9063




2
2024-03
0.4087
0.3400
36.9510
41.6715
0.0268
0.0268
0.9730




Mean
NaT
0.8699
0.7498
71.3098
85.0721
0.0584
0.0561
0.7293




SD
NaT
0.4581
0.4219
33.2838
43.6013
0.0335
0.0298
0.2987


























Fitting 3 folds for each of 10 candidates, totalling 30 fits













[Parallel(n_jobs=-1)]: Using backend LokyBackend with 10 concurrent workers.
[Parallel(n_jobs=-1)]: Done  30 out of  30 | elapsed:    1.9s finished













Tuning: omp_cds_dt




























 
cutoff
MASE
RMSSE
MAE
RMSE
MAPE
SMAPE
R2






0
2022-03
1.0662
0.8210
83.0038
89.3081
0.0712
0.0686
0.7366




1
2023-03
0.5204
0.4508
44.6565
53.5896
0.0364
0.0361
0.9432




2
2024-03
0.5792
0.4769
52.3710
58.4544
0.0410
0.0399
0.9468




Mean
NaT
0.7219
0.5829
60.0104
67.1174
0.0495
0.0482
0.8756




SD
NaT
0.2446
0.1687
16.5610
15.8164
0.0155
0.0145
0.0982


























Fitting 3 folds for each of 10 candidates, totalling 30 fits













[Parallel(n_jobs=-1)]: Using backend LokyBackend with 10 concurrent workers.
[Parallel(n_jobs=-1)]: Done  30 out of  30 | elapsed:    0.9s finished













Tuning: gbr_cds_dt




























 
cutoff
MASE
RMSSE
MAE
RMSE
MAPE
SMAPE
R2






0
2022-03
0.5874
0.5166
45.7298
56.1968
0.0397
0.0388
0.8957




1
2023-03
1.5374
1.1867
131.9332
141.0611
0.0950
0.1003
0.6065




2
2024-03
0.7360
0.6098
66.5468
74.7480
0.0505
0.0497
0.9130




Mean
NaT
0.9536
0.7710
81.4033
90.6686
0.0617
0.0630
0.8051




SD
NaT
0.4172
0.2964
36.7268
36.4288
0.0239
0.0268
0.1406


























Fitting 3 folds for each of 10 candidates, totalling 30 fits













[Parallel(n_jobs=-1)]: Using backend LokyBackend with 10 concurrent workers.
[Parallel(n_jobs=-1)]: Done  30 out of  30 | elapsed:    1.5s finished

























3.4 Blend and Stack (Setup B)¶


















In [21]:






# Blend – weighted average of top 3 models
blended_B = exp2.blend_models(best_B)
print("Blended model created – Setup B")








































 
cutoff
MASE
RMSSE
MAE
RMSE
MAPE
SMAPE
R2






0
2022-03
0.8326
0.6504
64.8159
70.7484
0.0536
0.0536
0.8347




1
2023-03
0.8681
0.6515
74.4963
77.4452
0.0545
0.0550
0.8814




2
2024-03
0.6663
0.6255
60.2456
76.6786
0.0492
0.0473
0.9085




Mean
NaT
0.7890
0.6425
66.5193
74.9574
0.0524
0.0520
0.8749




SD
NaT
0.0880
0.0120
5.9412
2.9926
0.0023
0.0034
0.0304


























Blended model created – Setup B

























3.5 Decomposition, ACF and Diagnostics (Setup B)¶


















In [22]:






# Seasonal decomposition and ACF – best tuned model
exp2.plot_model(resultados_t_B['exp_smooth'], plot='decomp')
exp2.plot_model(resultados_t_B['exp_smooth'], plot='acf')













































In [23]:






for model_name in tune_B:
    print(f'Diagnostics: {model_name}')
    exp2.plot_model(estimator=resultados_t_B[model_name], plot='diagnostics')

























Diagnostics: exp_smooth



















Diagnostics: arima



















Diagnostics: et_cds_dt
In sample predictions has not been implemented for this estimator of type 'BaseCdsDtForecaster' in `sktime`. When this is implemented, it will be enabled by default in pycaret.
In sample predictions has not been implemented for this estimator of type 'BaseCdsDtForecaster' in `sktime`. When this is implemented, it will be enabled by default in pycaret.
Diagnostics: omp_cds_dt
In sample predictions has not been implemented for this estimator of type 'BaseCdsDtForecaster' in `sktime`. When this is implemented, it will be enabled by default in pycaret.
In sample predictions has not been implemented for this estimator of type 'BaseCdsDtForecaster' in `sktime`. When this is implemented, it will be enabled by default in pycaret.
Diagnostics: gbr_cds_dt
In sample predictions has not been implemented for this estimator of type 'BaseCdsDtForecaster' in `sktime`. When this is implemented, it will be enabled by default in pycaret.
In sample predictions has not been implemented for this estimator of type 'BaseCdsDtForecaster' in `sktime`. When this is implemented, it will be enabled by default in pycaret.





















In [24]:






for model_name in tune_B:
    print(f'In-sample: {model_name}')
    exp2.plot_model(resultados_t_B[model_name], plot='insample')

























In-sample: exp_smooth



















In-sample: arima



















In-sample: et_cds_dt
In sample predictions has not been implemented for this estimator of type 'BaseCdsDtForecaster' in `sktime`. When this is implemented, it will be enabled by default in pycaret.
In-sample: omp_cds_dt
In sample predictions has not been implemented for this estimator of type 'BaseCdsDtForecaster' in `sktime`. When this is implemented, it will be enabled by default in pycaret.
In-sample: gbr_cds_dt
In sample predictions has not been implemented for this estimator of type 'BaseCdsDtForecaster' in `sktime`. When this is implemented, it will be enabled by default in pycaret.

























3.6 Finalize and Store Forecasts (Setup B)¶


















In [25]:






forecasts_B        = {}
resultados_final_B = {}

# Include blend and stack alongside individual models
all_models_B = {**resultados_B, 'blend': blended_B}

for model_name, model_obj in all_models_B.items():
    source      = resultados_t_B.get(model_name, model_obj)
    final_model = exp2.finalize_model(source)
    pred        = exp2.predict_model(final_model, fh=12)
    forecasts_B[model_name]        = pred['y_pred']
    resultados_final_B[model_name] = final_model
    print(f'Forecast – {model_name}:')
    display(pred)
    # Forecast with 90% confidence interval
    exp2.plot_model(final_model, plot='forecast', data_kwargs={'fh': 12})
    print()

























Forecast – exp_smooth:





















y_pred






2026-04
1560.9654




2026-05
1677.9206




2026-06
1772.7468




2026-07
1952.0170




2026-08
1965.9407




2026-09
1720.8029




2026-10
1637.8686




2026-11
1346.1215




2026-12
1316.0814




2027-01
1256.8653




2027-02
1248.8532




2027-03
1402.8660
























Forecast – arima:





















y_pred






2026-04
1566.4898




2026-05
1704.6223




2026-06
1767.7433




2026-07
1923.9976




2026-08
1971.5737




2026-09
1708.8255




2026-10
1640.9376




2026-11
1326.3116




2026-12
1323.4354




2027-01
1244.0834




2027-02
1200.0322




2027-03
1450.0576
























Forecast – et_cds_dt:





















y_pred






2026-04
1538.1621




2026-05
1648.7140




2026-06
1751.9956




2026-07
1913.4137




2026-08
1933.8756




2026-09
1693.3180




2026-10
1605.3448




2026-11
1326.0590




2026-12
1295.6060




2027-01
1199.4461




2027-02
1198.7948




2027-03
1437.5339
























Forecast – omp_cds_dt:





















y_pred






2026-04
1580.8557




2026-05
1673.4297




2026-06
1758.9376




2026-07
1917.8768




2026-08
1928.3096




2026-09
1688.5507




2026-10
1600.3482




2026-11
1324.8890




2026-12
1295.2040




2027-01
1205.1776




2027-02
1202.0565




2027-03
1431.2530
























Forecast – gbr_cds_dt:





















y_pred






2026-04
1596.0229




2026-05
1729.8815




2026-06
1850.1600




2026-07
2057.7315




2026-08
2085.9122




2026-09
1851.0805




2026-10
1768.1470




2026-11
1479.5906




2026-12
1464.3070




2027-01
1373.3573




2027-02
1382.6150




2027-03
1670.9396
























Forecast – blend:





















y_pred






2026-04
1557.8026




2026-05
1664.1409




2026-06
1748.8814




2026-07
1906.3237




2026-08
1925.7698




2026-09
1711.8875




2026-10
1618.0851




2026-11
1377.9164




2026-12
1351.4142




2027-01
1303.8262




2027-02
1301.5762




2027-03
1437.5363


















































4. Forecast Comparison – All Models¶
Forecasts collected from predict_model during the finalize loop — no dependency on pull().


















In [26]:






# Build comparison tables from stored dictionaries
df_forecast_A = pd.DataFrame(forecasts_A)
df_forecast_A.index = df_forecast_A.index.astype(str)
df_forecast_A.columns = [f'{c}_A' for c in df_forecast_A.columns]

df_forecast_B = pd.DataFrame(forecasts_B)
df_forecast_B.index = df_forecast_B.index.astype(str)
df_forecast_B.columns = [f'{c}_B' for c in df_forecast_B.columns]

df_comparison = pd.concat([df_forecast_A, df_forecast_B], axis=1)
df_comparison.index.name = 'Period'

print('12-Month Forecast – Setup A (with COVID) vs Setup B (without COVID):')
print(df_comparison.round(0).astype(int).to_string())

























12-Month Forecast – Setup A (with COVID) vs Setup B (without COVID):
         exp_smooth_A  arima_A  ets_A  lasso_cds_dt_A  lr_cds_dt_A  blend_A  exp_smooth_B  arima_B  et_cds_dt_B  omp_cds_dt_B  gbr_cds_dt_B  blend_B
Period                                                                                                                                              
2026-04          1582     1550   1574            1542         1558     1587          1561     1566         1538          1581          1596     1558
2026-05          1721     1657   1711            1629         1641     1705          1678     1705         1649          1673          1730     1664
2026-06          1833     1736   1823            1705         1709     1784          1773     1768         1752          1759          1850     1749
2026-07          2042     1882   2032            1932         1840     1948          1952     1924         1913          1918          2058     1906
2026-08          2070     1926   2061            2057         1832     1968          1966     1972         1934          1928          2086     1926
2026-09          1794     1755   1785            1793         1625     1718          1721     1709         1693          1689          1851     1712
2026-10          1706     1701   1697            1681         1531     1634          1638     1641         1605          1600          1768     1618
2026-11          1370     1489   1360            1320         1289     1334          1346     1326         1326          1325          1480     1378
2026-12          1340     1467   1327            1285         1243     1306          1316     1323         1296          1295          1464     1351
2027-01          1255     1410   1239            1149         1158     1221          1257     1244         1199          1205          1373     1304
2027-02          1254     1412   1237            1124         1161     1205          1249     1200         1199          1202          1383     1302
2027-03          1465     1546   1444            1269         1290     1399          1403     1450         1438          1431          1671     1438





















In [27]:






# Line chart – all Setup B models including blend and stack
fig, ax = plt.subplots(figsize=(14, 6))

colors_map = {
    'exp_smooth' : '#2ecc71',
    'arima'      : '#3498db',
    'ets'        : '#9b59b6',
    'knn_cds_dt' : '#e67e22',
    'llar_cds_dt': '#1abc9c',
    'lasso_cds_dt':'#e74c3c',
    'blend'      : '#2c3e50',
    'stack'      : '#8e44ad'
}

for model_name, series in forecasts_B.items():
    lw   = 3 if model_name in ['blend', 'stack'] else 1.5
    ls   = '-' if model_name in ['blend', 'stack'] else '--'
    color = colors_map.get(model_name, 'grey')
    ax.plot(series.index.astype(str), series.values,
            marker='o', label=f'{model_name} (no COVID)',
            color=color, lw=lw, ls=ls, ms=5)

# Overlay exp_smooth from Setup A
if 'exp_smooth' in forecasts_A:
    s = forecasts_A['exp_smooth']
    ax.plot(s.index.astype(str), s.values,
            'r--s', label='exp_smooth (with COVID)', lw=2, ms=5)

ax.set_xlabel('Month')
ax.set_ylabel('Passengers (thousands)')
ax.set_title('PyCaret – 12-Month Forecast: All Models + Ensemble')
ax.legend(loc='upper right', fontsize=8, ncol=2)
ax.grid(True, alpha=0.3)
plt.xticks(rotation=30, ha='right')
plt.tight_layout()
plt.show()
























No description has been provided for this image



















In [28]:






# Bar chart – peak month forecast by model
july_str = [i for i in list(forecasts_B.values())[0].index.astype(str) if '-07' in i]

if july_str:
    july_period = july_str[0]
    july_vals   = {m: forecasts_B[m][forecasts_B[m].index.astype(str) == july_period].values[0]
                   for m in forecasts_B}

    fig, ax = plt.subplots(figsize=(12, 5))
    colors  = [colors_map.get(m, 'grey') for m in july_vals]
    bars    = ax.bar(july_vals.keys(), july_vals.values(), color=colors, alpha=0.85)

    for b in bars:
        ax.text(b.get_x()+b.get_width()/2, b.get_height()+5,
                f'{b.get_height():,.0f}k', ha='center', fontsize=9)

    ax.set_ylabel('Passengers (thousands)')
    ax.set_title(f'PyCaret Setup B – Peak Month ({july_period}) Forecast by Model')
    ax.grid(True, alpha=0.3, axis='y')
    plt.xticks(rotation=20, ha='right')
    plt.tight_layout()
    plt.show()
























No description has been provided for this image



















In [29]:






# Blend vs Stack vs best individual – direct comparison
fig, ax = plt.subplots(figsize=(12, 5))

highlight = ['exp_smooth', 'arima', 'blend', 'stack']
styles    = ['g--', 'b--', 'k-', 'm-']
lws       = [1.5, 1.5, 2.5, 2.5]

for model_name, style, lw in zip(highlight, styles, lws):
    if model_name in forecasts_B:
        s = forecasts_B[model_name]
        ax.plot(s.index.astype(str), s.values,
                style, label=model_name, lw=lw, marker='o', ms=5)

ax.set_xlabel('Month')
ax.set_ylabel('Passengers (thousands)')
ax.set_title('PyCaret Setup B – Individual vs Ensemble Forecasts')
ax.legend()
ax.grid(True, alpha=0.3)
plt.xticks(rotation=30, ha='right')
plt.tight_layout()
plt.show()
























No description has been provided for this image



















In [30]:






# exp_smooth: with COVID vs without COVID
if 'exp_smooth' in forecasts_A and 'exp_smooth' in forecasts_B:
    s_A = forecasts_A['exp_smooth']
    s_B = forecasts_B['exp_smooth']

    fig, ax = plt.subplots(figsize=(12, 5))
    ax.plot(s_A.index.astype(str), s_A.values,
            'r--o', label='exp_smooth – With COVID', lw=2, ms=6)
    ax.plot(s_B.index.astype(str), s_B.values,
            'g-o',  label='exp_smooth – No COVID',   lw=2, ms=6)
    ax.set_xlabel('Month')
    ax.set_ylabel('Passengers (thousands)')
    ax.set_title('exp_smooth: Impact of COVID Period on Forecast')
    ax.legend()
    ax.grid(True, alpha=0.3)
    plt.xticks(range(len(s_A)), s_A.index.astype(str), rotation=30, ha='right')
    plt.tight_layout()
    plt.show()
























No description has been provided for this image

























4.4 Forecast vs Actual CSO Data¶


















In [31]:






# Dados reais (Abr 2025 – Mar 2026) + Forecast ETS Setup A (Abr 2026 – Mar 2027)
# ETS foi o melhor modelo no Setup A (com COVID)
data_A = {
    '2025-04': 1519.066, '2025-05': 1657.095, '2025-06': 1720.507,
    '2025-07': 1877.294, '2025-08': 1924.106, '2025-09': 1661.162,
    '2025-10': 1593.932, '2025-11': 1279.279, '2025-12': 1276.540,
    '2026-01': 1197.109, '2026-02': 1152.538, '2026-03': 1402.866,
    '2026-04': 1573.684, '2026-05': 1711.488, '2026-06': 1822.999,
    '2026-07': 2032.111, '2026-08': 2060.745, '2026-09': 1784.922,
    '2026-10': 1696.599, '2026-11': 1360.367, '2026-12': 1326.905,
    '2027-01': 1239.111, '2027-02': 1237.357, '2027-03': 1443.539
}

df_ets_A = pd.DataFrame.from_dict(data_A, orient='index', columns=['Dublin_airport'])
df_ets_A.index.name = 'Date'
df_ets_A['MoM_%'] = df_ets_A['Dublin_airport'].pct_change() * 100
df_ets_A['YoY_%'] = df_ets_A['Dublin_airport'].pct_change(periods=12) * 100
df_ets_A = df_ets_A.round(2)
df_ets_A['Source'] = ['Actual'] * 12 + ['ETS Forecast (Setup A)'] * 12
print('ETS Setup A – Actual + Forecast:')
print(df_ets_A.to_string())

























ETS Setup A – Actual + Forecast:
         Dublin_airport  MoM_%  YoY_%                  Source
Date                                                         
2025-04         1519.07    NaN    NaN                  Actual
2025-05         1657.10   9.09    NaN                  Actual
2025-06         1720.51   3.83    NaN                  Actual
2025-07         1877.29   9.11    NaN                  Actual
2025-08         1924.11   2.49    NaN                  Actual
2025-09         1661.16 -13.67    NaN                  Actual
2025-10         1593.93  -4.05    NaN                  Actual
2025-11         1279.28 -19.74    NaN                  Actual
2025-12         1276.54  -0.21    NaN                  Actual
2026-01         1197.11  -6.22    NaN                  Actual
2026-02         1152.54  -3.72    NaN                  Actual
2026-03         1402.87  21.72    NaN                  Actual
2026-04         1573.68  12.18   3.60  ETS Forecast (Setup A)
2026-05         1711.49   8.76   3.28  ETS Forecast (Setup A)
2026-06         1823.00   6.52   5.96  ETS Forecast (Setup A)
2026-07         2032.11  11.47   8.25  ETS Forecast (Setup A)
2026-08         2060.74   1.41   7.10  ETS Forecast (Setup A)
2026-09         1784.92 -13.38   7.45  ETS Forecast (Setup A)
2026-10         1696.60  -4.95   6.44  ETS Forecast (Setup A)
2026-11         1360.37 -19.82   6.34  ETS Forecast (Setup A)
2026-12         1326.90  -2.46   3.95  ETS Forecast (Setup A)
2027-01         1239.11  -6.62   3.51  ETS Forecast (Setup A)
2027-02         1237.36  -0.14   7.36  ETS Forecast (Setup A)
2027-03         1443.54  16.66   2.90  ETS Forecast (Setup A)





















In [32]:






# Dados reais (Abr 2025 – Mar 2026) + Forecast exp_smooth Setup B (Abr 2026 – Mar 2027)
# Exponential Smoothing foi o melhor modelo no Setup B (sem COVID)
data_B = {
    '2025-04': 1519.066, '2025-05': 1657.095, '2025-06': 1720.507,
    '2025-07': 1877.294, '2025-08': 1924.106, '2025-09': 1661.162,
    '2025-10': 1593.932, '2025-11': 1279.279, '2025-12': 1276.540,
    '2026-01': 1197.109, '2026-02': 1152.538, '2026-03': 1402.866,
    '2026-04': 1560.965, '2026-05': 1677.921, '2026-06': 1772.747,
    '2026-07': 1952.017, '2026-08': 1965.941, '2026-09': 1720.803,
    '2026-10': 1637.869, '2026-11': 1346.122, '2026-12': 1316.081,
    '2027-01': 1256.865, '2027-02': 1248.853, '2027-03': 1402.866
}

df_exp_B = pd.DataFrame.from_dict(data_B, orient='index', columns=['Dublin_airport'])
df_exp_B.index.name = 'Date'
df_exp_B['MoM_%'] = df_exp_B['Dublin_airport'].pct_change() * 100
df_exp_B['YoY_%'] = df_exp_B['Dublin_airport'].pct_change(periods=12) * 100
df_exp_B = df_exp_B.round(2)
df_exp_B['Source'] = ['Actual'] * 12 + ['exp_smooth Forecast (Setup B)'] * 12
print('exp_smooth Setup B – Actual + Forecast:')
print(df_exp_B.to_string())

























exp_smooth Setup B – Actual + Forecast:
         Dublin_airport  MoM_%  YoY_%                         Source
Date                                                                
2025-04         1519.07    NaN    NaN                         Actual
2025-05         1657.10   9.09    NaN                         Actual
2025-06         1720.51   3.83    NaN                         Actual
2025-07         1877.29   9.11    NaN                         Actual
2025-08         1924.11   2.49    NaN                         Actual
2025-09         1661.16 -13.67    NaN                         Actual
2025-10         1593.93  -4.05    NaN                         Actual
2025-11         1279.28 -19.74    NaN                         Actual
2025-12         1276.54  -0.21    NaN                         Actual
2026-01         1197.11  -6.22    NaN                         Actual
2026-02         1152.54  -3.72    NaN                         Actual
2026-03         1402.87  21.72    NaN                         Actual
2026-04         1560.96  11.27   2.76  exp_smooth Forecast (Setup B)
2026-05         1677.92   7.49   1.26  exp_smooth Forecast (Setup B)
2026-06         1772.75   5.65   3.04  exp_smooth Forecast (Setup B)
2026-07         1952.02  10.11   3.98  exp_smooth Forecast (Setup B)
2026-08         1965.94   0.71   2.17  exp_smooth Forecast (Setup B)
2026-09         1720.80 -12.47   3.59  exp_smooth Forecast (Setup B)
2026-10         1637.87  -4.82   2.76  exp_smooth Forecast (Setup B)
2026-11         1346.12 -17.81   5.23  exp_smooth Forecast (Setup B)
2026-12         1316.08  -2.23   3.10  exp_smooth Forecast (Setup B)
2027-01         1256.86  -4.50   4.99  exp_smooth Forecast (Setup B)
2027-02         1248.85  -0.64   8.36  exp_smooth Forecast (Setup B)
2027-03         1402.87  12.33   0.00  exp_smooth Forecast (Setup B)



























5. References¶
Ali, M. (2020) PyCaret: An open source, low-code machine learning library in Python. Available at: https://pycaret.org (Accessed: March 2026).


Central Statistics Office (2025) Air and Sea Travel Statistics – ASM01. Available at: https://data.cso.ie/table/ASM01 (Accessed: January 2026).


Moez Ali (2020) PyCaret: An open source, low-code machine learning library in Python. Available at: https://pycaret.org (Accessed: March 2026).


PJalgotrader (2024) PyCaret Time Series Notebook – Deep Forecasting USU. Available at: https://github.com/PJalgotrader/Deep_forecasting-USU/blob/main/Platforms%20and%20tools/PyCaret/PyCaret-timeseries.ipynb (Accessed: March 2026).


PyCaret Documentation (2024) Other Setup Parameters – Preprocessing. Available at: https://pycaret.gitbook.io/docs/get-started/preprocessing/other-setup-parameters (Accessed: March 2026).


PyCaret Documentation (2024) Datasets API Reference. Available at: https://pycaret.readthedocs.io/en/latest/api/datasets.html#pycaret.datasets.get_data (Accessed: March 2026).


PyCaret Documentation (2024) Time Series Forecasting API. Available at: https://pycaret.readthedocs.io/en/stable/api/time_series.html (Accessed: March 2026).


Sktime developers (2024) sktime: A unified framework for machine learning with time series. Available at: https://www.sktime.net (Accessed: March 2026).


Hyndman, R.J. and Athanasopoulos, G. (2021) Forecasting: Principles and Practice, 3rd ed. OTexts. Available at: https://otexts.com/fpp3/ (Accessed: March 2026).


YouTube (2024) PyCaret Time Series Forecasting Tutorial. Available at: https://www.youtube.com/watch?v=V7K-pFxHop4 (Accessed: March 2026).


YouTube (2024) Time Series Forecasting with PyCaret. Available at: https://www.youtube.com/watch?v=uypdqSPdN60 (Accessed: March 2026).