library(PerformanceAnalytics)

test_that("SmoothingIndex successfully demeans returns yielding mathematically correct ARMA estimates (fixes #86)", {
  skip_on_cran()
  
  # Reproduce reporter's highly off-center synthetic dataset
  set.seed(12345)
  unsmooth <- rnorm(25000, mean = 3, sd = 1.5)
  
  # Smooth them with theoretically true thetas = c(0.5, 0.3, 0.2)
  smooth <- stats::filter(unsmooth, c(0.5, 0.3, 0.2), sides = 1)
  
  # Ignore NAs generated by filter() lagging
  smooth_clean <- na.omit(as.numeric(smooth))
  
  # 1. Manually evaluate the corrected arima fit on demeaned data 
  fit_right <- arima(smooth_clean - mean(smooth_clean, na.rm = TRUE), c(0, 0, 2), include.mean = FALSE)
  thetas_right <- c(1, coef(fit_right)) / (1 + sum(coef(fit_right)))
  expected_thetas <- round(thetas_right, 2)
  
  # Assert that the theoretical math aligns perfectly with the reporter's evaluation (0.50, 0.30, 0.20)
  expect_equal(as.numeric(expected_thetas), c(0.50, 0.30, 0.20))
  
  # 2. Evaluate the PerformanceAnalytics method implementation
  # The smoothing index evaluates sum(thetas^2).
  # If thetas are (0.50, 0.30, 0.20), sum(thetas^2) = 0.25 + 0.09 + 0.04 = 0.38.
  
  si <- SmoothingIndex(smooth_clean, MIN=2, MAX=2)
  # si evaluates sum(xi^2) natively. 
  expect_equal(as.numeric(si), 0.38, tolerance = 1e-2)
})