ci(lint): run mypy

[jmoralez]

• Adds mypy to the pre-commit hooks and runs it in the lint task.
• Fixes all the errors that were produced by mypy.
• Bumps the minimum supported python version to 3.9, since 3.8 reached its EOL on Oct 7th.
• Changes the type hints for standard collections to use them directly, since that's supported in python>=3.9.

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Experiment Results

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	8.4907	1.5413	0.0056	0.0041

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	0.8949	2.1321	0.0046	0.0039

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	178.293	268.13	269.23	1331.02
mape	0.0234	0.0311	0.0304	0.1692
mse	121589	219485	213677	4.68961e+06
total_time	0.8844	1.951	0.0055	0.005

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	465.497	346.972	398.956	1119.26
mape	0.062	0.0436	0.0512	0.1583
mse	835021	403760	656723	3.17316e+06
total_time	4.4403	6.022	0.0058	0.0052

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	558.673	459.757	602.926	1340.95
mape	0.0697	0.0565	0.0787	0.17
mse	1.22723e+06	739114	1.61572e+06	6.04619e+06
total_time	1.5436	1.458	0.0059	0.0052

Plot: