ForeComp (version 0.9.0)

Plot_Tradeoff: Visualizes the size distortion maximum power loss tradeoff from the Diebold-Mariano test for equal predictive accuracy

Description

`Plot_Tradeoff` creates a plot to show sensitivity of statistical significance to the choice of bandwidth and how size distortion and maximum power loss vary. It is designed for the Diebold-Mariano test for equal predictive accuracy (Diebold and Mariano, 2002). For a size-power tradeoff plot, see Lazarus, Lewis, Stock, and Watson (2018) and Lazarus, Lewis, and Stock (2021).

Usage

Plot_Tradeoff(
  data,
  f1 = NULL,
  f2 = NULL,
  y = NULL,
  loss_function = NULL,
  n_sim = 1000,
  m_set = NULL,
  verbose = TRUE,
  no_m_label = FALSE
)

Value

A list of length 2. The first element is a ggplot2 object of the size-power tradeoff. The second element is the underlying data used to construct the plot in element 1.

Arguments

data

A data frame.

f1

Column containing forecaster 1's predictions. Should be a string.

f2

Column containing forecaster 2's predictions. Should be a string.

y

Column containing the realized value for the outcome variable. Should be a string.

loss_function

The transformation applied to the forecast error. Defaults to squared error loss. The user supplied function should take two inputs and a scalar output, loss = loss_function(f, y). For example, quadratic loss function would be defined as loss_function=function(f,y){(f-y)^2}.

n_sim

The number of simulations used to generate the ARIMA model. Defaults to 1,000.

m_set

The truncation parameter. Defaults to c(1:10, seq( 11, floor(nrow(data)/2), 10)). For a standard long-run variance calculation (for example, using Bartlett kernel), it controls the number of terms used in estimating the autocovariance matrix. It should be a vector of integers with the values of M you would like to plot.

verbose

TRUE to print out the progress to the console. Defaults to TRUE.

no_m_label

TRUE to plot without m labels. Defaults to FALSE.

Author

Nathan Schor and Minchul Shin

References

Diebold, F. X. & Mariano, R. S. (2002), Comparing Predictive Accuracy, Journal of Business & Economic Statistics, 20(1), 134-144.

Lazarus, E., Lewis, D. J., Stock, J. H. & Watson, M. W. (2018), HAR Inference: Recommendations for Practice, Journal of Business & Economic Statistics, 36(4), 541-559.

Lazarus, E., Lewis, D. J. & Stock, J. H. (2021), The Size-Power Tradeoff in HAR Inference, Econometrica, 89(5), 2497-2516.

Examples

# A typical example
set.seed(1234)
output = Plot_Tradeoff(
  data = TBILL,
  f1   = "SPFfor_Step1",
  f2   = "NCfor_Step1",
  y    = "Realiz1",
  m_set = seq(from = 1, to = 70, by = 10)
)
output[[1]] # The first element is a ggplot2 object of the size-power tradeoff.
output[[2]] # The second element is the underlying data used to construct the plot in element 1.

# An example with a user supplied loss function
# To use the mean absolute error as a loss function rather than a quadratic loss function
set.seed(1234)
output = Plot_Tradeoff(
  data = TBILL,
  f1   = "SPFfor_Step1",
  f2   = "NCfor_Step1",
  y    = "Realiz1",
  loss_function = function(f,y){ abs(f-y) },
  m_set = seq(from = 1, to = 50, by = 10)
)

# An example without (f1, f2, y). The function will take the first three columns and use them
set.seed(1234)
tmpdata = TBILL[, c("SPFfor_Step1", "NCfor_Step1", "Realiz1")] # data with [f1, f2, y]
Plot_Tradeoff(
  data = tmpdata,
  m_set = seq(from = 1, to = 50, by = 10)
)