/// <summary>
/// Event fired each time the we add/remove securities from the data feed
/// </summary>
/// <param name="algorithm">The algorithm instance that experienced the change in securities</param>
/// <param name="changes">The security additions and removals from the algorithm</param>
public override void OnSecuritiesChanged(QCAlgorithm algorithm, SecurityChanges changes)
{
NotifiedSecurityChanges.UpdateCollection(Securities, changes);
var symbols = Securities.Select(x => x.Symbol).ToArray();
var history = algorithm.History(symbols, _lookback, _resolution);
var vectors = GetPriceVectors(history);
if (vectors.LongLength == 0)
{
algorithm.Debug($"PearsonCorrelationPairsTradingAlphaModel.OnSecuritiesChanged(): The requested historical data does not have series of prices with the same date/time. Please consider increasing the looback period. Current lookback: {_lookback}");
}
else
{
var pearsonMatrix = Correlation.PearsonMatrix(vectors).UpperTriangle();
var maxValue = pearsonMatrix.Enumerate().Where(x => Math.Abs(x) < 1).Max();
if (maxValue >= _minimumCorrelation)
{
var maxTuple = pearsonMatrix.Find(x => x == maxValue);
_bestPair = Tuple.Create(symbols[maxTuple.Item1], symbols[maxTuple.Item2]);
}
}
base.OnSecuritiesChanged(algorithm, changes);
}
/// <summary>
/// Builds a correlation matrix for an array of columns
/// </summary>
/// <param name="columns">Array of columns for correlation</param>
/// <param name="algorithm">Algorithm enumeration of Pearson and Spearman (default)</param>
/// <returns>Returns the correlation matrix</returns>
public static Matrix <double> CorrelationMatrix(this double[][] columns, Algorithm algorithm = Algorithm.Spearman)
{
switch (algorithm)
{
case Algorithm.Pearson:
return(Correlation.PearsonMatrix(columns));
case Algorithm.Spearman:
return(Correlation.SpearmanMatrix(columns));
default:
return(Correlation.SpearmanMatrix(columns));
}
}
private void clusterCovariance_Click(object sender, EventArgs e)
{
debugData.Columns.Clear();
double[][] v = Correlation.PearsonMatrix(analyzer.GetClusterOfInput((int)ClusterBox.SelectedItem).ToArray()).ToRowArrays();
foreach (double item in v[0])
{
debugData.Columns.Add("", "");
}
// debugData.Columns[0].Width = 0;
debugData.Rows.Add(v.Count());
for (int i = 0; i < v.Count(); i++)
{
double[] row = v[i];
for (int j = 0; j < row.Count(); j++)
{
debugData.Rows[i].Cells[j].Value = v[i][j];
// debugData.Text += item.Select(x => new String(x.ToString().Take(4).ToArray())).Aggregate((a, b) => a + " | " + b);
//debugData.Text += '\n';
}
}
}
/// <summary>
/// Initialise the data and resolution required, as well as the cash and start-end dates for your algorithm. All algorithms must initialized.
/// </summary>
public override void Initialize()
{
SetStartDate(2013, 10, 07); //Set Start Date
SetEndDate(2013, 10, 11); //Set End Date
SetCash(100000); //Set Strategy Cash
// Find more symbols here: http://quantconnect.com/data
AddEquity("SPY", Resolution.Daily);
AddEquity("AIG", Resolution.Daily);
AddEquity("BAC", Resolution.Daily);
AddEquity("IBM", Resolution.Daily);
var allHistoryBars = new List <double[]>();
SymbolDataList = new List <SymbolData>();
foreach (var security in Securities)
{
var history = History(security.Key, TimeSpan.FromDays(365));
allHistoryBars.Add(history.Select(x => (double)x.Value).ToArray());
SymbolDataList.Add(new SymbolData(security.Key, history));
}
// Diagonal Matrix with each security risk (standard deviation)
var S = Matrix <double> .Build.DenseOfDiagonalArray(SymbolDataList.Select(x => (double)x.Risk).ToArray());
// Computes Correlation Matrix (using Math.NET Numerics Statistics)
var R = Correlation.PearsonMatrix(allHistoryBars);
// Computes Covariance Matrix (using Math.NET Numerics Linear Algebra)
Sigma = S * R * S;
ComputeLagrangeMultiplier();
ComputeWeights();
ComputePortfolioRisk();
Log($"Lagrange Multiplier: {_lagrangeMultiplier.ToStringInvariant("7:F4")}");
Log($"Portfolio Risk: {_portfolioRisk.ToStringInvariant("7:P2")} ");
}
private void runNeighbourhoodModel(double[][] utilityMatrix, Dictionary <int, int> userIndexMap)
{
var correlation = Correlation.PearsonMatrix(utilityMatrix);
int k = (int)Math.Floor(Math.Sqrt(userIndexMap.Count - 1));
for (var i = 0; i < userIndexMap.Count; i++)
{
var current_user = correlation.Column(i);
List <int> neighbours = new List <int>();
List <double> similarity = new List <double>();
//set the cross corrs = -1 so they are not considered neighbours
current_user[i] = -1;
//add the top k neighbours to the neibourhood table
for (var n = 0; n < k; n++)
{
int top = current_user.MaximumIndex();
similarity.Add(current_user[top]);
neighbours.Add(userIndexMap[top]);
current_user[top] = -1;
}
unc.AddUserNeighbourhood(userIndexMap[i], neighbours, similarity);
}
}
