Forecast with an LSTM

Train an LSTM that forecasts the next value of a seasonal series.

You get one training series, a 1D tensor. It has a daily and a weekly cycle on top of a level near 50, plus noise. Write train_forecaster(series, window). It must:

1. normalise the series with the mean and standard deviation of the training series,
2. cut it into windows of window values, each with the value that follows it as the target (Tensor.unfold does this in one call),
3. train an nn.LSTM with a linear head on the last hidden state, using mini-batches from a DataLoader,
4. return a predict(windows) function. It takes a (B, window) tensor of raw values and returns a (B,) tensor of forecasts in raw units.

Function signature

def train_forecaster(series, window):

Example

Input

series = torch.tensor([50.1, 54.3, 57.9, ...])     # 1000 values
predict = train_forecaster(series, window=24)
predict(torch.stack([series[-24:]]))

Output

tensor([53.8])     # one forecast for the step after the window

Reasoning

The forecast for a window is the model output for its last hidden state, turned back into raw units with * std + mean. The cycles repeat, so the shape of the last 24 values tells the model where in each cycle the next step falls.

Constraints and notes

• The tests forecast windows from the 400 steps after the training series (data the model never saw) and need a mean squared error below 1.0 and below 20% of the "repeat the last value" baseline, which is about 8.7.
• Without normalisation, a level of 50 with a small initial network gives large gradients and a slow start. Use the training statistics only.
• nn.LSTM(1, hidden, batch_first=True) expects (B, T, 1). Add the feature axis with unsqueeze(-1).
• Return predictions under torch.no_grad() and keep training to a few seconds.