Smoothing market volatility

Overview

This page compares a variety of standard smoothers. The data is based on a Value Weighted Return on the market (monthly) from the time period 1920 through to 1995. The goal is to find the historical volatility structure.

The data is available as a JMP file FinMark.jmp or as raw text file FinMark.txt. The smoothers considered are

Splines
Running medians
Lowess
Super smoother

Description of figures

Figure 1. The monthly returns plotted against time.
Figure 2. The monthly returns squared plotted against time.
Figure 3. The log of the monthly returns squared plotted against time.
Figure 4. Smoothing spline (default through cross-validation).
Figure 5. A variety of splines.
Figure 6. Tukey's runnning medians.
Figure 7. Tukey's runnning medians, with a window size of 21.
Figure 8. Tukey's runnning medians, with the residuals smoothed.
Figure 9. Lowess smooth, default (f = 2/3).
Figure 10. A variety of Lowess smooths.
Figure 11. Super smoother, (default through cross-validation).
Figure 12. A variety of super smoothers.

Figure 1. The monthly returns plotted against time.

Figure 2. The monthly returns squared plotted against time.

Figure 3. The log of the monthly returns squared plotted against time.

Figure 4. Smoothing spline (default through cross-validation).

Figure 5. A variety of splines.

Figure 6. Tukey's runnning medians.

Figure 7. Tukey's runnning medians, with a window size of 21.

Figure 8. Tukey's runnning medians, with the residuals smoothed.

Figure 9. Lowess smooth, default (f = 2/3).

Figure 10. A variety of Lowess smooths.

Figure 11. Super smoother, (default through cross-validation).

Figure 12. A variety of super smoothers.