Added ARIMA time series Model

machine_learning/arima.py

@@ -0,0 +1,85 @@
+"""
+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(p=2, d=1, q=0)
+>>> model.fit(series)
+ARIMAModel(...)
+>>> model.predict(series, n_periods=2)
+array([10.99999999, 12.00000001])
+"""
+
+import numpy as np
+from typing import Optional
+
+class ARIMAModel:
+ def __init__(self, p: int = 1, d: int = 0, q: int = 0) -> None:
+ """Initialize ARIMA model.
+ Args:
+ p: AR order
+ d: Differencing order
+ q: MA order (not used in this implementation)
+ """
+ self.p = p
+ self.d = d
+ self.q = q
+ self.coef_: Optional[np.ndarray] = None
+ self.resid_: Optional[np.ndarray] = None
+
+ def difference(self, series: np.ndarray, order: int) -> np.ndarray:
+ """Apply differencing to make series stationary."""
+ for _ in range(order):
+ series = np.diff(series)
+ return 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(p=2, d=1, q=0)
+ >>> model.fit(series)
+ ARIMAModel(...)
+ """
+ y = np.asarray(time_series)
+ y_diff = self.difference(y, self.d)
+ # Build lagged feature matrix
+ feature_matrix = np.column_stack([np.roll(y_diff, i) for i in range(1, self.p + 1)])
+ feature_matrix = feature_matrix[self.p:]
+ target = y_diff[self.p:]
+ # Add intercept
+ feature_matrix = np.hstack([np.ones((feature_matrix.shape[0], 1)), 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(p=2, d=1, q=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.p:])
+ for _ in range(n_periods):
+ # Build feature vector for prediction
+ features = [1] + y_pred[-self.p:][::-1]
+ next_val = np.dot(features, self.coef_)
+ y_pred.append(next_val)
+ return np.array(y_pred[self.p:])