[FEAT] Add colab badges to docs

[AzulGarza]

• feat: add utils with colab badge function
• fix: rm unwated message plot
• feat: add colab badges to tutorials
• fix: ensure correct integration colab

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Experiment 1: air-passengers

Description:

variable	experiment
h	12
season_length	12
freq	MS
level	None
n_windows	1

Results:

metric	timegpt-1	timegpt-1-long-horizon	SeasonalNaive	Naive
mae	12.6793	11.0623	47.8333	76
mape	0.027	0.0232	0.0999	0.1425
mse	213.935	199.132	2571.33	10604.2
total_time	4.649	6.295	7.8332	0.7154

Plot:

Experiment 2: air-passengers

Description:

variable	experiment
h	24
season_length	12
freq	MS
level	None
n_windows	1

Results:

metric	timegpt-1	timegpt-1-long-horizon	SeasonalNaive	Naive
mae	58.1031	58.4587	71.25	115.25
mape	0.1257	0.1267	0.1552	0.2358
mse	4040.21	4110.79	5928.17	18859.2
total_time	2.7693	2.3955	0.0087	0.0069

Plot:

Experiment 3: electricity-multiple-series

Description:

variable	experiment
h	24
season_length	24
freq	H
level	None
n_windows	1

Results:

metric	timegpt-1	timegpt-1-long-horizon	SeasonalNaive	Naive
mae	142.394	196.363	269.23	1331.02
mape	0.0203	0.0234	0.0304	0.1692
mse	63464.7	123119	213677	4.68961e+06
total_time	4.4799	3.4923	0.017	0.0167

Plot:

Experiment 4: electricity-multiple-series

Description:

variable	experiment
h	168
season_length	24
freq	H
level	None
n_windows	1

Results:

metric	timegpt-1	timegpt-1-long-horizon	SeasonalNaive	Naive
mae	522.427	353.528	398.956	1119.26
mape	0.069	0.0454	0.0512	0.1583
mse	966294	422332	656723	3.17316e+06
total_time	3.7269	3.1086	0.0175	0.0177

Plot:

Experiment 5: electricity-multiple-series

Description:

variable	experiment
h	336
season_length	24
freq	H
level	None
n_windows	1

Results:

metric	timegpt-1	timegpt-1-long-horizon	SeasonalNaive	Naive
mae	478.362	361.033	602.926	1340.95
mape	0.0622	0.046	0.0787	0.17
mse	805039	441118	1.61572e+06	6.04619e+06
total_time	4.9273	3.4639	0.0176	0.0175

Plot:

[github-actions]

Experiment 1: air-passengers

Description:

variable	experiment
h	12
season_length	12
freq	MS
level	None
n_windows	1

Results:

metric	timegpt-1	timegpt-1-long-horizon	SeasonalNaive	Naive
mae	12.6793	11.0623	47.8333	76
mape	0.027	0.0232	0.0999	0.1425
mse	213.936	199.132	2571.33	10604.2
total_time	2.2806	1.9789	6.6159	0.5893

Plot:

Experiment 2: air-passengers

Description:

variable	experiment
h	24
season_length	12
freq	MS
level	None
n_windows	1

Results:

metric	timegpt-1	timegpt-1-long-horizon	SeasonalNaive	Naive
mae	58.1031	58.4587	71.25	115.25
mape	0.1257	0.1267	0.1552	0.2358
mse	4040.21	4110.79	5928.17	18859.2
total_time	2.0137	1.9922	0.0058	0.0053

Plot:

Experiment 3: electricity-multiple-series

Description:

variable	experiment
h	24
season_length	24
freq	H
level	None
n_windows	1

Results:

metric	timegpt-1	timegpt-1-long-horizon	SeasonalNaive	Naive
mae	142.394	196.363	269.23	1331.02
mape	0.0203	0.0234	0.0304	0.1692
mse	63464.7	123119	213677	4.68961e+06
total_time	2.5583	2.4772	0.0149	0.0144

Plot:

Experiment 4: electricity-multiple-series

Description:

variable	experiment
h	168
season_length	24
freq	H
level	None
n_windows	1

Results:

metric	timegpt-1	timegpt-1-long-horizon	SeasonalNaive	Naive
mae	522.427	353.528	398.956	1119.26
mape	0.069	0.0454	0.0512	0.1583
mse	966294	422332	656723	3.17316e+06
total_time	3.1511	2.6297	0.0151	0.0146

Plot:

Experiment 5: electricity-multiple-series

Description:

variable	experiment
h	336
season_length	24
freq	H
level	None
n_windows	1

Results:

metric	timegpt-1	timegpt-1-long-horizon	SeasonalNaive	Naive
mae	478.362	361.033	602.926	1340.95
mape	0.0622	0.046	0.0787	0.17
mse	805039	441118	1.61572e+06	6.04619e+06
total_time	4.5824	3.1854	0.0159	0.015

Plot: