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Replicating Neely et al. (2014)

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 that are significant at conventional levels. This is the central finding of Neely et al. (2014): technical signals carry information beyond what macro variables provide.

References

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