Timeseries Engineering

On a random walk, “tomorrow equals today” has a mean absolute error of 0.79; forecasting the training average gives 8.87; adding the historical drift does no better than naive (0.79). No model — LSTM or otherwise — can beat naive on a pure random walk, which is why every forecasting result should be reported against it.

• Plotted one step ahead, a naive-like model looks impressively accurate; the plot hides that it is just copying yesterday.
• In the M-competitions, machine-learning methods often trailed simple statistical ones (Makridakis et al. 2018), especially on single series.
• LSTMs need careful tuning and many series; their gains are real on large, related datasets.

rng = np.random.default_rng(11)
y = 100 + rng.normal(0, 1, 2_000).cumsum()       # a random walk, like many prices
test = y[1_000:]
naive = np.abs(test[1:] - test[:-1]).mean()       # tomorrow = today
mean_fc = np.abs(test[1:] - y[:1_000].mean()).mean()   # tomorrow = the training average
drift = np.abs(test[1:] - (test[:-1] + np.diff(y[:1_000]).mean())).mean()

Assumes import numpy as np and import pandas as pd. Each snippet simulates or makes up its own series, as the comments say.

# PyTorch — LSTM for multi-step forecasting
class LSTMForecaster(nn.Module):
    def __init__(self, n_features, hidden, n_out):
        super().__init__()
        self.lstm = nn.LSTM(n_features, hidden,
                            num_layers=2, batch_first=True, dropout=0.2)
        self.fc = nn.Linear(hidden, n_out)
    def forward(self, x):
        out, _ = self.lstm(x)
        return self.fc(out[:, -1, :])