action portfoliooptimizer_post_assets_returns_simulation_bootstrap {
  label: "Bootstrap"
  description: "Simulate the return(s) of one or several asset(s) for one or several time period(s) using a bootstrap method.\n\nReferences\n* [Efron, B. (1979), Bootstrap methods: Another look at the jackknife, The Annals of Statistics 7, 1-26](https://projecteuclid.org/journals/annals-of-statistics/volume-7/issue-1/Bootstrap-Methods-Another-Look-at-the-Jackknife/10.1214/aos/1176344552.full)\n* [Politis, D. N. and Romano, J. P., A circular block resampling procedure for stationary data, in R. Lepage and L. Billard, eds, Exploring the Limits of Bootstrap, Wiley, New York, pp. 263-270](https://statistics.stanford.edu/technical-reports/circular-block-resampling-procedure-stationary-data)\n* [Politis, D. N. and Romano, J. P., The stationary bootstrap, Journal of the American Statistical Association 89, 1303-1313](https://www.jstor.org/stable/2290993)\n"
  provider: portfoliooptimizer
  method: POST
  path: "/assets/returns/simulation/bootstrap"
  encoding: json
  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 over the time period t; all the assetReturns arrays must have the same length"
              items: {
                type: "number"
              }
            }
          }
        }
      }
      bootstrapAverageBlockLength: {
        type: "number"
        description: "The average length of the blocks to use in case the bootstrap method is 'stationaryBlock', in time periods; if not provided, defaults to the inverse of 3.15 * the common length of the assetReturns arrays^1/3"
      }
      bootstrapBlockLength: {
        type: "integer"
        description: "The length of the blocks to use in case the bootstrap method is 'circularBlock', in time periods; if not provided, defaults to [3.15 * the common length of the assetReturns arrays^1/3]"
      }
      bootstrapMethod: {
        type: "string"
        description: "The bootstrap method to use"
        enum: ["iid", "circularBlock", "stationaryBlock"]
      }
      simulations: {
        type: "integer"
        description: "The number of simulations to perform"
      }
      simulationsLength: {
        type: "integer"
        description: "The number of time period(s) to simulate per simulation; if not provided, defaults to the common length of the assetReturns arrays"
      }
    }
  }
  output: {
    type: "object"
    required: ["simulations"]
    properties: {
      simulations: {
        type: "array"
        items: {
          type: "object"
          required: ["assets"]
          properties: {
            assets: {
              type: "array"
              description: "assets[i] is the data for the i-th asset"
              items: {
                type: "object"
                required: ["assetReturns"]
                properties: {
                  assetReturns: {
                    type: "array"
                    description: "assetReturns[t] is the simulated return of the i-th asset for the t-th time period, in percentage"
                    items: {
                      type: "number"
                    }
                  }
                }
              }
            }
          }
        }
      }
    }
  }
}