Reject the two point window Beta, Correlation and Covariance describe

Indicators/Beta.cs

@@ -58,10 +58,10 @@ public class Beta : DualSymbolIndicator<IBaseDataBar>
         public Beta(string name, Symbol targetSymbol, Symbol referenceSymbol, int period)
             : base(name, targetSymbol, referenceSymbol, 2)
         {
-            // Assert the period is greater than two, otherwise the beta can not be computed
+            // Assert the period is greater than one, otherwise the beta can not be computed
             if (period < 2)
             {
-                throw new ArgumentException($"Period parameter for Beta indicator must be greater than 2 but was {period}.");
+                throw new ArgumentException($"Period parameter for Beta indicator must be greater than 1 but was {period}.");
             }
 
             _targetReturns = new RollingWindow<double>(period);

Indicators/Correlation.cs

@@ -61,7 +61,7 @@ public Correlation(string name, Symbol targetSymbol, Symbol referenceSymbol, int
             : base(name, targetSymbol, referenceSymbol, period)
         {
             // Assert the period is greater than two, otherwise the correlation can not be computed
-            if (period < 2)
+            if (period < 3)
             {
                 throw new ArgumentException($"Period parameter for Correlation indicator must be greater than 2 but was {period}");
             }

Indicators/Covariance.cs

@@ -51,10 +51,10 @@ public class Covariance : DualSymbolIndicator<IBaseDataBar>
         public Covariance(string name, Symbol targetSymbol, Symbol referenceSymbol, int period)
             : base(name, targetSymbol, referenceSymbol, 2)
         {
-            // Assert the period is greater than two, otherwise the covariance can not be computed
+            // Assert the period is greater than one, otherwise the covariance can not be computed
             if (period < 2)
             {
-                throw new ArgumentException($"Period parameter for Covariance indicator must be greater than 2 but was {period}.");
+                throw new ArgumentException($"Period parameter for Covariance indicator must be greater than 1 but was {period}.");
             }
 
             _targetReturns = new RollingWindow<double>(period);

Tests/Indicators/BetaIndicatorTests.cs

@@ -312,5 +312,23 @@ public override void IndicatorShouldHaveSymbolAfterUpdates()
                 Assert.AreEqual(Symbols.AAPL, indicator.Current.Symbol);
             }
         }
+
+        [Test]
+        public void PeriodBelowMinimumThrows()
+        {
+            // One return is not a sample, so the smallest period this can accept is two
+            var period = 1;
+
+            var exception = Assert.Throws<ArgumentException>(() => new Beta(Symbols.SPY, Symbols.AAPL, period));
+            Assert.That(exception.Message, Is.EqualTo($"Period parameter for Beta indicator must be greater than 1 but was {period}."));
+        }
+
+        [Test]
+        public void PeriodOfTwoIsAccepted()
+        {
+            // Two returns give a finite, well defined beta, unlike the correlation
+            // of two points, which is 1 or -1 whatever the data says
+            Assert.DoesNotThrow(() => new Beta(Symbols.SPY, Symbols.AAPL, 2));
+        }
     }
 }

Tests/Indicators/CorrelationPearsonTests.cs

@@ -223,5 +223,17 @@ public void CorrelationWithDifferentTimeZones()
             }
             Assert.AreEqual(1, (double)indicator.Current.Value);
         }
+
+        [Test]
+        public void PeriodBelowMinimumThrows()
+        {
+            // A two point window leaves no spread to measure: the correlation of two
+            // points is 1 or -1 whatever the data says, so three is the smallest period
+            // that carries information
+            var period = 2;
+
+            var exception = Assert.Throws<ArgumentException>(() => new Correlation(Symbols.SPY, Symbols.AAPL, period));
+            Assert.That(exception.Message, Is.EqualTo($"Period parameter for Correlation indicator must be greater than 2 but was {period}"));
+        }
     }
 }

Tests/Indicators/CovarianceTests.cs

@@ -287,5 +287,23 @@ public override void IndicatorShouldHaveSymbolAfterUpdates()
                 Assert.AreEqual(Symbols.AAPL, indicator.Current.Symbol);
             }
         }
+
+        [Test]
+        public void PeriodBelowMinimumThrows()
+        {
+            // One return is not a sample, so the smallest period this can accept is two
+            var period = 1;
+
+            var exception = Assert.Throws<ArgumentException>(() => new Covariance(Symbols.SPY, Symbols.AAPL, period));
+            Assert.That(exception.Message, Is.EqualTo($"Period parameter for Covariance indicator must be greater than 1 but was {period}."));
+        }
+
+        [Test]
+        public void PeriodOfTwoIsAccepted()
+        {
+            // Two returns give a finite, well defined covariance, unlike the correlation
+            // of two points, which is 1 or -1 whatever the data says
+            Assert.DoesNotThrow(() => new Covariance(Symbols.SPY, Symbols.AAPL, 2));
+        }
     }
 }