Lag features are a simple way to turn past values in a time series into input features for a model. You’ll build a lagged feature matrix from a 1D sequence so it can be fed into standard ML models.

## Requirements

Implement the function
```python
import numpy as np

def make_lag_features(series, lags):
    \"""
    Builds lag features for a 1D time series.

    Given a time series `series` of length n and a list of positive lags,
    create a feature matrix X where each row t contains the past values:
        X[t, j] = series[t - lags[j]]
    for all lags, and a target vector y where:
        y[t] = series[t]

    Formally, for each valid time index t:
    $$
    X_{t,j} = s_{t-\ell_j}, \quad y_t = s_t
    $$
    where s is the series and ℓ_j is the j-th lag.

    Args:
        series (np.ndarray): Time-ordered values, length n.
        lags (list[int]): Positive lag steps (e.g., [1, 2, 7]).

    Returns:
        tuple[np.ndarray, np.ndarray]: (X, y) where:
          - X is a 2D array of rows, each row has len(lags) floats
          - y is a 1D array of targets aligned with X
    \"""
    # Your solution below
```

**Rules:**
- Use the lags exactly as provided (don’t sort them).
- Only create rows for indices where all lagged values exist (i.e., start at `t = max(lags)`).
- Return `X` and `y` as NumPy arrays.
- Do not use pandas or any time-series helper libraries.
- Keep the implementation in this single function.

## Example

```python
series = np.array([10.0, 11.0, 13.0, 12.0, 15.0])
lags = [1, 3]

X, y = make_lag_features(series, lags)
print(X)
print(y)
```

Output:
```python
[[13. 10.]
 [12. 11.]]
[12. 15.]
```


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Lag features

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94. Lag features

Examples

Constraints

Similar Questions

Argument	Type
lags	list
series	np.ndarray