TestCompressionTest.R

testRobustness <- function(t = (252 * 7)) {
  # Generate an underlying signal.
  signal <- sin(seq(1, t)) / 50
  signal <- signal - mean(signal)
  
  # For different noise levels
  sds <- seq(0.0, 0.020, 0.0005)
  cratios <- c()
  for (s in sds) {
    # Generate a noisy signal
    noise <- rnorm(t, mean = 0, sd = s)
    returns <- signal + noise
    # Binarize the data.
    returns[returns < 0] <- 0
    returns[returns > 0] <- 1
    # Convert into raw hexadecimal.
    hexrets <- bin2rawhex(returns)
    # Compute the compression ratio
    cratios <- c(cratios, length(memCompress(hexrets)) / 
                   length(hexrets))
    
    # Plot the returns for the eye ball test.
    dates <- seq.Date(Sys.Date(), Sys.Date() + (252 * 7) - 1, 1)
    # plot.ts(xts(signal + noise, order.by = dates))
    
    if (s %in% c(0.010, 0.015, 0.020)) {
      charts.PerformanceSummary(xts(signal + noise, order.by = dates))
    }
  }
  
  # Plot the compression ratios.
  plot(sds, cratios)
}


bettingStrategyProof <- function(t = (252 * 7), w = 5, sd = 0.02, sims = 30) {
  # Store market and strategy returns.
  markets <- NULL
  strats <- NULL
  
  for (i in 1:sims) {
    # Generate an underlying signal.
    signal <- sin(seq(1, t)) / 50
    signal <- signal - mean(signal)
    
    # Add some noise to get a return series.
    returns <- signal + rnorm(t, mean = 0.0, sd = sd)
    
    # Keep track of our weights.
    weights <- rep(0.0, w)
    for (t in (w + 1):length(returns)) {
      # Calculate the cumulative return to yesterday.
      cumret <- mean(1 + returns[(t-w):(t-1)]) - 1
      
      # Determine if we are risk-on or risk-off:
      if (cumret < 0) weights <- c(weights, 1.0)
      else weights <- c(weights, -1.0)
    }
    
    # Turn our hypothetical returns into time series.
    returns.weighted <- returns * weights
    dates <- dates <- seq.Date(Sys.Date(), Sys.Date() + 
                                 length(returns) - 1, 1)
    
    # Keep track of each of the market returns.
    if (is.null(markets)) markets <- xts(returns, order.by = dates)
    else markets <- merge.xts(markets, xts(returns, order.by = dates))
    
    # Keep track of each of the strategy returns.
    if (is.null(strats)) strats <- xts(returns.weighted, order.by = dates)
    else strats <- merge.xts(strats, xts(returns.weighted, order.by = dates))
  }
  
  # Plot the returns generated by our toy markets.
  charts.PerformanceSummary(xts(markets, order.by = dates), 
                            colorset = (1:ncol(markets)), 
                            legend.loc = NULL)
  
  # Plot the returns generated by out strategy.
  charts.PerformanceSummary(xts(strats, order.by = dates), 
                            colorset = (1:ncol(strats)), 
                            legend.loc = NULL)
  
  # Plot the averages over the simulations to make the picture clearer.
  mean.markets <- xts(rowSums(markets) / sims, order.by = index(markets))
  mean.strats <- xts(rowSums(strats) / sims, order.by = index(markets))
  charts.PerformanceSummary(merge.xts(mean.markets, mean.strats), 
                            legend.loc = NULL)
}