# 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

- 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.