Down the Rabbit-Hole

Subarashiki Hibi is a visual novel developed by KeroQ. The game revolves around a prophecy predicting the world will end on July 20th, 2012, generated by the "Web Bot Project"—an AI system that analyzes web data to forecast future events.

Implement a time series forecasting pipeline from scratch.

You are given a univariate time series (a sequence of numeric values at regular intervals). Your task is to implement two forecasting models — Simple Moving Average (SMA) and Exponential Smoothing (ES) — evaluate them on a held-out test set, and output predictions and metrics.

"We cannot infer the events of the future from those of the present. Superstition is the belief in the causal nexus."

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Input Format

n train_size window alpha
v_1
v_2
...
v_n

• n is the total number of time steps.
• train_size is the number of time steps in the training set (the first train_size values). The remaining n - train_size values form the test set.
• window is the lookback window size used by the SMA model.
• alpha is the smoothing factor for the ES model (0 < alpha <= 1).
• Each subsequent line is a single floating-point value.

It is guaranteed that train_size >= window and train_size < n.

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Output Format

SMA
p_1 p_2 ... p_m
RMSE: <value>
ES
p_1 p_2 ... p_m
RMSE: <value>

• m = n - train_size (the number of test-set time steps).
• For each model, output its name, then its m predictions (space-separated on one line), then its RMSE on the test set.
• RMSE values must be printed with exactly 4 decimal places.
• Predictions must be printed with exactly 4 decimal places.

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Models to Implement

Simple Moving Average (SMA)

To predict time step t, average the window most recent values prior to t.

That is:

SMA(t) = (v[t-window] + v[t-window+1] + ... + v[t-1]) / window

• For the first test prediction (t = train_size), the window pulls from the tail of the training set.
• Each subsequent prediction uses the actual value at the prior time step (not the predicted value). This is a single-step-ahead forecast using ground-truth history.

Exponential Smoothing (ES)

The ES forecast is computed as a running weighted average. The recurrence is:

S[0] = v[0]
S[t] = alpha * v[t-1] + (1 - alpha) * S[t-1],  for t >= 1

The prediction for time step t is S[t].

• S must be computed over the entire sequence up to each point. For test predictions, the recurrence continues using actual values (not predictions).
• The prediction for t = train_size is S[train_size], computed using v[train_size - 1] and S[train_size - 1].

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Evaluation

RMSE is defined as:

RMSE = sqrt( (1/m) * sum_{i=0}^{m-1} (pred[i] - actual[i])^2 )

where actual[i] = v[train_size + i].

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Behavioral Requirements

• You must not use any forecasting, statistics, or ML library. Basic math (sqrt, etc.) is permitted.
• Predictions must use actual (ground-truth) values for history at every step — not previously generated predictions. This is called "one-step-ahead" forecasting.
• The train/test split is strictly positional: first train_size values are train, the rest are test. No shuffling or reordering.

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Notes

• The ES model does not have a separate "training" phase — it simply runs its recurrence from t = 0 onward. The train/test split only determines which predictions are evaluated.
• Both models are deterministic given the same input. There is no fitting or parameter search.