[FEAT] TabPFN test on VN1-competition

[elephaint]

Work done by @marcopeix, few small changes from my end.

Run the following commands from a terminal, using a nixtla environment (see Contributing.md), from folder experiments\vn1-competition,:

1. make download_data
2. pip install tabpfn-time-series datasets
3. python experiments/vn1-competition/test_tabpfn.py

Following results should display (takes a loooonng time):

[github-actions]

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	1.2887	1.4137	0.0045	0.0034

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	4040.22	4110.79	5928.17	18859.2
total_time	0.906	0.8872	0.0037	0.0034

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	1.0852	2.2406	0.0047	0.0041

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	465.532	346.972	398.956	1119.26
mape	0.062	0.0436	0.0512	0.1583
mse	835120	403760	656723	3.17316e+06
total_time	0.9753	1.9046	0.0053	0.0044

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	1.0205	1.0297	0.005	0.0044

Plot:

[marcopeix]

Minor comment: we should place this in experiments/vn1-competition/src/.
@cchallu, do we want to merge this?

[marcopeix]

Closing as I'm not sure if we want to merge it, but keeping the branch just in case.