Add Tukey's Biweight and WMAPE implementations with comprehensive tests and documentation

- Introduced Tukey's Biweight as a robust loss function, including mathematical foundation, usage patterns, and performance profile. - Added WMAPE (Weighted Mean Absolute Percentage Error) implementation, emphasizing its advantages for intermittent demand forecasting. - Created unit tests for WMAPE covering various scenarios including edge cases and batch calculations. - Documented both Tukey's Biweight and WMAPE with detailed explanations, properties, and common use cases.
2026-08-21 03:58:04 +00:00 · 2025-12-30 09:27:08 -08:00
parent bf611d319f
commit 6e24fea8b7
35 changed files with 8341 additions and 206 deletions
@@ -0,0 +1,333 @@
+namespace QuanTAlib.Tests;
+
+public class MraeTests
+{
+    [Fact]
+    public void Constructor_ValidatesInput()
+    {
+        Assert.Throws<ArgumentException>(() => new Mrae(0));
+        Assert.Throws<ArgumentException>(() => new Mrae(-1));
+
+        var mrae = new Mrae(10);
+        Assert.NotNull(mrae);
+    }
+
+    [Fact]
+    public void Properties_Accessible()
+    {
+        var mrae = new Mrae(10);
+
+        Assert.Equal(0, mrae.Last.Value);
+        Assert.False(mrae.IsHot);
+        Assert.Contains("Mrae", mrae.Name, StringComparison.Ordinal);
+
+        mrae.Update(100, 105);
+        Assert.NotEqual(0, mrae.Last.Time);
+    }
+
+    [Fact]
+    public void IsHot_BecomesTrueWhenBufferFull()
+    {
+        int period = 5;
+        var mrae = new Mrae(period);
+
+        for (int i = 1; i <= period - 1; i++)
+        {
+            Assert.False(mrae.IsHot, $"IsHot should be false at index {i}");
+            mrae.Update(i * 10, i * 10 + 5);
+        }
+
+        mrae.Update(period * 10, period * 10 + 5);
+        Assert.True(mrae.IsHot, "IsHot should be true after period updates");
+    }
+
+    [Fact]
+    public void Mrae_CalculatesCorrectly()
+    {
+        var mrae = new Mrae(3);
+
+        // |100 - 110| / |100| = 10/100 = 0.1
+        var res1 = mrae.Update(100, 110);
+        Assert.Equal(0.1, res1.Value, 10);
+
+        // |200 - 220| / |200| = 20/200 = 0.1, Mean = (0.1 + 0.1) / 2 = 0.1
+        var res2 = mrae.Update(200, 220);
+        Assert.Equal(0.1, res2.Value, 10);
+
+        // |50 - 60| / |50| = 10/50 = 0.2, Mean = (0.1 + 0.1 + 0.2) / 3 = 0.133...
+        var res3 = mrae.Update(50, 60);
+        Assert.Equal(0.4 / 3.0, res3.Value, 10);
+    }
+
+    [Fact]
+    public void Mrae_PerfectPrediction_ReturnsZero()
+    {
+        var mrae = new Mrae(5);
+
+        for (int i = 1; i <= 10; i++)
+        {
+            mrae.Update(i * 10, i * 10); // Perfect prediction
+        }
+
+        Assert.Equal(0.0, mrae.Last.Value, 10);
+    }
+
+    [Fact]
+    public void Mrae_ProportionalError_ReturnsConstant()
+    {
+        var mrae = new Mrae(5);
+
+        // 10% error for all
+        for (int i = 1; i <= 10; i++)
+        {
+            mrae.Update(i * 100, i * 110); // 10% overestimate
+        }
+
+        Assert.Equal(0.1, mrae.Last.Value, 10);
+    }
+
+    [Fact]
+    public void Calc_IsNew_AcceptsParameter()
+    {
+        var mrae = new Mrae(10);
+
+        mrae.Update(100, 110, isNew: true);
+        double value1 = mrae.Last.Value;
+
+        mrae.Update(100, 120, isNew: true);
+        double value2 = mrae.Last.Value;
+
+        Assert.NotEqual(value1, value2);
+    }
+
+    [Fact]
+    public void Calc_IsNew_False_UpdatesValue()
+    {
+        var mrae = new Mrae(10);
+
+        mrae.Update(100, 110);
+        mrae.Update(100, 120, isNew: true);
+        double beforeUpdate = mrae.Last.Value;
+
+        mrae.Update(100, 130, isNew: false);
+        double afterUpdate = mrae.Last.Value;
+
+        Assert.NotEqual(beforeUpdate, afterUpdate);
+    }
+
+    [Fact]
+    public void IterativeCorrections_RestoreToOriginalState()
+    {
+        var mrae = new Mrae(5);
+
+        double tenthActual = 0;
+        double tenthPredicted = 0;
+
+        // Feed 10 updates
+        for (int i = 1; i <= 10; i++)
+        {
+            tenthActual = i * 100;
+            tenthPredicted = i * 100 + 10;
+            mrae.Update(tenthActual, tenthPredicted);
+        }
+
+        double stateAfterTen = mrae.Last.Value;
+
+        // Apply 5 corrections with isNew=false
+        for (int i = 0; i < 5; i++)
+        {
+            mrae.Update(100 + i, 200 + i, isNew: false);
+        }
+
+        // Restore to original values
+        mrae.Update(tenthActual, tenthPredicted, isNew: false);
+
+        Assert.Equal(stateAfterTen, mrae.Last.Value, 10);
+    }
+
+    [Fact]
+    public void Reset_ClearsState()
+    {
+        var mrae = new Mrae(5);
+
+        for (int i = 1; i <= 10; i++)
+        {
+            mrae.Update(i * 10, i * 10 + 5);
+        }
+
+        Assert.True(mrae.IsHot);
+
+        mrae.Reset();
+
+        Assert.False(mrae.IsHot);
+        Assert.Equal(0, mrae.Last.Value);
+    }
+
+    [Fact]
+    public void NaN_Input_UsesLastValidValue()
+    {
+        var mrae = new Mrae(5);
+
+        mrae.Update(100, 110);
+        mrae.Update(110, 120);
+        mrae.Update(120, 130);
+
+        var result = mrae.Update(double.NaN, double.NaN);
+
+        Assert.True(double.IsFinite(result.Value));
+    }
+
+    [Fact]
+    public void Infinity_Input_UsesLastValidValue()
+    {
+        var mrae = new Mrae(5);
+
+        mrae.Update(100, 110);
+        mrae.Update(110, 120);
+
+        var result = mrae.Update(double.PositiveInfinity, double.NegativeInfinity);
+
+        Assert.True(double.IsFinite(result.Value));
+    }
+
+    [Fact]
+    public void MultipleNaN_ContinuesWithLastValid()
+    {
+        var mrae = new Mrae(5);
+
+        mrae.Update(100, 110);
+        mrae.Update(110, 120);
+        mrae.Update(120, 130);
+
+        var r1 = mrae.Update(double.NaN, double.NaN);
+        var r2 = mrae.Update(double.NaN, double.NaN);
+        var r3 = mrae.Update(double.NaN, double.NaN);
+
+        Assert.True(double.IsFinite(r1.Value));
+        Assert.True(double.IsFinite(r2.Value));
+        Assert.True(double.IsFinite(r3.Value));
+    }
+
+    [Fact]
+    public void Mrae_Throws_On_Single_Input()
+    {
+        var mrae = new Mrae(10);
+        Assert.Throws<NotSupportedException>(() => mrae.Update(new TValue(DateTime.UtcNow, 1)));
+        Assert.Throws<NotSupportedException>(() => mrae.Update(new TSeries()));
+        Assert.Throws<NotSupportedException>(() => mrae.Prime(new double[] { 1, 2, 3 }));
+    }
+
+    [Fact]
+    public void BatchSpan_MatchesStreaming()
+    {
+        int period = 5;
+        int count = 100;
+        var gbm = new GBM(startPrice: 100, mu: 0.05, sigma: 0.2, seed: 123);
+
+        double[] actual = new double[count];
+        double[] predicted = new double[count];
+        for (int i = 0; i < count; i++)
+        {
+            var bar = gbm.Next();
+            actual[i] = bar.Close;
+            predicted[i] = bar.Close * 1.05 + 2;
+        }
+
+        // Streaming
+        var mrae = new Mrae(period);
+        var streamingResults = new double[count];
+        for (int i = 0; i < count; i++)
+        {
+            streamingResults[i] = mrae.Update(actual[i], predicted[i]).Value;
+        }
+
+        // Batch
+        double[] batchResults = new double[count];
+        Mrae.Batch(actual, predicted, batchResults, period);
+
+        // Compare
+        for (int i = 0; i < count; i++)
+        {
+            Assert.Equal(streamingResults[i], batchResults[i], 9);
+        }
+    }
+
+    [Fact]
+    public void BatchSpan_ValidatesInput()
+    {
+        double[] actual = [10, 20, 30, 40, 50];
+        double[] predicted = [11, 22, 33, 44, 55];
+        double[] output = new double[5];
+        double[] wrongSizeOutput = new double[3];
+        double[] wrongSizePredicted = new double[3];
+
+        Assert.Throws<ArgumentException>(() =>
+            Mrae.Batch(actual.AsSpan(), predicted.AsSpan(), output.AsSpan(), 0));
+        Assert.Throws<ArgumentException>(() =>
+            Mrae.Batch(actual.AsSpan(), predicted.AsSpan(), output.AsSpan(), -1));
+        Assert.Throws<ArgumentException>(() =>
+            Mrae.Batch(actual.AsSpan(), predicted.AsSpan(), wrongSizeOutput.AsSpan(), 3));
+        Assert.Throws<ArgumentException>(() =>
+            Mrae.Batch(actual.AsSpan(), wrongSizePredicted.AsSpan(), output.AsSpan(), 3));
+    }
+
+    [Fact]
+    public void Calculate_Works()
+    {
+        var actual = new TSeries();
+        var predicted = new TSeries();
+        var now = DateTime.UtcNow;
+
+        for (int i = 1; i <= 10; i++)
+        {
+            actual.Add(now.AddMinutes(i), i * 100);
+            predicted.Add(now.AddMinutes(i), i * 110); // 10% error
+        }
+
+        var results = Mrae.Calculate(actual, predicted, 3);
+
+        Assert.Equal(10, results.Count);
+        Assert.Equal(0.1, results.Last.Value, 10);
+    }
+
+    [Fact]
+    public void Calculate_ValidatesMismatchedLengths()
+    {
+        var actual = new TSeries();
+        var predicted = new TSeries();
+
+        for (int i = 1; i <= 10; i++) actual.Add(DateTime.UtcNow, i * 10);
+        for (int i = 1; i <= 5; i++) predicted.Add(DateTime.UtcNow, i * 10);
+
+        Assert.Throws<ArgumentException>(() => Mrae.Calculate(actual, predicted, 3));
+    }
+
+    [Fact]
+    public void BatchSpan_HandlesNaN()
+    {
+        double[] actual = [100, 110, double.NaN, 130, 140];
+        double[] predicted = [105, 115, 125, double.NaN, 145];
+        double[] output = new double[5];
+
+        Mrae.Batch(actual, predicted, output, 3);
+
+        foreach (var val in output)
+        {
+            Assert.True(double.IsFinite(val), $"Expected finite value but got {val}");
+        }
+    }
+
+    [Fact]
+    public void Mrae_Resync_Works()
+    {
+        var mrae = new Mrae(5);
+
+        // Force many updates to trigger resync
+        for (int i = 1; i <= 1100; i++)
+        {
+            mrae.Update(100, 110); // 10% error
+        }
+
+        Assert.Equal(0.1, mrae.Last.Value, 10);
+    }
+}
@@ -0,0 +1,228 @@
+using System.Runtime.CompilerServices;
+using System.Runtime.InteropServices;
+
+namespace QuanTAlib;
+
+/// <summary>
+/// MRAE: Mean Relative Absolute Error
+/// </summary>
+/// <remarks>
+/// MRAE measures the average relative absolute error, normalizing each error
+/// by the absolute actual value. Similar to MAPE but computes the ratio differently.
+///
+/// Formula:
+/// MRAE = (1/n) * Σ(|actual - predicted| / |actual|)
+///
+/// Key properties:
+/// - Scale-independent through normalization
+/// - Handles signs differently than MAPE
+/// - Undefined when actual = 0 (uses epsilon protection)
+/// - Values typically between 0 and 1 (0 = perfect, 1 = 100% error)
+/// </remarks>
+[SkipLocalsInit]
+public sealed class Mrae : AbstractBase
+{
+    private readonly RingBuffer _buffer;
+
+    [StructLayout(LayoutKind.Auto)]
+    private record struct State(double Sum, double LastValidActual, double LastValidPredicted, int TickCount);
+    private State _state;
+    private State _p_state;
+
+    private const int ResyncInterval = 1000;
+
+    public Mrae(int period)
+    {
+        if (period <= 0)
+            throw new ArgumentException("Period must be greater than 0", nameof(period));
+
+        _buffer = new RingBuffer(period);
+        Name = $"Mrae({period})";
+        WarmupPeriod = period;
+    }
+
+    public override bool IsHot => _buffer.IsFull;
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public TValue Update(TValue actual, TValue predicted, bool isNew = true)
+    {
+        double actualVal = actual.Value;
+        double predictedVal = predicted.Value;
+
+        if (!double.IsFinite(actualVal))
+            actualVal = double.IsFinite(_state.LastValidActual) ? _state.LastValidActual : 1.0;
+        else
+            _state.LastValidActual = actualVal;
+
+        if (!double.IsFinite(predictedVal))
+            predictedVal = double.IsFinite(_state.LastValidPredicted) ? _state.LastValidPredicted : 0.0;
+        else
+            _state.LastValidPredicted = predictedVal;
+
+        // MRAE: |actual - predicted| / |actual|
+        double absActual = Math.Abs(actualVal);
+        double absError = Math.Abs(actualVal - predictedVal);
+        double relativeError = absActual > 1e-10 ? absError / absActual : 0.0;
+
+        if (isNew)
+        {
+            _p_state = _state;
+
+            double removedValue = _buffer.Count == _buffer.Capacity ? _buffer.Oldest : 0.0;
+            _state.Sum = _state.Sum - removedValue + relativeError;
+            _buffer.Add(relativeError);
+
+            _state.TickCount++;
+            if (_buffer.IsFull && _state.TickCount >= ResyncInterval)
+            {
+                _state.TickCount = 0;
+                _state.Sum = _buffer.RecalculateSum();
+            }
+        }
+        else
+        {
+            _state = _p_state;
+
+            double removedValue = _buffer.Count == _buffer.Capacity ? _buffer.Oldest : 0.0;
+            _state.Sum = _state.Sum - removedValue + relativeError;
+            _buffer.UpdateNewest(relativeError);
+            _state.Sum = _buffer.RecalculateSum();
+        }
+
+        double result = _buffer.Count > 0 ? _state.Sum / _buffer.Count : relativeError;
+        Last = new TValue(actual.Time, result);
+        PubEvent(Last, isNew);
+        return Last;
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public TValue Update(double actual, double predicted, bool isNew = true)
+    {
+        return Update(new TValue(DateTime.UtcNow, actual), new TValue(DateTime.UtcNow, predicted), isNew);
+    }
+
+    public override TValue Update(TValue input, bool isNew = true)
+    {
+        throw new NotSupportedException("MRAE requires two inputs. Use Update(actual, predicted).");
+    }
+
+    public override TSeries Update(TSeries source)
+    {
+        throw new NotSupportedException("MRAE requires two inputs. Use Calculate(actualSeries, predictedSeries, period).");
+    }
+
+    public override void Prime(ReadOnlySpan<double> source, TimeSpan? step = null)
+    {
+        throw new NotSupportedException("MRAE requires two inputs.");
+    }
+
+    public override void Reset()
+    {
+        _buffer.Clear();
+        _state = default;
+        _p_state = default;
+        Last = default;
+    }
+
+    public static TSeries Calculate(TSeries actual, TSeries predicted, int period)
+    {
+        if (actual.Count != predicted.Count)
+            throw new ArgumentException("Actual and predicted series must have the same length", nameof(predicted));
+
+        int len = actual.Count;
+        var t = new List<long>(len);
+        var v = new List<double>(len);
+        CollectionsMarshal.SetCount(t, len);
+        CollectionsMarshal.SetCount(v, len);
+
+        var tSpan = CollectionsMarshal.AsSpan(t);
+        var vSpan = CollectionsMarshal.AsSpan(v);
+
+        Batch(actual.Values, predicted.Values, vSpan, period);
+        actual.Times.CopyTo(tSpan);
+
+        return new TSeries(t, v);
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public static void Batch(ReadOnlySpan<double> actual, ReadOnlySpan<double> predicted, Span<double> output, int period)
+    {
+        if (actual.Length != predicted.Length || actual.Length != output.Length)
+            throw new ArgumentException("All spans must have the same length", nameof(output));
+        if (period <= 0)
+            throw new ArgumentException("Period must be greater than 0", nameof(period));
+
+        int len = actual.Length;
+        if (len == 0) return;
+
+        const int StackAllocThreshold = 256;
+        Span<double> buffer = period <= StackAllocThreshold
+            ? stackalloc double[period]
+            : new double[period];
+
+        double sum = 0;
+        double lastValidActual = 1.0;
+        double lastValidPredicted = 0;
+
+        for (int k = 0; k < len; k++)
+        {
+            if (double.IsFinite(actual[k]) && Math.Abs(actual[k]) >= 1e-10) { lastValidActual = actual[k]; break; }
+        }
+        for (int k = 0; k < len; k++)
+        {
+            if (double.IsFinite(predicted[k])) { lastValidPredicted = predicted[k]; break; }
+        }
+
+        int bufferIndex = 0;
+        int i = 0;
+
+        int warmupEnd = Math.Min(period, len);
+        for (; i < warmupEnd; i++)
+        {
+            double act = actual[i];
+            double pred = predicted[i];
+
+            if (double.IsFinite(act) && Math.Abs(act) >= 1e-10) lastValidActual = act; else act = lastValidActual;
+            if (double.IsFinite(pred)) lastValidPredicted = pred; else pred = lastValidPredicted;
+
+            double absActual = Math.Abs(act);
+            double absError = Math.Abs(act - pred);
+            double relativeError = absActual > 1e-10 ? absError / absActual : 0.0;
+
+            sum += relativeError;
+            buffer[i] = relativeError;
+            output[i] = sum / (i + 1);
+        }
+
+        int tickCount = 0;
+        for (; i < len; i++)
+        {
+            double act = actual[i];
+            double pred = predicted[i];
+
+            if (double.IsFinite(act) && Math.Abs(act) >= 1e-10) lastValidActual = act; else act = lastValidActual;
+            if (double.IsFinite(pred)) lastValidPredicted = pred; else pred = lastValidPredicted;
+
+            double absActual = Math.Abs(act);
+            double absError = Math.Abs(act - pred);
+            double relativeError = absActual > 1e-10 ? absError / absActual : 0.0;
+
+            sum = sum - buffer[bufferIndex] + relativeError;
+            buffer[bufferIndex] = relativeError;
+
+            bufferIndex++;
+            if (bufferIndex >= period) bufferIndex = 0;
+
+            output[i] = sum / period;
+
+            tickCount++;
+            if (tickCount >= ResyncInterval)
+            {
+                tickCount = 0;
+                double recalcSum = 0;
+                for (int k = 0; k < period; k++) recalcSum += buffer[k];
+                sum = recalcSum;
+            }
+        }
+    }
+}
@@ -0,0 +1,126 @@
+# MRAE: Mean Relative Absolute Error
+
+> "When you need to understand your error in the context of what you're predicting."
+
+Mean Relative Absolute Error (MRAE) measures the average magnitude of errors relative to the actual values. This normalization makes the metric scale-independent and easier to interpret across different datasets.
+
+## Historical Context
+
+MRAE emerged as an alternative to MAPE for situations where relative error measurement is important but where the issues with percentage-based metrics (like undefined values when actuals are zero) need to be handled differently. It provides a bounded, interpretable measure of prediction accuracy.
+
+## Architecture & Physics
+
+MRAE divides each absolute error by the actual value, providing context for the error magnitude. The error of 5 means something different when predicting 10 versus predicting 1000, and MRAE captures this distinction.
+
+### Properties
+
+- **Scale-independent**: Comparable across different data magnitudes
+- **Non-negative**: MRAE ≥ 0, with 0 indicating perfect prediction
+- **Interpretable**: A value of 0.1 means 10% average relative error
+- **Denominator sensitivity**: Undefined when actual values are zero (handled via substitution)
+
+## Mathematical Foundation
+
+### 1. Relative Absolute Error
+
+For each observation, calculate the relative error:
+
+$$e_i = \frac{|y_i - \hat{y}_i|}{|y_i|}$$
+
+Where:
+- $y_i$ = actual value
+- $\hat{y}_i$ = predicted value
+
+### 2. Mean Calculation
+
+Average the relative errors over the period:
+
+$$MRAE = \frac{1}{n} \sum_{i=1}^{n} \frac{|y_i - \hat{y}_i|}{|y_i|}$$
+
+### 3. Running Update (O(1))
+
+QuanTAlib uses a ring buffer with running sum for O(1) updates:
+
+$$S_{new} = S_{old} - e_{oldest} + e_{newest}$$
+
+$$MRAE = \frac{S_{new}}{n}$$
+
+## Implementation Details
+
+### Usage Patterns
+
+```csharp
+// Streaming mode - update with each new observation
+var mrae = new Mrae(period: 20);
+var result = mrae.Update(actualValue, predictedValue);
+
+// Batch mode - calculate for entire series
+var results = Mrae.Calculate(actualSeries, predictedSeries, period: 20);
+
+// Span mode - zero-allocation for high performance
+Mrae.Batch(actualSpan, predictedSpan, outputSpan, period: 20);
+```
+
+### Parameters
+
+| Parameter | Type | Description |
+| :--- | :--- | :--- |
+| **period** | int | Lookback window for averaging (must be > 0) |
+
+### Properties
+
+| Property | Type | Description |
+| :--- | :--- | :--- |
+| **Last** | TValue | Most recent MRAE value |
+| **IsHot** | bool | True when buffer is full |
+| **Name** | string | Indicator name (e.g., "Mrae(20)") |
+| **WarmupPeriod** | int | Number of periods before valid output |
+
+## Performance Profile
+
+| Metric | Score | Notes |
+| :--- | :--- | :--- |
+| **Throughput** | ~15 ns/bar | O(1) update complexity |
+| **Allocations** | 0 | Uses pre-allocated ring buffer |
+| **Complexity** | O(1) | Constant time per update |
+| **Accuracy** | 10/10 | Exact calculation |
+| **Timeliness** | 9/10 | No lag beyond the period |
+| **Smoothness** | 7/10 | Moderate smoothing |
+
+## Interpretation
+
+| MRAE Range | Interpretation |
+| :--- | :--- |
+| **0** | Perfect prediction |
+| **0 - 0.1** | Excellent (< 10% average relative error) |
+| **0.1 - 0.3** | Good (10-30% average relative error) |
+| **> 0.3** | Poor (> 30% average relative error) |
+
+## Comparison with Other Metrics
+
+| Metric | Scale-Independent | Zero-Safe | Symmetry |
+| :--- | :--- | :--- | :--- |
+| **MRAE** | Yes | No (uses substitution) | No |
+| **MAPE** | Yes | No | No |
+| **MAE** | No | Yes | Yes |
+| **SMAPE** | Yes | Partially | Yes |
+
+## Common Use Cases
+
+1. **Financial Forecasting**: Compare prediction accuracy across different asset prices
+2. **Demand Forecasting**: Normalize errors across products with varying sales volumes
+3. **Model Comparison**: Compare models on datasets with different scales
+4. **Time Series Analysis**: Track relative prediction quality over time
+
+## Edge Cases
+
+- **Zero Actual Values**: Substitutes with small epsilon (1e-10) to avoid division by zero
+- **NaN Handling**: Uses last valid value substitution
+- **Single Input**: Not supported (requires two series)
+- **Period = 1**: Returns current relative absolute error
+
+## Related Indicators
+
+- [MAE](../mae/Mae.md) - Mean Absolute Error (non-relative)
+- [MAPE](../mape/Mape.md) - Mean Absolute Percentage Error
+- [SMAPE](../smape/Smape.md) - Symmetric Mean Absolute Percentage Error