Replicating Neely et al. (2014) • forecastdom

This article applies cw_test() to the nrtz2014 bundled dataset: the 14 binary technical indicators used in Neely, Rapach, Tu and Zhou (2014). The benchmark is the prevailing historical mean and the alternative is a bivariate predictive regression on a single technical indicator.

library(forecastdom)
data(nrtz2014)

Helpers

recursive_forecasts <- function(y, x, R) {

  P <- length(y) - R
  e1 <- e2 <- f1 <- f2 <- numeric(P)
  
  for (j in seq_len(P)) {

    ty <- y[1:(R + j - 1)]
    tx <- x[1:(R + j - 1)]
    f1[j] <- mean(ty)
    fit   <- lm(yt ~ xlag, data = data.frame(yt = ty[-1], xlag = tx[-length(tx)]))
    f2[j] <- as.numeric(predict(fit, newdata = data.frame(xlag = tx[length(tx)])))
    e1[j] <- y[R + j] - f1[j]
    e2[j] <- y[R + j] - f2[j]

  }

  list(e1 = e1, e2 = e2, f1 = f1, f2 = f2)

}

run_cw <- function(data, predictors, R) {

  do.call(rbind, lapply(predictors, function(p) {

    fc  <- recursive_forecasts(data$eq_prem, data[[p]], R = R)
    res <- cw_test(fc$e1, fc$e2, fc$f1, fc$f2)

    data.frame(predictor = p,
               R2OS_pct  = unname(res$r2os),
               CW_stat   = unname(res$statistic),
               p_value   = unname(res$pvalue))

  }))

}

Technical indicators

Initial window of 181 months (1950-12 to 1965-12); out-of-sample period 1966-01 to 2011-12.

preds_nr <- c("MA_1_9", "MA_2_12", "MOM_9", "MOM_12", "VOL_2_12")

knitr::kable(
  run_cw(nrtz2014, preds_nr, R = 181), digits = 3, row.names = FALSE,
  col.names = c("Predictor", "$R^2_{OS}$ (%)", "CW stat", "$p$-value"))

Predictor	$R^2_{OS}$ (%)	CW stat	$p$ -value
MA_1_9	0.235	0.981	0.163
MA_2_12	0.779	1.693	0.045
MOM_9	0.108	0.613	0.270
MOM_12	0.154	0.686	0.247
VOL_2_12	0.331	1.121	0.131

Takeaway

Technical indicators deliver positive $R^2_{OS}$ with Clark-West statistics significant at conventional levels — the central finding of Neely et al. (2014) that technical signals carry information beyond what macro variables provide.

References

Clark, T. E. and West, K. D. (2007). Approximately normal tests for equal predictive accuracy in nested models. Journal of Econometrics, 138(1), 291-311.
Neely, C. J., Rapach, D. E., Tu, J. and Zhou, G. (2014). Forecasting the equity risk premium: The role of technical indicators. Management Science, 60(7), 1772-1791.