Add validation tests for USF and enhance ATR indicator tests

- Introduced Usf.Validation.Tests.cs to validate the USF (Ehlers Ultimate Smoother Filter) for consistency across batch, streaming, and span modes, as well as mathematical properties and coefficient calculations.
- Added comprehensive tests for the ATR indicator in Atr.Quantower.Tests.cs, including constructor validation, historical data processing, and handling of NaN/Infinity inputs.
- Enhanced Atr.Tests.cs with additional tests for iterative corrections, warmup behavior, and true range calculations.
- Updated Atr.cs to ensure warmup period is derived from RMA.
- Added new tests for Adosc in Adosc.Tests.cs to validate handling of NaN and Infinity inputs, and to ensure batch calculations match iterative results.
- Created a new Volatility.csproj to organize volatility-related implementations.

lib/statistics/beta/Beta.Quantower.Tests.cs

@@ -0,0 +1,128 @@
+using Xunit;
+using TradingPlatform.BusinessLayer;
+using QuanTAlib;
+
+namespace QuanTAlib.Tests;
+
+public class BetaIndicatorTests
+{
+    [Fact]
+    public void BetaIndicator_Constructor_SetsDefaults()
+    {
+        var indicator = new BetaIndicator();
+
+        Assert.Equal(20, indicator.Period);
+        Assert.Equal(SourceType.Close, indicator.AssetSource);
+        Assert.Equal(SourceType.Close, indicator.MarketSource);
+        Assert.True(indicator.ShowColdValues);
+        Assert.Equal("Beta Coefficient", indicator.Name);
+        Assert.True(indicator.SeparateWindow);
+        Assert.True(indicator.OnBackGround);
+    }
+
+    [Fact]
+    public void BetaIndicator_MinHistoryDepths_EqualsTwo()
+    {
+        var indicator = new BetaIndicator { Period = 20 };
+
+        Assert.Equal(2, BetaIndicator.MinHistoryDepths);
+        IWatchlistIndicator watchlistIndicator = indicator;
+        Assert.Equal(2, watchlistIndicator.MinHistoryDepths);
+    }
+
+    [Fact]
+    public void BetaIndicator_ShortName_IncludesParameters()
+    {
+        var indicator = new BetaIndicator { Period = 14 };
+
+        Assert.Contains("14", indicator.ShortName, StringComparison.Ordinal);
+        Assert.Contains("Beta", indicator.ShortName, StringComparison.Ordinal);
+    }
+
+    [Fact]
+    public void BetaIndicator_Initialize_CreatesInternalBeta()
+    {
+        var indicator = new BetaIndicator { Period = 10 };
+
+        // Initialize should not throw
+        indicator.Initialize();
+
+        // After init, line series should exist
+        Assert.Single(indicator.LinesSeries);
+        Assert.Equal("Beta", indicator.LinesSeries[0].Name);
+    }
+
+    [Fact]
+    public void BetaIndicator_ProcessUpdate_HistoricalBar_ComputesValue()
+    {
+        var indicator = new BetaIndicator { Period = 5 };
+        indicator.Initialize();
+
+        // Add historical data - need enough bars for warmup
+        var now = DateTime.UtcNow;
+        for (int i = 0; i < 20; i++)
+        {
+            indicator.HistoricalData.AddBar(now.AddMinutes(i), 100 + i, 110 + i, 90 + i, 105 + i);
+
+            // Process update for each bar to simulate history loading
+            var args = new UpdateArgs(UpdateReason.HistoricalBar);
+            indicator.ProcessUpdate(args);
+        }
+
+        // Line series should have a value
+        double beta = indicator.LinesSeries[0].GetValue(0);
+
+        Assert.True(double.IsFinite(beta));
+    }
+
+    [Fact]
+    public void BetaIndicator_ProcessUpdate_NewBar_ComputesValue()
+    {
+        var indicator = new BetaIndicator { Period = 5 };
+        indicator.Initialize();
+
+        var now = DateTime.UtcNow;
+        
+        // Add initial bars
+        for (int i = 0; i < 10; i++)
+        {
+            indicator.HistoricalData.AddBar(now.AddMinutes(i), 100 + i, 110 + i, 90 + i, 105 + i);
+            indicator.ProcessUpdate(new UpdateArgs(UpdateReason.HistoricalBar));
+        }
+
+        // Add a new bar
+        indicator.HistoricalData.AddBar(now.AddMinutes(10), 110, 120, 100, 115);
+        indicator.ProcessUpdate(new UpdateArgs(UpdateReason.NewBar));
+
+        Assert.Equal(11, indicator.LinesSeries[0].Count);
+        Assert.True(double.IsFinite(indicator.LinesSeries[0].GetValue(0)));
+    }
+
+    [Fact]
+    public void BetaIndicator_DifferentSourceTypes_Work()
+    {
+        var assetSources = new[]
+        {
+            SourceType.Open,
+            SourceType.High,
+            SourceType.Low,
+            SourceType.Close,
+        };
+
+        foreach (var source in assetSources)
+        {
+            var indicator = new BetaIndicator { Period = 5, AssetSource = source, MarketSource = SourceType.Close };
+            indicator.Initialize();
+
+            var now = DateTime.UtcNow;
+            for (int i = 0; i < 10; i++)
+            {
+                indicator.HistoricalData.AddBar(now.AddMinutes(i), 100 + i, 110 + i, 90 + i, 105 + i);
+                indicator.ProcessUpdate(new UpdateArgs(UpdateReason.HistoricalBar));
+            }
+
+            Assert.True(double.IsFinite(indicator.LinesSeries[0].GetValue(0)),
+                $"AssetSource {source} should produce finite value");
+        }
+    }
+}

lib/statistics/beta/Beta.Quantower.cs

@@ -0,0 +1,68 @@
+using System.Drawing;
+using System.Runtime.CompilerServices;
+using TradingPlatform.BusinessLayer;
+
+namespace QuanTAlib;
+
+[SkipLocalsInit]
+public sealed class BetaIndicator : Indicator, IWatchlistIndicator
+{
+    [InputParameter("Period", sortIndex: 1, 1, 2000, 1, 0)]
+    public int Period { get; set; } = 20;
+
+    [InputParameter("Asset Source", sortIndex: 2)]
+    public SourceType AssetSource { get; set; } = SourceType.Close;
+
+    [InputParameter("Market Source", sortIndex: 3)]
+    public SourceType MarketSource { get; set; } = SourceType.Close;
+
+    [InputParameter("Show cold values", sortIndex: 21)]
+    public bool ShowColdValues { get; set; } = true;
+
+    private Beta? _beta;
+    private readonly LineSeries? _series;
+    private Func<IHistoryItem, double>? _assetSelector;
+    private Func<IHistoryItem, double>? _marketSelector;
+
+    public static int MinHistoryDepths => 2;
+    int IWatchlistIndicator.MinHistoryDepths => MinHistoryDepths;
+
+    public override string ShortName => $"Beta({Period})";
+    public override string SourceCodeLink => "https://github.com/mihakralj/QuanTAlib/blob/main/lib/statistics/beta/Beta.Quantower.cs";
+
+    public BetaIndicator()
+    {
+        OnBackGround = true;
+        SeparateWindow = true;
+        Name = "Beta Coefficient";
+        Description = "Measures the volatility of an asset in relation to the overall market.";
+
+        _series = new(name: "Beta", color: IndicatorExtensions.Statistics, width: 2, style: LineStyle.Solid);
+        AddLineSeries(_series);
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    protected override void OnInit()
+    {
+        _beta = new Beta(Period);
+        _assetSelector = AssetSource.GetPriceSelector();
+        _marketSelector = MarketSource.GetPriceSelector();
+        base.OnInit();
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    protected override void OnUpdate(UpdateArgs args)
+    {
+        var item = this.HistoricalData[this.Count - 1, SeekOriginHistory.Begin];
+        double assetVal = _assetSelector!(item);
+        double marketVal = _marketSelector!(item);
+        var time = this.HistoricalData.Time();
+
+        var assetInput = new TValue(time, assetVal);
+        var marketInput = new TValue(time, marketVal);
+
+        TValue result = _beta!.Update(assetInput, marketInput, args.IsNewBar());
+
+        _series!.SetValue(result.Value, _beta.IsHot, ShowColdValues);
+    }
+}

lib/statistics/beta/Beta.Tests.cs

@@ -9,6 +9,11 @@ public class BetaTests
     public void Constructor_ValidatesPeriod()
     {
         Assert.Throws<ArgumentOutOfRangeException>(() => new Beta(0));
+        Assert.Throws<ArgumentOutOfRangeException>(() => new Beta(-1));
+
+        // Valid period should not throw
+        var beta = new Beta(1);
+        Assert.NotNull(beta);
     }
 
     [Fact]
@@ -16,6 +21,23 @@ public class BetaTests
     {
         var beta = new Beta(10);
         Assert.Throws<NotSupportedException>(() => beta.Update(new TValue(DateTime.UtcNow, 100)));
+        Assert.Throws<NotSupportedException>(() => beta.Update(new TSeries()));
+        Assert.Throws<NotSupportedException>(() => beta.Prime(new double[] { 1, 2, 3 }));
+    }
+
+    [Fact]
+    public void Properties_Accessible()
+    {
+        var beta = new Beta(10);
+
+        Assert.Equal(0, beta.Last.Value);
+        Assert.False(beta.IsHot);
+        Assert.Contains("Beta", beta.Name, StringComparison.Ordinal);
+        Assert.Equal(11, beta.WarmupPeriod); // period + 1 for first return
+
+        beta.Update(100, 100);
+        beta.Update(101, 101);
+        Assert.NotEqual(0, beta.Last.Time);
     }
 
     [Fact]
@@ -76,21 +98,159 @@ public class BetaTests
         }
     }
 
+    [Fact]
+    public void Calc_IsNew_False_UpdatesValue()
+    {
+        var beta = new Beta(5);
+
+        // Initialize
+        beta.Update(100, 100);
+
+        // Add 5 more updates with different ratios to get non-1 beta
+        beta.Update(102, 101); // Asset up 2%, market up 1%
+        beta.Update(104, 102); // Asset up ~2%, market up ~1%
+        beta.Update(108, 103); // Asset up ~4%, market up ~1%
+        beta.Update(112, 104); // Asset up ~4%, market up ~1%
+        beta.Update(116, 105); // Asset up ~4%, market up ~1%
+
+        double valueBefore = beta.Last.Value;
+
+        // Update last value with isNew=false with very different values
+        beta.Update(90, 110, isNew: false); // Drastically different
+        double valueAfter = beta.Last.Value;
+
+        // Value should change since we're updating the last bar
+        Assert.NotEqual(valueBefore, valueAfter);
+    }
+
+    [Fact]
+    public void IterativeCorrections_RestoreToOriginalState()
+    {
+        var beta = new Beta(5);
+
+        // Initialize with 10 updates
+        beta.Update(100, 100);
+        for (int i = 1; i <= 9; i++)
+        {
+            beta.Update(100 + i, 100 + i);
+        }
+
+        double stateAfterTen = beta.Last.Value;
+
+        // Apply 5 corrections with isNew=false
+        for (int i = 0; i < 5; i++)
+        {
+            beta.Update(200 + i, 200 + i, isNew: false);
+        }
+
+        // Restore to original value
+        beta.Update(109, 109, isNew: false);
+
+        Assert.Equal(stateAfterTen, beta.Last.Value, precision: 10);
+    }
+
     [Fact]
     public void Reset_ClearsState()
     {
         var beta = new Beta(5);
         for (int i = 0; i < 10; i++)
         {
-            beta.Update(100 + i, 100 + i);
+            beta.Update(100 + i * 2, 100 + i); // Different ratios
         }
         Assert.True(beta.IsHot);
 
         beta.Reset();
         Assert.False(beta.IsHot);
 
-        // Re-initialize
+        // Re-initialize and verify it can accept new values
+        // After reset, beta should be able to calculate fresh values
         beta.Update(100, 100);
-        Assert.False(beta.IsHot);
+        Assert.False(beta.IsHot); // Not hot yet, needs period+1 updates
+
+        // Feed more updates to reach hot state again
+        for (int i = 1; i <= 5; i++)
+        {
+            beta.Update(100 + i, 100 + i);
+        }
+        Assert.True(beta.IsHot);
+        
+        // With equal proportional changes, beta should be 1
+        Assert.Equal(1.0, beta.Last.Value, precision: 6);
+    }
+
+    [Fact]
+    public void NaN_Input_ReturnsFiniteValue()
+    {
+        var beta = new Beta(5);
+
+        // Initialize
+        beta.Update(100, 100);
+
+        // Add some valid values
+        beta.Update(101, 101);
+        beta.Update(102, 102);
+
+        // Add NaN - Beta should handle gracefully
+        var result = beta.Update(double.NaN, double.NaN);
+
+        // Result should be finite (may be 0 or previous value)
+        Assert.True(double.IsFinite(result.Value));
+    }
+
+    [Fact]
+    public void Infinity_Input_ReturnsFiniteValue()
+    {
+        var beta = new Beta(5);
+
+        // Initialize
+        beta.Update(100, 100);
+
+        // Add some valid values
+        beta.Update(101, 101);
+        beta.Update(102, 102);
+
+        // Add Infinity - Beta should handle gracefully
+        var result = beta.Update(double.PositiveInfinity, double.PositiveInfinity);
+
+        // Result should be finite (may be 0 or previous value)
+        Assert.True(double.IsFinite(result.Value));
+    }
+
+    [Fact]
+    public void ZeroMarketVariance_ReturnsZero()
+    {
+        // When market returns are constant (zero variance), beta is undefined
+        // The implementation should return 0 in this case
+        var beta = new Beta(5);
+
+        // Initialize
+        beta.Update(100, 100);
+
+        // Same market price (zero returns/variance)
+        for (int i = 0; i < 10; i++)
+        {
+            beta.Update(100 + i, 100); // Asset changes, market constant
+        }
+
+        // Beta should be 0 (or undefined) when market variance is 0
+        Assert.Equal(0, beta.Last.Value);
+    }
+
+    [Fact]
+    public void Resync_DoesNotDrift()
+    {
+        // Run for > 1000 updates to trigger Resync
+        var beta = new Beta(10);
+        var gbm = new GBM(startPrice: 100, mu: 0.05, sigma: 0.2, seed: 123);
+
+        beta.Update(100, 100); // Initialize
+
+        for (int i = 0; i < 1100; i++)
+        {
+            var bar = gbm.Next();
+            beta.Update(bar.Close * 1.5, bar.Close); // Asset follows market with beta ~1.5
+        }
+
+        Assert.True(double.IsFinite(beta.Last.Value));
     }
 }