Time series cross-validation 4: forecasting the S&P 500

I finally got around to publishing my time series cross-validation package to github, and I plan to push it out to CRAN  shortly.

You can clone the repo using github for mac, for windows, or linux, and then run the following script to check it out:
This script downloads monthly data for S&P 500 (adjusted for splits and dividends), and, for each month form 1995 to the present, fits a naive model, an auto.arima() model, and an ets() model to the past 5 year's worth of data and uses those models to predict S&P 500 prices for the next 12 months (note that the progress bar doesn't update if you register a parallel backend.  I can't figure out how to fix this bug):

The naive model outperforms the arima and exponential smoothing models, both of which take into account seasonal patterns, trends, and mean-reversion!  Furthermore, we're not just using any arima/exponential smoothing model: at each step we're selecting the best model, based on the last 5 years worth of data.  (The ets model slightly outperforms the naive model at the 3 month horizon, but not the 2 month or 4 month horizons).

Forecasting equities prices is hard!