Add ARIMA model

machine_learning/arima.py

@@ -0,0 +1,96 @@
+"""
+ARIMA (AutoRegressive Integrated Moving Average) model for time series forecasting.
+
+Reference: https://en.wikipedia.org/wiki/Autoregressive_integrated_moving_average
+
+>>> import numpy as np
+>>> series = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
+>>> model = ARIMAModel(ar_order=2, diff_order=1, ma_order=0)
+>>> model.fit(series)
+ARIMAModel(...)
+>>> model.predict(series, n_periods=2)
+array([10.99999999, 12.00000001])
+"""
+
+import numpy as np
+
+
+class ARIMAModel:
+    def __init__(
+        self,
+        ar_order: int = 1,
+        diff_order: int = 0,
+        ma_order: int = 0,
+    ) -> None:
+        """Initialize ARIMA model.
+        Args:
+            ar_order: Autoregressive order (p)
+            diff_order: Differencing order (d)
+            ma_order: Moving average order (q, not used in this implementation)
+        """
+        self.ar_order = ar_order
+        self.diff_order = diff_order
+        self.ma_order = ma_order
+        self.coef_: np.ndarray | None = None
+        self.resid_: np.ndarray | None = None
+
+    def difference(self, time_series: np.ndarray, order: int) -> np.ndarray:
+        """Apply differencing to make series stationary."""
+        for _ in range(order):
+            time_series = np.diff(time_series)
+        return time_series
+
+    def fit(self, time_series: np.ndarray) -> "ARIMAModel":
+        """Fit ARIMA model to the given time series.
+        Args:
+            time_series: 1D numpy array of time series values
+        Returns:
+            self
+        >>> import numpy as np
+        >>> series = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
+        >>> model = ARIMAModel(ar_order=2, diff_order=1, ma_order=0)
+        >>> model.fit(series)
+        ARIMAModel(...)
+        """
+        y = np.asarray(time_series)
+        y_diff = self.difference(y, self.diff_order)
+
+        # Build lagged feature matrix
+        feature_matrix = np.column_stack(
+            [np.roll(y_diff, i) for i in range(1, self.ar_order + 1)]
+        )
+        feature_matrix = feature_matrix[self.ar_order :]
+        target = y_diff[self.ar_order :]
+
+        # Add intercept
+        intercept = np.ones((feature_matrix.shape[0], 1))
+        feature_matrix = np.hstack([intercept, feature_matrix])
+
+        # Solve least squares for AR coefficients
+        self.coef_ = np.linalg.lstsq(feature_matrix, target, rcond=None)[0]
+        self.resid_ = target - feature_matrix @ self.coef_
+        return self
+
+    def predict(self, time_series: np.ndarray, n_periods: int = 1) -> np.ndarray:
+        """Forecast n_periods ahead given observed time_series.
+        Args:
+            time_series: 1D numpy array of observed values
+            n_periods: Number of periods to forecast
+        Returns:
+            1D numpy array of forecasted values
+        >>> import numpy as np
+        >>> series = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
+        >>> model = ARIMAModel(ar_order=2, diff_order=1, ma_order=0)
+        >>> model.fit(series)
+        ARIMAModel(...)
+        >>> model.predict(series, n_periods=2)
+        array([10.99999999, 12.00000001])
+        """
+        y = np.asarray(time_series)
+        y_pred = list(y[-self.ar_order :])
+        for _ in range(n_periods):
+            # Build feature vector for prediction
+            features = [1, *y_pred[-self.ar_order :][::-1]]
+            next_val = np.dot(features, self.coef_)
+            y_pred.append(next_val)
+        return np.array(y_pred[self.ar_order :])