New Feature: Implement Covariance Indicator #6982 (#9144)

* Implements Covariance as Lean Indicator

* Add COV helper method and fix AcceptsVolumeRenkoBarsAsInput test

* Fix AcceptsRenkoBarsAsInput test to use smaller period for faster execution

* Fix slow Renko tests by limiting data processed to 50 rows

Author: yyxxddjj

Algorithm/QCAlgorithm.Indicators.cs

@@ -490,6 +490,26 @@ public Correlation C(Symbol target, Symbol reference, int period, CorrelationTyp
             return correlation;
         }
 
+        /// <summary>
+        /// Creates a Covariance indicator for the given target symbol in relation with the reference used.
+        /// The indicator will be automatically updated on the given resolution.
+        /// </summary>
+        /// <param name="target">The target symbol whose Covariance value we want</param>
+        /// <param name="reference">The reference symbol to compare with the target symbol</param>
+        /// <param name="period">The period of the Covariance indicator</param>
+        /// <param name="resolution">The resolution</param>
+        /// <param name="selector">Selects a value from the BaseData to send into the indicator, if null defaults to casting the input value to a TradeBar</param>
+        /// <returns>The Covariance indicator for the given parameters</returns>
+        [DocumentationAttribute(Indicators)]
+        public Covariance COV(Symbol target, Symbol reference, int period, Resolution? resolution = null, Func<IBaseData, IBaseDataBar> selector = null)
+        {
+            var name = CreateIndicatorName(QuantConnect.Symbol.None, $"COV({period})", resolution);
+            var covariance = new Covariance(name, target, reference, period);
+            InitializeIndicator(covariance, resolution, selector, target, reference);
+
+            return covariance;
+        }
+
         /// <summary>
         /// Creates a new CommodityChannelIndex indicator. The indicator will be automatically
         /// updated on the given resolution.

Indicators/Covariance.cs

@@ -0,0 +1,134 @@
+/*
+ * QUANTCONNECT.COM - Democratizing Finance, Empowering Individuals.
+ * Lean Algorithmic Trading Engine v2.0. Copyright 2014 QuantConnect Corporation.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+*/
+
+using System;
+using QuantConnect.Data.Market;
+using MathNet.Numerics.Statistics;
+
+namespace QuantConnect.Indicators
+{
+    /// <summary>
+    /// This indicator computes the Covariance of two assets using the given Look-Back period.
+    /// The Covariance of two assets is a measure of their co-movement.
+    /// </summary>
+    public class Covariance : DualSymbolIndicator<IBaseDataBar>
+    {
+        /// <summary>
+        /// RollingWindow of returns of the target symbol in the given period
+        /// </summary>
+        private readonly RollingWindow<double> _targetReturns;
+
+        /// <summary>
+        /// RollingWindow of returns of the reference symbol in the given period
+        /// </summary>
+        private readonly RollingWindow<double> _referenceReturns;
+
+        /// <summary>
+        /// Gets a flag indicating when the indicator is ready and fully initialized
+        /// </summary>
+        public override bool IsReady => _targetReturns.IsReady && _referenceReturns.IsReady;
+
+        /// <summary>
+        /// Creates a new Covariance indicator with the specified name, target, reference,
+        /// and period values
+        /// </summary>
+        /// <param name="name">The name of this indicator</param>
+        /// <param name="targetSymbol">The target symbol of this indicator</param>
+        /// <param name="period">The period of this indicator</param>
+        /// <param name="referenceSymbol">The reference symbol of this indicator</param>
+        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
+            if (period < 2)
+            {
+                throw new ArgumentException($"Period parameter for Covariance indicator must be greater than 2 but was {period}.");
+            }
+
+            _targetReturns = new RollingWindow<double>(period);
+            _referenceReturns = new RollingWindow<double>(period);
+            WarmUpPeriod += (period - 2) + 1;
+        }
+
+        /// <summary>
+        /// Creates a new Covariance indicator with the specified target, reference,
+        /// and period values
+        /// </summary>
+        /// <param name="targetSymbol">The target symbol of this indicator</param>
+        /// <param name="period">The period of this indicator</param>
+        /// <param name="referenceSymbol">The reference symbol of this indicator</param>
+        public Covariance(Symbol targetSymbol, Symbol referenceSymbol, int period)
+            : this($"COV({period})", targetSymbol, referenceSymbol, period)
+        {
+        }
+
+        /// <summary>
+        /// Creates a new Covariance indicator with the specified name, period, target and
+        /// reference values
+        /// </summary>
+        /// <param name="name">The name of this indicator</param>
+        /// <param name="period">The period of this indicator</param>
+        /// <param name="targetSymbol">The target symbol of this indicator</param>
+        /// <param name="referenceSymbol">The reference symbol of this indicator</param>
+        /// <remarks>Constructor overload for backward compatibility.</remarks>
+        public Covariance(string name, int period, Symbol targetSymbol, Symbol referenceSymbol)
+            : this(name, targetSymbol, referenceSymbol, period)
+        {
+        }
+
+        /// <summary>
+        /// Computes the returns with the new given data point and the last given data point
+        /// </summary>
+        /// <param name="rollingWindow">The collection of data points from which we want
+        /// to compute the return</param>
+        /// <returns>The returns with the new given data point</returns>
+        private static double GetNewReturn(IReadOnlyWindow<IBaseDataBar> rollingWindow)
+        {
+            return (double)(rollingWindow[0].Close.SafeDivision(rollingWindow[1].Close) - 1);
+        }
+
+        /// <summary>
+        /// Computes the covariance value of the target in relation with the reference
+        /// using the target and reference returns
+        /// </summary>
+        protected override decimal ComputeIndicator()
+        {
+            if (TargetDataPoints.IsReady)
+            {
+                _targetReturns.Add(GetNewReturn(TargetDataPoints));
+            }
+
+            if (ReferenceDataPoints.IsReady)
+            {
+                _referenceReturns.Add(GetNewReturn(ReferenceDataPoints));
+            }
+
+            var covarianceComputed = _targetReturns.Covariance(_referenceReturns);
+
+            // Avoid division with NaN or by zero
+            return (decimal)(!covarianceComputed.IsNaNOrZero() ? covarianceComputed : 0);
+        }
+
+        /// <summary>
+        /// Resets this indicator to its initial state
+        /// </summary>
+        public override void Reset()
+        {
+            _targetReturns.Reset();
+            _referenceReturns.Reset();
+            base.Reset();
+        }
+    }
+}