Petro4Cast · Baseline Forecasting

Winning benchmark per fuel

Blue is actual demand, green is the forward forecast with its 95% interval. Each horizon is tuned and judged separately. MASE below 1 beats a seasonal-naive forecast.

12 weeks24 weeks

Gasoline SARIMAX0.818 MASE

Next 12 weeks: average 8,696 kb/d↓ 0.1% vs last actual

Gasoline SARIMAX0.717 MASE

Next 24 weeks: average 8,607 kb/d↓ 5.3% vs last actual

All runs for gasoline →

12 weeks24 weeks

Distillate (diesel) SARIMAX0.840 MASE

Next 12 weeks: average 3,827 kb/d↓ 2.3% vs last actual

Distillate (diesel) SARIMAX0.819 MASE

Next 24 weeks: average 3,853 kb/d↑ 3.2% vs last actual

All runs for distillate (diesel) →

12 weeks24 weeks

Jet fuel SARIMAX0.773 MASE

Next 12 weeks: average 1,735 kb/d↑ 8.0% vs last actual

Jet fuel ETS0.764 MASE

Next 24 weeks: average 1,725 kb/d↑ 5.6% vs last actual

All runs for jet fuel →

All runs per fuel

Ten runs per fuel: five training windows, two horizons, SARIMAX against ETS on every one. The winner per horizon is the benchmark the causal model is scored against.

GasolineDistillate (diesel)Jet fuel

12-week horizon24-week horizon

SARIMAX, trained from 2010, 12-week horizon: test MASE 0.818. Beats seasonal-naive by 18%. This is the bar the causal model has to clear.
p=3 d=1 q=1 K=6 trend=n log=False

All runs, 12 weeks

Window	Horizon	Model	MASE	MAPE
2000	12w	SARIMAX	0.836	3.27%
2000	12w	ETS	0.889	3.49%
2005	12w	SARIMAX	0.848	3.31%
2005	12w	ETS	0.919	3.61%
2010	12w	SARIMAX	0.818	3.20%	winner
2010	12w	ETS	0.949	3.72%
2015	12w	SARIMAX	0.839	3.29%
2015	12w	ETS	1.001	3.92%
2020	12w	SARIMAX	1.154	4.51%
2020	12w	ETS	1.067	4.21%

Best run: 2010, 12 weeks

ForecastDecomposition

Drag to zoom, double-click to reset, click legend entries to hide series.

Bars split each week's forecast change against the last actual week into a seasonal part and an underlying level/trend part; the line is the net change.

What each model component contributes

Component	Fitted values	What it explains
AR - autoregressive	`p=3 (coef +0.41, +0.14, +0.07)`	Momentum: this week's forecast leans on the previous 3 weeks of demand with these weights.
I - integrated / trend	`d=1`	The model forecasts week-over-week changes, so the latest level is the baseline.
MA - moving average	`q=1 (coef -0.94)`	Shock smoothing: forecast errors from the last 1 week adjust this week's forecast, so one-off surprises fade instead of propagating.
S - seasonality (via X)	`K=6 Fourier pairs, 947 kbd peak-to-trough`	Repeating yearly cycle - the calendar's contribution to demand (summer driving, winter heating, holiday travel).
X - exogenous drivers	`seasonal curves only`	In this benchmark the only external inputs are the seasonal curves above. Price, activity and weather drivers enter in the causal model.

Other runs

2000 · SARIMAX · MASE 0.836

p=0 d=1 q=2 K=6 trend=n log=False

2000 · ETS · MASE 0.889

err=add trend=add damped=True seas=mul log=False

2005 · SARIMAX · MASE 0.848

p=1 d=1 q=1 K=6 trend=n log=False

2005 · ETS · MASE 0.919

err=add trend=add damped=False seas=mul log=False

2010 · ETS · MASE 0.949

err=add trend=add damped=False seas=mul log=False

2015 · SARIMAX · MASE 0.839

p=1 d=1 q=2 K=6 trend=n log=False

2015 · ETS · MASE 1.001

err=add trend=add damped=False seas=mul log=False

2020 · SARIMAX · MASE 1.154

p=0 d=1 q=3 K=6 trend=n log=False

2020 · ETS · MASE 1.067

err=add trend=add damped=False seas=None log=False

SARIMAX, trained from 2000, 24-week horizon: test MASE 0.717. Beats seasonal-naive by 28%. This is the bar the causal model has to clear.
p=3 d=1 q=1 K=6 trend=c log=True

All runs, 24 weeks

Window	Horizon	Model	MASE	MAPE
2000	24w	SARIMAX	0.717	2.91%	winner
2000	24w	ETS	0.932	3.79%
2005	24w	SARIMAX	0.722	2.93%
2005	24w	ETS	0.843	3.43%
2010	24w	SARIMAX	0.743	3.01%
2010	24w	ETS	0.873	3.55%
2015	24w	SARIMAX	0.794	3.20%
2015	24w	ETS	0.921	3.75%
2020	24w	SARIMAX	0.789	3.21%
2020	24w	ETS	1.166	4.76%

Best run: 2000, 24 weeks

ForecastDecomposition

Drag to zoom, double-click to reset, click legend entries to hide series.

Bars split each week's forecast change against the last actual week into a seasonal part and an underlying level/trend part; the line is the net change.

What each model component contributes

Component	Fitted values	What it explains
AR - autoregressive	`p=3 (coef +0.48, +0.10, +0.10)`	Momentum: this week's forecast leans on the previous 3 weeks of demand with these weights.
I - integrated / trend	`d=1, intercept +4.78e-06`	The model forecasts week-over-week changes, so the latest level is the baseline. A fitted baseline trend is added on top.
MA - moving average	`q=1 (coef -0.96)`	Shock smoothing: forecast errors from the last 1 week adjust this week's forecast, so one-off surprises fade instead of propagating.
S - seasonality (via X)	`K=6 Fourier pairs, 10.7% peak-to-trough`	Repeating yearly cycle - the calendar's contribution to demand (summer driving, winter heating, holiday travel).
X - exogenous drivers	`seasonal curves only`	In this benchmark the only external inputs are the seasonal curves above. Price, activity and weather drivers enter in the causal model.

Other runs

2000 · ETS · MASE 0.932

err=mul trend=add damped=False seas=add log=False

2005 · SARIMAX · MASE 0.722

p=3 d=1 q=1 K=6 trend=n log=True

2005 · ETS · MASE 0.843

err=mul trend=None damped=False seas=mul log=False

2010 · SARIMAX · MASE 0.743

p=2 d=1 q=1 K=6 trend=n log=True

2010 · ETS · MASE 0.873

err=mul trend=None damped=False seas=mul log=False

2015 · SARIMAX · MASE 0.794

p=3 d=1 q=3 K=6 trend=c log=True

2015 · ETS · MASE 0.921

err=mul trend=None damped=False seas=mul log=False

2020 · SARIMAX · MASE 0.789

p=1 d=1 q=1 K=1 trend=n log=False

2020 · ETS · MASE 1.166

err=mul trend=add damped=True seas=mul log=False

12-week horizon24-week horizon

SARIMAX, trained from 2005, 12-week horizon: test MASE 0.840. Beats seasonal-naive by 16%. This is the bar the causal model has to clear.
p=2 d=0 q=0 K=3 trend=c log=False

All runs, 12 weeks

Window	Horizon	Model	MASE	MAPE
2000	12w	SARIMAX	0.863	7.00%
2000	12w	ETS	0.908	7.30%
2005	12w	SARIMAX	0.840	6.78%	winner
2005	12w	ETS	0.905	7.26%
2010	12w	SARIMAX	0.882	7.03%
2010	12w	ETS	0.903	7.24%
2015	12w	SARIMAX	0.867	6.91%
2015	12w	ETS	0.891	7.13%
2020	12w	SARIMAX	0.844	6.71%
2020	12w	ETS	0.878	6.95%

Best run: 2005, 12 weeks

ForecastDecomposition

Drag to zoom, double-click to reset, click legend entries to hide series.

Bars split each week's forecast change against the last actual week into a seasonal part and an underlying level/trend part; the line is the net change.

What each model component contributes

Component	Fitted values	What it explains
AR - autoregressive	`p=2 (coef +0.37, +0.18)`	Momentum: this week's forecast leans on the previous 2 weeks of demand with these weights.
I - integrated / trend	`d=0, intercept +1747 kbd`	The model forecasts demand levels directly. A fitted baseline trend is added on top.
MA - moving average	`q=0`	Not used: past forecast errors are not fed back in.
S - seasonality (via X)	`K=3 Fourier pairs, 345 kbd peak-to-trough`	Repeating yearly cycle - the calendar's contribution to demand (summer driving, winter heating, holiday travel).
X - exogenous drivers	`seasonal curves only`	In this benchmark the only external inputs are the seasonal curves above. Price, activity and weather drivers enter in the causal model.

Other runs

2000 · SARIMAX · MASE 0.863

p=3 d=0 q=2 K=3 trend=c log=True

2000 · ETS · MASE 0.908

err=mul trend=add damped=False seas=add log=False

2005 · ETS · MASE 0.905

err=mul trend=add damped=False seas=add log=False

2010 · SARIMAX · MASE 0.882

p=1 d=1 q=2 K=3 trend=n log=True

2010 · ETS · MASE 0.903

err=mul trend=add damped=False seas=add log=False

2015 · SARIMAX · MASE 0.867

p=0 d=1 q=1 K=3 trend=n log=True

2015 · ETS · MASE 0.891

err=mul trend=add damped=False seas=add log=False

2020 · SARIMAX · MASE 0.844

p=1 d=1 q=2 K=3 trend=c log=True

2020 · ETS · MASE 0.878

err=mul trend=None damped=False seas=mul log=False

SARIMAX, trained from 2000, 24-week horizon: test MASE 0.819. Beats seasonal-naive by 18%. This is the bar the causal model has to clear.
p=1 d=0 q=0 K=5 trend=c log=False

All runs, 24 weeks

Window	Horizon	Model	MASE	MAPE
2000	24w	SARIMAX	0.819	6.75%	winner
2000	24w	ETS	0.893	7.28%
2005	24w	SARIMAX	0.836	6.86%
2005	24w	ETS	0.883	7.17%
2010	24w	SARIMAX	0.857	7.00%
2010	24w	ETS	0.894	7.27%
2015	24w	SARIMAX	0.984	7.97%
2015	24w	ETS	0.891	7.23%
2020	24w	SARIMAX	0.836	6.78%
2020	24w	ETS	0.841	6.73%

Best run: 2000, 24 weeks

ForecastDecomposition

Drag to zoom, double-click to reset, click legend entries to hide series.

Bars split each week's forecast change against the last actual week into a seasonal part and an underlying level/trend part; the line is the net change.

What each model component contributes

Component	Fitted values	What it explains
AR - autoregressive	`p=1 (coef +0.43)`	Momentum: this week's forecast leans on the previous 1 week of demand with these weights.
I - integrated / trend	`d=0, intercept +2203 kbd`	The model forecasts demand levels directly. A fitted baseline trend is added on top.
MA - moving average	`q=0`	Not used: past forecast errors are not fed back in.
S - seasonality (via X)	`K=5 Fourier pairs, 410 kbd peak-to-trough`	Repeating yearly cycle - the calendar's contribution to demand (summer driving, winter heating, holiday travel).
X - exogenous drivers	`seasonal curves only`	In this benchmark the only external inputs are the seasonal curves above. Price, activity and weather drivers enter in the causal model.

Other runs

2000 · ETS · MASE 0.893

err=mul trend=add damped=False seas=add log=False

2005 · SARIMAX · MASE 0.836

p=3 d=0 q=0 K=5 trend=c log=False

2005 · ETS · MASE 0.883

err=mul trend=add damped=False seas=add log=False

2010 · SARIMAX · MASE 0.857

p=1 d=0 q=1 K=3 trend=c log=True

2010 · ETS · MASE 0.894

err=mul trend=add damped=False seas=add log=False

2015 · SARIMAX · MASE 0.984

p=3 d=1 q=0 K=3 trend=n log=True

2015 · ETS · MASE 0.891

err=mul trend=add damped=False seas=add log=False

2020 · SARIMAX · MASE 0.836

p=1 d=0 q=2 K=3 trend=c log=True

2020 · ETS · MASE 0.841

err=mul trend=None damped=False seas=mul log=False

12-week horizon24-week horizon

SARIMAX, trained from 2005, 12-week horizon: test MASE 0.773. Beats seasonal-naive by 23%. This is the bar the causal model has to clear.
p=0 d=1 q=1 K=4 trend=n log=False

All runs, 12 weeks

Window	Horizon	Model	MASE	MAPE
2000	12w	SARIMAX	0.783	6.79%
2000	12w	ETS	0.786	6.86%
2005	12w	SARIMAX	0.773	6.71%	winner
2005	12w	ETS	0.782	6.82%
2010	12w	SARIMAX	0.910	7.76%
2010	12w	ETS	0.792	6.90%
2015	12w	SARIMAX	1.050	8.97%
2015	12w	ETS	0.845	7.35%
2020	12w	SARIMAX	1.390	11.89%
2020	12w	ETS	0.825	7.12%

Best run: 2005, 12 weeks

ForecastDecomposition

Drag to zoom, double-click to reset, click legend entries to hide series.

Bars split each week's forecast change against the last actual week into a seasonal part and an underlying level/trend part; the line is the net change.

What each model component contributes

Component	Fitted values	What it explains
AR - autoregressive	`p=0`	Not used: no direct carry-over from recent weeks.
I - integrated / trend	`d=1`	The model forecasts week-over-week changes, so the latest level is the baseline.
MA - moving average	`q=1 (coef -0.79)`	Shock smoothing: forecast errors from the last 1 week adjust this week's forecast, so one-off surprises fade instead of propagating.
S - seasonality (via X)	`K=4 Fourier pairs, 159 kbd peak-to-trough`	Repeating yearly cycle - the calendar's contribution to demand (summer driving, winter heating, holiday travel).
X - exogenous drivers	`seasonal curves only`	In this benchmark the only external inputs are the seasonal curves above. Price, activity and weather drivers enter in the causal model.

Other runs

2000 · SARIMAX · MASE 0.783

p=0 d=1 q=3 K=4 trend=c log=False

2000 · ETS · MASE 0.786

err=mul trend=None damped=False seas=add log=False

2005 · ETS · MASE 0.782

err=add trend=add damped=False seas=add log=False

2010 · SARIMAX · MASE 0.910

p=2 d=0 q=1 K=6 trend=t log=False

2010 · ETS · MASE 0.792

err=mul trend=add damped=True seas=mul log=False

2015 · SARIMAX · MASE 1.050

p=1 d=0 q=3 K=5 trend=n log=False

2015 · ETS · MASE 0.845

err=add trend=None damped=False seas=mul log=False

2020 · SARIMAX · MASE 1.390

p=1 d=0 q=3 K=5 trend=n log=False

2020 · ETS · MASE 0.825

err=add trend=add damped=True seas=None log=False

ETS, trained from 2005, 24-week horizon: test MASE 0.764. Beats seasonal-naive by 24%. This is the bar the causal model has to clear.
err=mul trend=add damped=False seas=add log=False

All runs, 24 weeks

Window	Horizon	Model	MASE	MAPE
2000	24w	SARIMAX	0.816	7.16%
2000	24w	ETS	0.779	6.94%
2005	24w	SARIMAX	0.816	7.16%
2005	24w	ETS	0.764	6.80%	winner
2010	24w	SARIMAX	0.799	7.01%
2010	24w	ETS	0.768	6.75%
2015	24w	SARIMAX	0.827	7.25%
2015	24w	ETS	0.840	7.38%
2020	24w	SARIMAX	0.944	8.30%
2020	24w	ETS	1.031	9.18%

Best run: 2005, 24 weeks

ForecastDecomposition

Drag to zoom, double-click to reset, click legend entries to hide series.

Bars split each week's forecast change against the last actual week into a seasonal part and an underlying level/trend part; the line is the net change.

What each model component contributes

Component	Fitted values	What it explains
Level (baseline)	`current level 1,694 kbd, alpha=0.20`	The de-seasonalized baseline. Alpha 0.20 means 20% of each new week's surprise is absorbed into the baseline.
T - trend	`+1.40 kbd/week`	Current direction of travel of the baseline.
S - seasonality	`add, 276 kbd peak-to-trough`	Repeating yearly cycle - the calendar's contribution to demand.
E - error	`multiplicative`	How week-to-week noise is treated: a wobble proportional to the demand level.
X - exogenous drivers	`none`	ETS uses the demand history only. Price, activity and weather drivers enter in the causal model.

Other runs

2000 · SARIMAX · MASE 0.816

p=3 d=1 q=0 K=4 trend=n log=True

2000 · ETS · MASE 0.779

err=mul trend=add damped=False seas=add log=False

2005 · SARIMAX · MASE 0.816

p=3 d=1 q=2 K=4 trend=n log=True

2010 · SARIMAX · MASE 0.799

p=0 d=1 q=3 K=2 trend=n log=False

2010 · ETS · MASE 0.768

err=mul trend=add damped=True seas=mul log=False

2015 · SARIMAX · MASE 0.827

p=2 d=1 q=2 K=2 trend=n log=False

2015 · ETS · MASE 0.840

err=mul trend=add damped=True seas=mul log=False

2020 · SARIMAX · MASE 0.944

p=0 d=1 q=3 K=2 trend=n log=False

2020 · ETS · MASE 1.031

err=mul trend=add damped=False seas=add log=False

Stage 02Forecast demand on baseline models

What goes into this stage, what happens, and what comes out.

What goes in

Weekly product supplied for gasoline, distillate and jet fuel
Nothing else: no drivers, no exogenous inputs

What happens

Fit SARIMAX and ETS per fuel on rolling training windows
Tune each model on the same windows the causal model will face
Produce point forecasts and prediction intervals per horizon

What comes out

The accuracy floor per fuel, window and horizon
Interval coverage to compare calibration later

statsmodelsSARIMAXETSRolling originSee all four stages on the home page →