Fix correlation type

- Addressed bug causing mismatch between types of correlations.
- Updated C method to include CorrelationType.
- Created regression test to ensure proper validation.

Algorithm.CSharp/CorrelationTypeComparisonRegressionAlgorithm.cs

@@ -0,0 +1,139 @@
+/*
+ * 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.Collections.Generic;
+using QuantConnect.Data;
+using QuantConnect.Indicators;
+using QuantConnect.Interfaces;
+
+namespace QuantConnect.Algorithm.CSharp
+{
+    /// <summary>
+    /// Compares two correlation types and asserts they are not equal during the algorithm's execution.
+    /// </summary>
+    public class CorrelationTypeComparisonRegressionAlgorithm : QCAlgorithm, IRegressionAlgorithmDefinition
+    {
+        private Correlation _correlationPearson;
+        private Correlation _correlationSpearman;
+
+        /// <summary>
+        /// Initialise the data and resolution required, as well as the start-end dates for your algorithm. All algorithms must initialized.
+        /// </summary>
+        public override void Initialize()
+        {
+            SetStartDate(2013, 10, 08);  //Set Start Date
+            SetEndDate(2013, 10, 17);    //Set End Date
+            var symbol = AddEquity("AAPL", Resolution.Daily).Symbol;
+            var spy = AddEquity("SPY", Resolution.Daily).Symbol;
+            _correlationPearson = C(symbol, spy, 5, CorrelationType.Pearson);
+            _correlationSpearman = C(symbol, spy, 5, CorrelationType.Spearman);
+        }
+
+        /// <summary>
+        /// OnData event is the primary entry point for your algorithm. Each new data point will be pumped in here.
+        /// </summary>
+        /// <param name="data">Slice object keyed by symbol containing the stock data</param>
+        public override void OnData(Slice slice)
+        {
+            if (_correlationPearson.IsReady && _correlationSpearman.IsReady)
+            {
+                var pearsonValue = _correlationPearson.Current.Value;
+                var spearmanValue = _correlationSpearman.Current.Value;
+
+                // Check that the correlation values are not the same
+                if (pearsonValue == spearmanValue)
+                {
+                    // Throw an exception if the correlation values are equal
+                    throw new RegressionTestException($"Error: Pearson and Spearman correlation values are the same: Pearson = {pearsonValue}, Spearman = {spearmanValue}. This should not happen.");
+                }
+            }
+        }
+
+        /// <summary>
+        /// End of algorithm run event handler. This method is called at the end of a backtest or live trading operation. Intended for closing out logs.
+        /// </summary>
+        public override void OnEndOfAlgorithm()
+        {
+            if (_correlationPearson.IsReady && _correlationSpearman.IsReady)
+            {
+                var pearsonValue = _correlationPearson.Current.Value;
+                var spearmanValue = _correlationSpearman.Current.Value;
+                if (pearsonValue == spearmanValue)
+                {
+                    throw new RegressionTestException($"Error: Pearson and Spearman correlation values are the same: Pearson = {pearsonValue}, Spearman = {spearmanValue}. This should not happen.");
+                }
+            }
+        }
+
+        /// <summary>
+        /// Final status of the algorithm
+        /// </summary>
+        public AlgorithmStatus AlgorithmStatus => AlgorithmStatus.Completed;
+
+        /// <summary>
+        /// This is used by the regression test system to indicate if the open source Lean repository has the required data to run this algorithm.
+        /// </summary>
+        public bool CanRunLocally => true;
+
+        /// <summary>
+        /// This is used by the regression test system to indicate which languages this algorithm is written in.
+        /// </summary>
+        public List<Language> Languages { get; } = new() { Language.CSharp };
+
+        /// <summary>
+        /// Data Points count of all timeslices of algorithm
+        /// </summary>
+        public long DataPoints => 80;
+
+        /// <summary>
+        /// Data Points count of the algorithm history
+        /// </summary>
+        public int AlgorithmHistoryDataPoints => 0;
+
+        /// <summary>
+        /// This is used by the regression test system to indicate what the expected statistics are from running the algorithm
+        /// </summary>
+        public Dictionary<string, string> ExpectedStatistics => new Dictionary<string, string>
+        {
+            {"Total Orders", "0"},
+            {"Average Win", "0%"},
+            {"Average Loss", "0%"},
+            {"Compounding Annual Return", "0%"},
+            {"Drawdown", "0%"},
+            {"Expectancy", "0"},
+            {"Start Equity", "100000"},
+            {"End Equity", "100000"},
+            {"Net Profit", "0%"},
+            {"Sharpe Ratio", "0"},
+            {"Sortino Ratio", "0"},
+            {"Probabilistic Sharpe Ratio", "0%"},
+            {"Loss Rate", "0%"},
+            {"Win Rate", "0%"},
+            {"Profit-Loss Ratio", "0"},
+            {"Alpha", "0"},
+            {"Beta", "0"},
+            {"Annual Standard Deviation", "0"},
+            {"Annual Variance", "0"},
+            {"Information Ratio", "-19.184"},
+            {"Tracking Error", "0.138"},
+            {"Treynor Ratio", "0"},
+            {"Total Fees", "$0.00"},
+            {"Estimated Strategy Capacity", "$0"},
+            {"Lowest Capacity Asset", ""},
+            {"Portfolio Turnover", "0%"},
+            {"OrderListHash", "d41d8cd98f00b204e9800998ecf8427e"}
+        };
+    }
+}

Algorithm/QCAlgorithm.Indicators.cs

@@ -451,7 +451,7 @@ public CoppockCurve CC(Symbol symbol, int shortRocPeriod = 11, int longRocPeriod
         public Correlation C(Symbol target, Symbol reference, int period, CorrelationType correlationType = CorrelationType.Pearson, Resolution? resolution = null, Func<IBaseData, IBaseDataBar> selector = null)
         {
             var name = CreateIndicatorName(QuantConnect.Symbol.None, $"C({period})", resolution);
-            var correlation = new Correlation(name, target, reference, period);
+            var correlation = new Correlation(name, target, reference, period, correlationType);
             InitializeIndicator(correlation, resolution, selector, target, reference);
 
             return correlation;