Now let's go on to our modeling step. As a reminder, our plan of action was as follows:

Perform EDA on the dataset to extract valuable insight about the process generating the time series (COMPLETED).
Build a baseline model (univariable model without exogenous variables) for benchmarking purposes. (Covered in this notebook)
Build a univariate model with all exogenous variables to check best possible performance. (Covered in this notebook)
Evaluate the model with exogenous variables and discuss any potential issues. (Covered in this notebook)
Overcome issues identified above. (Covered in this notebook)
Make future predictions with the best model.
Replicate flow with Automated Time Series Modeling (AutoML)

In [1]:

# Only enable critical logging (Optional)
import os
os.environ["PYCARET_CUSTOM_LOGGING_LEVEL"] = "CRITICAL"

In [2]:

def what_is_installed():
    from pycaret import show_versions
    show_versions()

try:
    what_is_installed()
except ModuleNotFoundError:
    !pip install pycaret
    what_is_installed()

System:
    python: 3.9.16 (main, Jan 11 2023, 16:16:36) [MSC v.1916 64 bit (AMD64)]
executable: C:\Users\Nikhil\.conda\envs\pycaret_dev_sktime_16p1\python.exe
   machine: Windows-10-10.0.19044-SP0

PyCaret required dependencies:
                 pip: 22.3.1
          setuptools: 65.6.3
             pycaret: 3.0.0rc9
             IPython: 8.10.0
          ipywidgets: 8.0.4
                tqdm: 4.64.1
               numpy: 1.23.5
              pandas: 1.5.3
              jinja2: 3.1.2
               scipy: 1.10.0
              joblib: 1.2.0
             sklearn: 1.2.1
                pyod: 1.0.8
            imblearn: 0.10.1
   category_encoders: 2.6.0
            lightgbm: 3.3.5
               numba: 0.56.4
            requests: 2.28.2
          matplotlib: 3.7.0
          scikitplot: 0.3.7
         yellowbrick: 1.5
              plotly: 5.13.0
             kaleido: 0.2.1
         statsmodels: 0.13.5
              sktime: 0.16.1
               tbats: 1.1.2
            pmdarima: 2.0.2
              psutil: 5.9.4

PyCaret optional dependencies:
                shap: 0.41.0
           interpret: Not installed
                umap: Not installed
    pandas_profiling: Not installed
  explainerdashboard: Not installed
             autoviz: Not installed
           fairlearn: Not installed
             xgboost: Not installed
            catboost: Not installed
              kmodes: Not installed
             mlxtend: Not installed
       statsforecast: Not installed
        tune_sklearn: Not installed
                 ray: Not installed
            hyperopt: Not installed
              optuna: Not installed
               skopt: Not installed
              mlflow: 2.1.1
              gradio: Not installed
             fastapi: Not installed
             uvicorn: Not installed
              m2cgen: Not installed
           evidently: Not installed
               fugue: 0.8.0
           streamlit: Not installed
             prophet: 1.1.2

In [3]:

import numpy as np
import pandas as pd
from pycaret.datasets import get_data
from pycaret.time_series import TSForecastingExperiment

In [4]:

# Global Figure Settings for notebook ----
# Depending on whether you are using jupyter notebook, jupyter lab, Google Colab, you may have to set the renderer appropriately
# NOTE: Setting to a static renderer here so that the notebook saved size is reduced.
global_fig_settings = {
    # "renderer": "notebook",
    "renderer": "png",
    "width": 1000,
    "height": 600,
}

In [5]:

data = get_data("airquality")

# Limiting the data for demonstration purposes.
data = data.iloc[-720:]
data["index"] = pd.to_datetime(data["Date"] + " " + data["Time"])
data.drop(columns=["Date", "Time"], inplace=True)
data.replace(-200, np.nan, inplace=True)
target = "CO(GT)"

exclude = ['NMHC(GT)', 'AH']
data.drop(columns=exclude, inplace=True)
data.head()

	Date	Time	CO(GT)	PT08.S1(CO)	NMHC(GT)	C6H6(GT)	PT08.S2(NMHC)	NOx(GT)	PT08.S3(NOx)	NO2(GT)	PT08.S4(NO2)	PT08.S5(O3)	T	RH	AH
0	2004-03-10	18:00:00	2.6	1360	150	11.9	1046	166	1056	113	1692	1268	13.6	48.9	0.7578
1	2004-03-10	19:00:00	2.0	1292	112	9.4	955	103	1174	92	1559	972	13.3	47.7	0.7255
2	2004-03-10	20:00:00	2.2	1402	88	9.0	939	131	1140	114	1555	1074	11.9	54.0	0.7502
3	2004-03-10	21:00:00	2.2	1376	80	9.2	948	172	1092	122	1584	1203	11.0	60.0	0.7867
4	2004-03-10	22:00:00	1.6	1272	51	6.5	836	131	1205	116	1490	1110	11.2	59.6	0.7888

Out[5]:

	CO(GT)	PT08.S1(CO)	C6H6(GT)	PT08.S2(NMHC)	NOx(GT)	PT08.S3(NOx)	NO2(GT)	PT08.S4(NO2)	PT08.S5(O3)	T	RH	index
8637	1.5	983.0	5.9	806.0	180.0	820.0	132.0	966.0	615.0	13.5	28.3	2005-03-05 15:00:00
8638	1.8	1018.0	7.3	868.0	255.0	751.0	162.0	1015.0	804.0	13.0	29.7	2005-03-05 16:00:00
8639	2.0	1101.0	8.4	916.0	251.0	721.0	159.0	1125.0	861.0	11.6	38.7	2005-03-05 17:00:00
8640	1.9	1116.0	7.7	888.0	258.0	695.0	156.0	1176.0	980.0	8.6	56.3	2005-03-05 18:00:00
8641	2.5	1161.0	9.1	945.0	344.0	654.0	177.0	1205.0	1077.0	8.5	57.9	2005-03-05 19:00:00

Step 2: Baseline Model - Univariate forecasting without exogenous variables¶

In [6]:

data_uni = data.copy()
data_uni.set_index("index", inplace=True)
data_uni = data_uni[target]

exp_uni = TSForecastingExperiment()
exp_uni.setup(
    data=data_uni, fh=48,
    numeric_imputation_target="ffill", numeric_imputation_exogenous="ffill",
    fig_kwargs=global_fig_settings, session_id=42
)

	Description	Value
0	session_id	42
1	Target	CO(GT)
2	Approach	Univariate
3	Exogenous Variables	Not Present
4	Original data shape	(720, 1)
5	Transformed data shape	(720, 1)
6	Transformed train set shape	(672, 1)
7	Transformed test set shape	(48, 1)
8	Rows with missing values	2.8%
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)	None
14	Ignore Seasonality Test	False
15	Seasonality Detection Algo	auto
16	Max Period to Consider	60
17	Seasonal Period(s) Tested	[24, 23, 25, 2, 48, 22, 47, 49, 26, 3, 12, 11, 21, 13, 46, 10, 50]
18	Significant Seasonal Period(s)	[24, 23, 25, 2, 48, 22, 47, 49, 26, 3, 12, 11, 21, 13, 46, 10, 50]
19	Significant Seasonal Period(s) without Harmonics	[48, 46, 50, 22, 47, 49, 26, 21]
20	Remove Harmonics	False
21	Harmonics Order Method	harmonic_max
22	Num Seasonalities to Use	1
23	All Seasonalities to Use	[24]
24	Primary Seasonality	24
25	Seasonality Present	True
26	Target Strictly Positive	True
27	Target White Noise	No
28	Recommended d	0
29	Recommended Seasonal D	0
30	Preprocess	True
31	Numerical Imputation (Target)	ffill
32	Transformation (Target)	None
33	Scaling (Target)	None
34	Feature Engineering (Target) - Reduced Regression	False
35	CPU Jobs	-1
36	Use GPU	False
37	Log Experiment	False
38	Experiment Name	ts-default-name
39	USI	6733

Out[6]:

<pycaret.time_series.forecasting.oop.TSForecastingExperiment at 0x24f8f19c700>

In [7]:

model = exp_uni.create_model("arima", order=(0,1,0), seasonal_order=(0,1,0,24))

	cutoff	MASE	RMSSE	MAE	RMSE	MAPE	SMAPE	R2
0	2005-03-27 14:00	1.5606	1.4904	1.1466	1.6039	0.6598	1.0119	-1.7616
1	2005-03-29 14:00	2.5919	1.9767	1.8655	2.1105	1.4991	0.7419	-2.7317
2	2005-03-31 14:00	1.4605	1.1539	1.0401	1.2124	1.2860	1.2780	-6.2314
Mean	NaT	1.8710	1.5403	1.3507	1.6422	1.1483	1.0106	-3.5749
SD	NaT	0.5114	0.3378	0.3666	0.3676	0.3562	0.2189	1.9197

In [8]:

exp_uni.plot_model(model)

On zooming in to the forecasts, we can see that the model is able to capture some of the trends (spikes) in the dataset, but not all. The performance of our baseline model indicates that mean MASE across the CV folds is 1.52 which is not that great. Any value > 1 indicates that the model is performing worse than even a naive model with one step ahead forecasts. This model needs more improvement. Let's see if adding exogenous variables can help improve the model performance.

Step 3: Improved Model - Univariate forecasting with exogenous variables¶

In [9]:

exp_exo = TSForecastingExperiment()
exp_exo.setup(
    data=data, target=target, index="index", fh=48,
    numeric_imputation_target="ffill", numeric_imputation_exogenous="ffill",
    fig_kwargs=global_fig_settings, session_id=42
)

	Description	Value
0	session_id	42
1	Target	CO(GT)
2	Approach	Univariate
3	Exogenous Variables	Present
4	Original data shape	(720, 11)
5	Transformed data shape	(720, 11)
6	Transformed train set shape	(672, 11)
7	Transformed test set shape	(48, 11)
8	Rows with missing values	3.8%
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)	None
14	Ignore Seasonality Test	False
15	Seasonality Detection Algo	auto
16	Max Period to Consider	60
17	Seasonal Period(s) Tested	[24, 23, 25, 2, 48, 22, 47, 49, 26, 3, 12, 11, 21, 13, 46, 10, 50]
18	Significant Seasonal Period(s)	[24, 23, 25, 2, 48, 22, 47, 49, 26, 3, 12, 11, 21, 13, 46, 10, 50]
19	Significant Seasonal Period(s) without Harmonics	[48, 46, 50, 22, 47, 49, 26, 21]
20	Remove Harmonics	False
21	Harmonics Order Method	harmonic_max
22	Num Seasonalities to Use	1
23	All Seasonalities to Use	[24]
24	Primary Seasonality	24
25	Seasonality Present	True
26	Target Strictly Positive	True
27	Target White Noise	No
28	Recommended d	0
29	Recommended Seasonal D	0
30	Preprocess	True
31	Numerical Imputation (Target)	ffill
32	Transformation (Target)	None
33	Scaling (Target)	None
34	Feature Engineering (Target) - Reduced Regression	False
35	Numerical Imputation (Exogenous)	ffill
36	Transformation (Exogenous)	None
37	Scaling (Exogenous)	None
38	CPU Jobs	-1
39	Use GPU	False
40	Log Experiment	False
41	Experiment Name	ts-default-name
42	USI	66fd

Out[9]:

<pycaret.time_series.forecasting.oop.TSForecastingExperiment at 0x24f994e6250>

In [10]:

model_exo = exp_exo.create_model("arima", order=(0,1,0), seasonal_order=(0,1,0,24))

	cutoff	MASE	RMSSE	MAE	RMSE	MAPE	SMAPE	R2
0	2005-03-27 14:00	0.2512	0.2282	0.1846	0.2455	0.1089	0.1192	0.9353
1	2005-03-29 14:00	0.2321	0.2227	0.1670	0.2378	0.1100	0.1219	0.9526
2	2005-03-31 14:00	0.2525	0.2733	0.1798	0.2872	0.1723	0.1572	0.5943
Mean	NaT	0.2453	0.2414	0.1771	0.2568	0.1304	0.1328	0.8274
SD	NaT	0.0093	0.0227	0.0074	0.0217	0.0296	0.0173	0.1650

In [11]:

exp_exo.plot_model(model_exo)

Step 4: Evaluate Model¶

Not bad, We have managed to improve MASE significantly which is much better than the univariate model and also a large improvement over a naive model. We should be happy with this improvement. Let's finalize the model by training it on the entire dataset so we can make true future forecasts.

In [12]:

final_model_exo = exp_exo.finalize_model(model_exo)

In [13]:

def safe_predict(exp, model):
    """Prediction wrapper for demo purposes."""
    try: 
        exp.predict_model(model)
    except ValueError as exception:
        print(exception)
        exo_vars = exp.exogenous_variables
        print(f"{len(exo_vars)} exogenous variables (X) needed in order to make future predictions:\n{exo_vars}")

safe_predict(exp_exo, final_model_exo)

Model was trained with exogenous variables but you have not passed any for predictions. Please pass exogenous variables to make predictions.
10 exogenous variables (X) needed in order to make future predictions:
['PT08.S1(CO)', 'C6H6(GT)', 'PT08.S2(NMHC)', 'NOx(GT)', 'PT08.S3(NOx)', 'NO2(GT)', 'PT08.S4(NO2)', 'PT08.S5(O3)', 'T', 'RH']

As we can see, this approach does not come without side effects. The problem is that we have 10 exogenous variables. Hence in order to get any unknown future values for CO concentration, we will need the future values for all these exogenous variables. This is generally obtained through some forecasting process itself. But each forecast will have errors and these errors can be compounded when there are a lot of exogenous variables.

Let's see if we can trim down these exogenous variables to a handful of useful variables without compromising on forecasting performance.

Step 5: Parsimonious Model - Univariate forecasting with limited exogenous variables¶

From the CCF Analysis, we found that many of the exogenous variables show a very similar correlation structure to the CO concentration. E.g. PT08.S1(CO), NOx(GT), C6H6(GT), PT08.S2(NMHC) values from 24 hours before (lag = 24) show a high positive correlation to CO concentration. Instead of keeping all of them, lets pick the one with the highest positive correlation at lag 24 which is NOx(GT).

Similarly, PT08.S3(NOx) values from 24 hours ago shows the highest negative correlation to CO concentration. Let's keep this variable as well.

Finally, in daily cycles, what happens 12 hours back can also impact the current value (e.g. values last night can impact the next day and vice versa). The variable with the highest correlation to CO concentration at lag = 12 is RH. We will keep this as well.

In [14]:

exp_slim = TSForecastingExperiment()
keep = [target, "index", 'NOx(GT)', "PT08.S3(NOx)", "RH"]
data_slim = data[keep]
exp_slim.setup(
    data=data_slim, target=target, index="index", fh=48,
    numeric_imputation_target="ffill", numeric_imputation_exogenous="ffill",
    fig_kwargs=global_fig_settings, session_id=42 
)

	Description	Value
0	session_id	42
1	Target	CO(GT)
2	Approach	Univariate
3	Exogenous Variables	Present
4	Original data shape	(720, 4)
5	Transformed data shape	(720, 4)
6	Transformed train set shape	(672, 4)
7	Transformed test set shape	(48, 4)
8	Rows with missing values	3.8%
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)	None
14	Ignore Seasonality Test	False
15	Seasonality Detection Algo	auto
16	Max Period to Consider	60
17	Seasonal Period(s) Tested	[24, 23, 25, 2, 48, 22, 47, 49, 26, 3, 12, 11, 21, 13, 46, 10, 50]
18	Significant Seasonal Period(s)	[24, 23, 25, 2, 48, 22, 47, 49, 26, 3, 12, 11, 21, 13, 46, 10, 50]
19	Significant Seasonal Period(s) without Harmonics	[48, 46, 50, 22, 47, 49, 26, 21]
20	Remove Harmonics	False
21	Harmonics Order Method	harmonic_max
22	Num Seasonalities to Use	1
23	All Seasonalities to Use	[24]
24	Primary Seasonality	24
25	Seasonality Present	True
26	Target Strictly Positive	True
27	Target White Noise	No
28	Recommended d	0
29	Recommended Seasonal D	0
30	Preprocess	True
31	Numerical Imputation (Target)	ffill
32	Transformation (Target)	None
33	Scaling (Target)	None
34	Feature Engineering (Target) - Reduced Regression	False
35	Numerical Imputation (Exogenous)	ffill
36	Transformation (Exogenous)	None
37	Scaling (Exogenous)	None
38	CPU Jobs	-1
39	Use GPU	False
40	Log Experiment	False
41	Experiment Name	ts-default-name
42	USI	55b0

Out[14]:

<pycaret.time_series.forecasting.oop.TSForecastingExperiment at 0x24f8ff93ee0>

In [15]:

model_slim = exp_slim.create_model("arima", order=(0,1,0), seasonal_order=(0,1,0,24))

	cutoff	MASE	RMSSE	MAE	RMSE	MAPE	SMAPE	R2
0	2005-03-27 14:00	0.5014	0.4028	0.3684	0.4334	0.2663	0.2255	0.7983
1	2005-03-29 14:00	0.2657	0.2369	0.1912	0.2529	0.1004	0.0993	0.9464
2	2005-03-31 14:00	0.3023	0.2847	0.2153	0.2992	0.2132	0.1967	0.5596
Mean	NaT	0.3565	0.3081	0.2583	0.3285	0.1933	0.1738	0.7681
SD	NaT	0.1035	0.0697	0.0784	0.0766	0.0692	0.0540	0.1593

In [16]:

exp_slim.plot_model(model_slim)

Not bad. MASE has only increased slightly, but we have managed to cut our exogenous variables significantly. This will help us when we make "true" unknown future predictions since we will need the "unknown" future values of these exogenous variables to make the forecast for the CO concentration.

Finalize the model¶

Train the slim model on the entire dataset so we can make true future forecasts
Save the model as a pickle file for deployment

In [17]:

final_slim_model = exp_slim.finalize_model(model_slim)

In [18]:

_ = exp_slim.save_model(final_slim_model, "final_slim_model")

Transformation Pipeline and Model Successfully Saved

In [19]:

safe_predict(exp_slim, final_slim_model)

Model was trained with exogenous variables but you have not passed any for predictions. Please pass exogenous variables to make predictions.
3 exogenous variables (X) needed in order to make future predictions:
['NOx(GT)', 'PT08.S3(NOx)', 'RH']

So we still need future values for 3 exogenous variables. We will get this in the next part using forecasting techniques.

The next steps would typically be done in a new session/notebook¶

Now that we have build our model, let's make future predictions. As a reminder, our plan of action was as follows:

Perform EDA on the dataset to extract valuable insight about the process generating the time series (COMPLETED).
Build a baseline model (univariable model without exogenous variables) for benchmarking purposes (COMPLETED).
Build a univariate model with all exogenous variables to check best possible performance (COMPLETED).
Evaluate the model with exogenous variables and discuss any potential issues (COMPLETED).
Overcome issues identified above (COMPLETED).
Make future predictions with the best model. (Covered in this notebook)
Replicate flow with Automated Time Series Modeling (AutoML)

In [20]:

exog_vars = ['NOx(GT)', 'PT08.S3(NOx)', 'RH']
data = data[exog_vars]
data.head()

Out[20]:

	NOx(GT)	PT08.S3(NOx)	RH
8637	180.0	820.0	28.3
8638	255.0	751.0	29.7
8639	251.0	721.0	38.7
8640	258.0	695.0	56.3
8641	344.0	654.0	57.9

Step 6: Making Future Predictions¶

Step 6A: Get future exogenous variable values using forecasting¶

In [21]:

exog_exps = []
exog_models = []
for exog_var in exog_vars:
    exog_exp = TSForecastingExperiment()
    exog_exp.setup(
        data=data[exog_var], fh=48,
        numeric_imputation_target="ffill", numeric_imputation_exogenous="ffill",
        fig_kwargs=global_fig_settings, session_id=42
    )

    # Users can customize how to model future exogenous variables i.e. add
    # more steps and models to potentially get better models at the expense
    # of higher modeling time.
    best = exog_exp.compare_models(
        sort="mase", include=["arima", "ets", "exp_smooth", "theta", "lightgbm_cds_dt",]        
    )
    final_exog_model = exog_exp.finalize_model(best)

    exog_exps.append(exog_exp)
    exog_models.append(final_exog_model)

# Step 2: Get future predictions for exog variables ----
future_exog = [
    exog_exp.predict_model(exog_model)
    for exog_exp, exog_model in zip(exog_exps, exog_models)
]
future_exog = pd.concat(future_exog, axis=1)
future_exog.columns = exog_vars

	Description	Value
0	session_id	42
1	Target	NOx(GT)
2	Approach	Univariate
3	Exogenous Variables	Not Present
4	Original data shape	(720, 1)
5	Transformed data shape	(720, 1)
6	Transformed train set shape	(672, 1)
7	Transformed test set shape	(48, 1)
8	Rows with missing values	0.8%
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)	None
14	Ignore Seasonality Test	False
15	Seasonality Detection Algo	auto
16	Max Period to Consider	60
17	Seasonal Period(s) Tested	[24, 48, 23, 25, 47, 49, 13, 12, 36, 11, 35, 60]
18	Significant Seasonal Period(s)	[24, 48, 23, 25, 47, 49, 13, 12, 36, 11, 35, 60]
19	Significant Seasonal Period(s) without Harmonics	[48, 23, 25, 47, 49, 13, 60, 36, 11, 35]
20	Remove Harmonics	False
21	Harmonics Order Method	harmonic_max
22	Num Seasonalities to Use	1
23	All Seasonalities to Use	[24]
24	Primary Seasonality	24
25	Seasonality Present	True
26	Target Strictly Positive	True
27	Target White Noise	No
28	Recommended d	1
29	Recommended Seasonal D	0
30	Preprocess	True
31	Numerical Imputation (Target)	ffill
32	Transformation (Target)	None
33	Scaling (Target)	None
34	Feature Engineering (Target) - Reduced Regression	False
35	CPU Jobs	-1
36	Use GPU	False
37	Log Experiment	False
38	Experiment Name	ts-default-name
39	USI	9afd

	Model	MASE	RMSSE	MAE	RMSE	MAPE	SMAPE	R2	TT (Sec)
arima	ARIMA	0.8406	0.9158	87.3689	133.0642	0.4273	0.3443	-1.3072	0.3200
exp_smooth	Exponential Smoothing	0.8954	0.8400	93.0132	121.9760	0.4828	0.5917	-0.9311	0.1567
theta	Theta Forecaster	1.0279	0.9437	107.4620	137.6886	0.5192	0.4990	-0.4072	0.0500
lightgbm_cds_dt	Light Gradient Boosting w/ Cond. Deseasonalize & Detrending	1.2021	1.1033	124.6215	160.1069	0.6995	0.5078	-2.5717	1.3467
ets	ETS	1.6466	1.5514	171.0757	225.4193	0.9284	0.5548	-4.3206	1.5733

	Description	Value
0	session_id	42
1	Target	PT08.S3(NOx)
2	Approach	Univariate
3	Exogenous Variables	Not Present
4	Original data shape	(720, 1)
5	Transformed data shape	(720, 1)
6	Transformed train set shape	(672, 1)
7	Transformed test set shape	(48, 1)
8	Rows with missing values	0.1%
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)	None
14	Ignore Seasonality Test	False
15	Seasonality Detection Algo	auto
16	Max Period to Consider	60
17	Seasonal Period(s) Tested	[24, 48, 25, 23, 47, 49, 12, 36, 11]
18	Significant Seasonal Period(s)	[24, 48, 25, 23, 47, 49, 12, 36, 11]
19	Significant Seasonal Period(s) without Harmonics	[48, 25, 23, 47, 49, 36, 11]
20	Remove Harmonics	False
21	Harmonics Order Method	harmonic_max
22	Num Seasonalities to Use	1
23	All Seasonalities to Use	[24]
24	Primary Seasonality	24
25	Seasonality Present	True
26	Target Strictly Positive	True
27	Target White Noise	No
28	Recommended d	1
29	Recommended Seasonal D	0
30	Preprocess	True
31	Numerical Imputation (Target)	ffill
32	Transformation (Target)	None
33	Scaling (Target)	None
34	Feature Engineering (Target) - Reduced Regression	False
35	CPU Jobs	-1
36	Use GPU	False
37	Log Experiment	False
38	Experiment Name	ts-default-name
39	USI	259b

	Model	MASE	RMSSE	MAE	RMSE	MAPE	SMAPE	R2	TT (Sec)
exp_smooth	Exponential Smoothing	1.2435	1.2056	126.5383	158.9241	0.1738	0.1695	-0.0211	0.1567
ets	ETS	1.3630	1.3140	138.7259	173.2545	0.1906	0.1879	-0.2091	0.6700
theta	Theta Forecaster	1.3716	1.3079	139.5929	172.4272	0.1909	0.1878	-0.1963	0.0433
arima	ARIMA	1.3929	1.3245	141.6775	174.6211	0.1792	0.1953	-0.3985	0.3967
lightgbm_cds_dt	Light Gradient Boosting w/ Cond. Deseasonalize & Detrending	1.6778	1.5491	170.7442	204.2588	0.2197	0.2541	-0.7666	1.2900

	Description	Value
0	session_id	42
1	Target	RH
2	Approach	Univariate
3	Exogenous Variables	Not Present
4	Original data shape	(720, 1)
5	Transformed data shape	(720, 1)
6	Transformed train set shape	(672, 1)
7	Transformed test set shape	(48, 1)
8	Rows with missing values	0.1%
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)	None
14	Ignore Seasonality Test	False
15	Seasonality Detection Algo	auto
16	Max Period to Consider	60
17	Seasonal Period(s) Tested	[2, 3, 24, 23, 25, 22, 4, 26, 21, 48, 47, 49, 46, 5, 27, 50, 20, 45, 51, 28, 19, 6, 44, 52]
18	Significant Seasonal Period(s)	[2, 3, 24, 23, 25, 22, 4, 26, 21, 48, 47, 49, 46, 5, 27, 50, 20, 45, 51, 28, 19, 6, 44, 52]
19	Significant Seasonal Period(s) without Harmonics	[52, 51, 48, 46, 50, 44, 21, 47, 49, 27, 20, 45, 28, 19]
20	Remove Harmonics	False
21	Harmonics Order Method	harmonic_max
22	Num Seasonalities to Use	1
23	All Seasonalities to Use	[2]
24	Primary Seasonality	2
25	Seasonality Present	True
26	Target Strictly Positive	True
27	Target White Noise	No
28	Recommended d	0
29	Recommended Seasonal D	0
30	Preprocess	True
31	Numerical Imputation (Target)	ffill
32	Transformation (Target)	None
33	Scaling (Target)	None
34	Feature Engineering (Target) - Reduced Regression	False
35	CPU Jobs	-1
36	Use GPU	False
37	Log Experiment	False
38	Experiment Name	ts-default-name
39	USI	eb49

	Model	MASE	RMSSE	MAE	RMSE	MAPE	SMAPE	R2	TT (Sec)
theta	Theta Forecaster	1.6218	1.4765	11.3749	13.1578	0.2481	0.2286	-0.0585	0.0433
arima	ARIMA	1.8001	1.6165	12.6310	14.4108	0.2548	0.2523	-0.2695	0.0833
lightgbm_cds_dt	Light Gradient Boosting w/ Cond. Deseasonalize & Detrending	2.7797	2.6115	19.4667	23.2519	0.5241	0.3609	-4.8711	0.7800
exp_smooth	Exponential Smoothing	5.2972	4.7592	37.2423	42.4918	0.7188	0.9298	-10.5261	0.1333
ets	ETS	5.3235	4.7812	37.4259	42.6872	0.7228	0.9349	-10.5911	0.1200

In [22]:

future_exog

Out[22]:

	NOx(GT)	PT08.S3(NOx)	RH
9357	247.2036	651.1830	13.0838
9358	274.0699	644.2770	13.1056
9359	298.6685	613.3309	13.0876
9360	231.8742	558.1970	13.1094
9361	398.1459	499.6994	13.0913
9362	378.3662	524.6385	13.1131
9363	252.7246	596.2236	13.0950
9364	246.6336	684.6523	13.1169
9365	180.6670	721.4174	13.0988
9366	125.5157	756.1241	13.1206
9367	76.9556	832.2936	13.1025
9368	74.8243	889.7899	13.1244
9369	67.0040	960.8931	13.1063
9370	56.4091	1017.3089	13.1281
9371	80.9777	1023.5586	13.1100
9372	185.6649	969.1069	13.1318
9373	597.4380	824.1328	13.1138
9374	589.2735	721.3926	13.1356
9375	526.1542	666.4044	13.1175
9376	475.0677	706.3715	13.1393
9377	356.0050	747.2181	13.1212
9378	295.9595	774.7065	13.1431
9379	237.9265	799.2786	13.1250
9380	267.9026	800.7291	13.1468
9381	250.0888	793.4989	13.1287
9382	276.9426	783.8131	13.1506
9383	301.5320	744.9767	13.1325
9384	234.7311	676.9468	13.1543
9385	400.9980	605.0705	13.1362
9386	381.2148	634.3049	13.1581
9387	255.5708	719.7775	13.1399
9388	249.4779	825.3166	13.1618
9389	183.5099	868.3771	13.1437
9390	128.3577	908.8575	13.1656
9391	79.7969	999.0097	13.1474
9392	77.6651	1066.5478	13.1693
9393	69.8444	1150.2087	13.1512
9394	59.2492	1216.1076	13.1731
9395	83.8177	1221.9631	13.1549
9396	188.5047	1155.4515	13.1768
9397	600.2777	981.3416	13.1586
9398	592.1131	857.9179	13.1806
9399	528.9938	791.5363	13.1624
9400	477.9073	837.9784	13.1843
9401	358.8445	885.3629	13.1661
9402	298.7990	916.8384	13.1880
9403	240.7660	944.8063	13.1699
9404	270.7421	945.4231	13.1918

Step 6B: Load Model and make future predcitons for the target variable¶

In [23]:

exp_future = TSForecastingExperiment()

In [24]:

final_slim_model = exp_future.load_model("final_slim_model")

Transformation Pipeline and Model Successfully Loaded

In [25]:

future_preds = exp_future.predict_model(