Add ARIMA model

DIRECTORY.md

@@ -686,6 +686,7 @@
 
 ## [Machine Learning](machine_learning)
   * [Apriori Algorithm](machine_learning/apriori_algorithm.py)
+  * [Arima](machine_learning/arima.py)
   * [Astar](machine_learning/astar.py)
   * [Automatic Differentiation](machine_learning/automatic_differentiation.py)
   * [Data Transformations](machine_learning/data_transformations.py)
@@ -712,14 +713,17 @@
   * [Loss Functions](machine_learning/loss_functions.py)
   * Lstm
     * [Lstm Prediction](machine_learning/lstm/lstm_prediction.py)
+  * [Mean Shift](machine_learning/mean_shift.py)
   * [Mfcc](machine_learning/mfcc.py)
   * [Mini Batch Gradient Descent](machine_learning/mini_batch_gradient_descent.py)
   * [Multilayer Perceptron Classifier](machine_learning/multilayer_perceptron_classifier.py)
+  * [Naive Bayes Text Classification](machine_learning/naive_bayes_text_classification.py)
   * [Polynomial Regression](machine_learning/polynomial_regression.py)
   * [Principle Component Analysis](machine_learning/principle_component_analysis.py)
   * [Q Learning](machine_learning/q_learning.py)
   * [Random Forest Classifier](machine_learning/random_forest_classifier.py)
   * [Random Forest Regressor](machine_learning/random_forest_regressor.py)
+  * [Rmsprop](machine_learning/rmsprop.py)
   * [Scoring Functions](machine_learning/scoring_functions.py)
   * [Self Organizing Map](machine_learning/self_organizing_map.py)
   * [Sequential Minimum Optimization](machine_learning/sequential_minimum_optimization.py)
@@ -736,6 +740,7 @@
   * [Arc Length](maths/arc_length.py)
   * [Area](maths/area.py)
   * [Area Under Curve](maths/area_under_curve.py)
+  * [Autocorrelation](maths/autocorrelation.py)
   * [Average Absolute Deviation](maths/average_absolute_deviation.py)
   * [Average Mean](maths/average_mean.py)
   * [Average Median](maths/average_median.py)
@@ -781,6 +786,7 @@
   * [Fibonacci](maths/fibonacci.py)
   * [Find Max](maths/find_max.py)
   * [Find Min](maths/find_min.py)
+  * [First Fundamental Form](maths/first_fundamental_form.py)
   * [Floor](maths/floor.py)
   * [Gamma](maths/gamma.py)
   * [Gaussian](maths/gaussian.py)
@@ -843,6 +849,7 @@
     * [Square Root](maths/numerical_analysis/square_root.py)
     * [Weierstrass Method](maths/numerical_analysis/weierstrass_method.py)
   * [Odd Sieve](maths/odd_sieve.py)
+  * [Padovan Sequence](maths/padovan_sequence.py)
   * [Pell Number](maths/pell_number.py)
   * [Perfect Cube](maths/perfect_cube.py)
   * [Perfect Number](maths/perfect_number.py)
@@ -872,6 +879,8 @@
   * [Reverse Factorial Recursive](maths/reverse_factorial_recursive.py)
   * [Segmented Sieve](maths/segmented_sieve.py)
   * Series
+    * [Alternate Harmonic Series](maths/series/alternate_harmonic_series.py)
+    * [Alternating Harmonic Series](maths/series/alternating_harmonic_series.py)
     * [Arithmetic](maths/series/arithmetic.py)
     * [Geometric](maths/series/geometric.py)
     * [Geometric Series](maths/series/geometric_series.py)
@@ -911,6 +920,7 @@
     * [Polygonal Numbers](maths/special_numbers/polygonal_numbers.py)
     * [Pronic Number](maths/special_numbers/pronic_number.py)
     * [Proth Number](maths/special_numbers/proth_number.py)
+    * [Spy Number](maths/special_numbers/spy_number.py)
     * [Triangular Numbers](maths/special_numbers/triangular_numbers.py)
     * [Trimorphic Number](maths/special_numbers/trimorphic_number.py)
     * [Ugly Numbers](maths/special_numbers/ugly_numbers.py)

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 :])