Exponentially Weighted Covariance Matrix

v1.0.0

Compute an exponentially weighted covariance matrix of assets returns.

References

Input

{
  "type": "object",
  "required": [
    "assets"
  ],
  "properties": {
    "assets": {
      "type": "array",
      "items": {
        "type": "object",
        "required": [
          "assetReturns"
        ],
        "properties": {
          "assetReturns": {
            "type": "array",
            "description": "assetReturns[t] is the return of the asset at the time t; all the assetReturns arrays must have the same length",
            "items": {
              "type": "number"
            }
          }
        }
      }
    },
    "decayFactor": {
      "type": "number",
      "description": "The exponential decay factor"
    }
  }
}

Output

{
  "type": "object",
  "required": [
    "assetsCovarianceMatrix"
  ],
  "properties": {
    "assetsCovarianceMatrix": {
      "type": "array",
      "description": "assetsCovarianceMatrix[i][j] is the sample covariance between the asset i returns and the asset j returns",
      "items": {
        "type": "array",
        "items": {
          "type": "number"
        }
      }
    }
  }
}