R/IndexMemberSelection.R

In IndexConstruction: Index Construction for Time Series Data

indexMemberSelection = function(market, price, vol, weighting = "market", weighting.all = "market", ic = "AIC", 
                                eval.seq = c("sequential", "all.together"), optimum = c("local", "global"), start.const = 1, steps = 1, 
                                fixed.value = NULL, derivation.period = 1, derivation.period.ic = 3, base.value = 1000, 
                                days.line) {
  
  if (class(price)[1] != "xts" | class(market)[1] != "xts") {
    stop("The data for 'price' and 'market' have to be in the format 'xts'. Please check the R library 'xts' to convert the data.")
  }
  if (class(vol)[1] != "xts" & is.null(vol) == FALSE) {
    stop("The data for 'vol' have to be in the format 'xts'. Please check the R library 'xts' to convert the data.")
  }
  if ((weighting != "market" & weighting != "volume") | (weighting.all != "market" & weighting.all != "volume")) {
    stop("The weighting scheme has to be either 'market' or 'volume'. Please chose either of the two options.")
  }
  if ((eval.seq != "sequential" & eval.seq != "all.together")) {
    stop("The evaluation scheme 'eval.seq' has to be either 'sequential' or 'all.together'. Please chose either of the two options.")
  }
  if ((optimum != "local" & optimum != "global")) {
    stop("The optimal point 'optimum' has to be either 'local' or 'global'. Please chose either of the two options.")
  }
  if ((ic != "AIC" & ic != "GCV" & ic != "GFCV" & ic != "SH" & ic != "Cp" & ic != "FPE")) {
    stop("The Information Criterion 'ic' has to be either 'AIC', 'GCV', 'GFCV', 'SH', 'Cp' or 'FPE'. Please chose either of the options.")
  }
  if ((weighting == "volume" | weighting.all == "volume") & is.null(vol)) {
    stop("When weighting by trading volume is chosen, a data entry for volume is required.")
  }
  if (length(days.line) < derivation.period.ic*2) {
    stop(paste("The number of periods to select the number of constituents for is not long enough. ", derivation.period.ic*2, " month of data are required for the derivation. Please provide a longer dataset or decrease the number of month over which the number of constituents shall be derived.", sep = ""))
  }
  if (length(days.line) > derivation.period.ic*2) {
    warning(paste("The number of periods to select the number of constituents for is larger than ", derivation.period.ic*2, " month. Is this intended?", sep = ""))
  }
  index_periods = max(floor(derivation.period.ic / derivation.period), 1)
  
  index_comp_numb = seq(start.const, dim(price)[[2]], steps)
  aic_matrix    = matrix(NA, nrow = 1, ncol = length(index_comp_numb))
  aic_compare    = matrix(NA, nrow = 1, ncol = length(index_comp_numb))
  max_coin_numb = c()
  crix = crix_all = crix_all_comp = c()
  
  current_lines         = days.line[seq(1, (derivation.period.ic + (derivation.period + 1)), 
                                        derivation.period)] + 1
  begin_line            = current_lines[2]
  
  ### total market index
  index_t_v_all         = index.comp(market = market, price = price, vol = vol, weighting = weighting.all, index.const = "all", base.value = base.value,
                                     index.periods = index_periods, order.derive = TRUE, current.lines.func = current_lines, 
                                     begin.line.func = begin_line, comp1 = FALSE, comp = TRUE, per = 1, numb.aic = 1, 
                                     crix = crix, crix.all = crix_all, crix.all.comp = crix_all_comp)
  max_coin_numb[1] = max(sapply(index_t_v_all[[2]], length))
  
  if (eval.seq == "all.together") {
    index_t_v_numb = index.comp(market = market, price = price, vol = vol, weighting = weighting, index.const = index_comp_numb[1], base.value = base.value,
                                index.periods = index_periods, order.derive = TRUE, current.lines.func = current_lines, 
                                begin.line.func = begin_line, comp1 = FALSE, comp = TRUE, per = 1, numb.aic = 1,
                                crix = crix, crix.all = crix_all, crix.all.comp = crix_all_comp)
  }
  
  ### indices with different numbers of constituents
  for (per1 in 1:(length(index_comp_numb)-1)){
    if (eval.seq == "sequential") {
      index_t_v_numb = index.comp(market = market, price = price, vol = vol, weighting = weighting, index.const = index_comp_numb[per1], base.value = base.value,
                                  index.periods = index_periods, order.derive = TRUE, current.lines.func = current_lines,
                                  begin.line.func = begin_line, comp1 = FALSE, comp = TRUE, per = 1, numb.aic = 1,
                                  crix = crix, crix.all = crix_all, crix.all.comp = crix_all_comp)
    }
    
    if (is.null(index_t_v_numb)) {break}
    d = c()
    p = c()
    for (l in 1:length(index_t_v_numb[[2]])) {
      if (l == 1) {
        for (k in 1:length(index_t_v_numb[[2]])) {
          if (eval.seq == "sequential") {
            p[k] = length(which(!is.na(index_t_v_numb[[2]][[k]][(index_comp_numb[per1] + 1):index_comp_numb[per1 + 1]]) == TRUE))
          } else if (eval.seq == "all.together") {
            p[k] = length(which(!is.na(index_t_v_numb[[2]][[k]][(index_comp_numb[1] + 1):index_comp_numb[per1 + 1]]) == TRUE))
          }
        }
      }
      if (eval.seq == "all.together" && any(p != per1*steps)) {break}
      if (eval.seq == "sequential") {
        a = price[paste(current_lines[l+1]-1, "::", current_lines[l+2] - 1, sep = ""), index_t_v_numb[[2]][[l]][(index_comp_numb[per1] + 1):index_comp_numb[per1 + 1]]]
      } else if (eval.seq == "all.together") {
        a = price[paste(current_lines[l+1]-1, "::", current_lines[l+2] - 1, sep = ""), index_t_v_numb[[2]][[l]][(index_comp_numb[1] + 1):index_comp_numb[per1 + 1]]]
      }
      
      a[a == 0] = NA
      a = na.locf(a, na.rm = FALSE)
      a = na.locf(a, fromLast = TRUE)
      b = diff(log(a))
      # this part is only relevant for sequential
      if (dim(b)[[2]] < max(p)) {
        while(dim(b)[[2]] < max(p)) {
          b = cbind(b, 0)
        }
      }
      #
      colnames(b) = 1:dim(b)[[2]]
      d = rbind(d,b[-1,])
    }
    if (eval.seq == "all.together" && any(p != per1*steps)) {break}
    if (per1 == 1) {
      plot_diff_first = diff(log(c(base.value, index_t_v_all[[1]]))) - diff(log(c(base.value, index_t_v_numb[[1]])))
    }
    plot_diff = diff(log(c(base.value, index_t_v_all[[1]]))) - diff(log(c(base.value, index_t_v_numb[[1]])))
    data_x = d
    erg = lm(plot_diff ~ data_x - 1)
    
    ### evaluation of current index with an IC method
    aic_compare[1, per1] = IndexEval(plot.diff = erg$residuals, index.numb = length(erg$coefficients), ic = ic, plot.diff.first = plot_diff_first)
    aic_matrix[1, per1] = IndexEval(plot.diff = plot_diff, index.numb = 0, ic = ic, plot.diff.first = plot_diff_first)
    
    if (optimum == "local" && eval.seq == "sequential") {
      if (aic_matrix[1, per1] <= aic_compare[1, per1]){
        break
      }
    } else if (optimum == "local" && eval.seq == "all.together") {
      if (per1 >= 2){
        if (aic_compare[1, per1-1] <= aic_compare[1, per1]){
          break
        }
      } else if (per1 == 1) {
        if (aic_matrix[1, per1] <= aic_compare[1, per1]){
          break
        }
      }
    }
  }
  
  ### choice of optimal index members
  if (optimum == "local" && eval.seq == "sequential") {
    if (per1 > 1) {
      index_members = index_comp_numb[per1 - 1]
    } else if (per1 == 1) {
      index_members = index_comp_numb[per1]
    }
  } else if (optimum == "local" && eval.seq == "all.together") {
    index_members = index_comp_numb[per1]
  } else if (optimum == "global" && eval.seq == "sequential") { # works for Sequential and AllTogether
    index_members = which.min(aic_compare[1,]) * steps
  } else if (optimum == "global" && eval.seq == "all.together") { # works for Sequential and AllTogether
    index_members = which.min(c(aic_matrix[1, 1], aic_compare[1,])) * steps
  }
  
  return(index_members)
}