S&P 500 Realized-Variance Forecasts (Li, Liao & Quaedvlieg, 2022)

Daily 5-minute realized variance of the S&P 500 with one-step-ahead out-of-sample forecasts from six competing models, plus lagged VIX as a conditioning variable. The forecasts and realized variances are from the replication package of Li, Liao and Quaedvlieg (2022) on Zenodo; the underlying RV series is from Bollerslev, Patton and Quaedvlieg (2016).

Usage

llq2022

Format

A data frame with 3,071 rows and 9 variables. Sample period is 2001-05-11 to 2013-08-30 (daily, trading days).

date: Trading-day Date.
rv: Realized variance of the S&P 500 (5-minute returns), in percent-squared units.
AR1: AR(1) forecast of rv.
AR22: AR(22) forecast of rv.
AR22_Lasso: AR(22) forecast with adaptive lasso (Matlab).
HAR: HAR forecast of Corsi (2009).
HARQ: HARQ forecast of Bollerslev, Patton and Quaedvlieg (2016).
ARFIMA: Fractionally integrated AR forecast.
vix_lag: VIX close from the previous trading day, used as conditioning variable.

Source

Replication package of Li, Liao and Quaedvlieg (2022), https://zenodo.org/record/4884813. Realized variance series adapted from Bollerslev, Patton and Quaedvlieg (2016), retrieved from Quaedvlieg's website. VIX from CBOE.

References

Bollerslev, T., Patton, A. J. and Quaedvlieg, R. (2016). Exploiting the errors: a simple approach for improved volatility forecasting. Journal of Econometrics, 192(1), 1-18.

Corsi, F. (2009). A simple approximate long-memory model of realized volatility. Journal of Financial Econometrics, 7(2), 174-196.

Li, J., Liao, Z. and Quaedvlieg, R. (2022). Conditional Superior Predictive Ability. Review of Economic Studies, 89(2), 843-875.

Examples

data(llq2022)
head(llq2022)
#>         date        rv       AR1      AR22 AR22_Lasso       HAR      HARQ
#> 1 2001-05-11 0.7243850 1.0698651 1.1289011   1.171590 1.1434876 1.0010733
#> 2 2001-05-14 0.3354836 1.1244540 1.2136301   1.087886 1.1011758 1.0339046
#> 3 2001-05-15 1.0203289 0.9767768 1.2081933   1.022675 0.9649115 0.8087672
#> 4 2001-05-16 1.1973001 1.2370204 1.5126464   1.397227 1.1236571 1.1482442
#> 5 2001-05-17 1.0602978 1.3043962 0.9361198   1.249116 1.1766679 1.2428822
#> 6 2001-05-18 0.7158839 1.2529316 1.0499908   1.165115 1.1594285 1.1759845
#>     ARFIMA vix_lag
#> 1 1.165878   24.00
#> 2 1.157042   23.54
#> 3 1.026976   24.26
#> 4 1.166857   23.71
#> 5 1.248433   21.89
#> 6 1.238309   21.47
# Squared-error losses per model:
losses <- (llq2022[, c("AR1","AR22","AR22_Lasso","HAR","HARQ","ARFIMA")] -
             llq2022$rv)^2
colMeans(losses)
#>        AR1       AR22 AR22_Lasso        HAR       HARQ     ARFIMA 
#>   3.909076   5.519847   3.377019   3.228492   2.685493   2.738671