Stats › Volatility and VIX › Volatility long memory
The long memory parameter is 0.4 in currencies, 0.35 in equities, and 0.15 lower if you drop the logarithm
| Series | Estimate | Standard error |
|---|---|---|
| Mark against dollar, log volatility | 0.387 | 0.028 |
| Yen against dollar | 0.413 | 0.028 |
| Yen against mark | 0.430 | 0.028 |
| Multivariate common estimate | 0.401 | not reported |
| Thirty US stocks, median | 0.349 | not per stock |
| The same, mean and standard deviation | 0.350 | 0.046 across stocks |
| Realised correlations across those stocks, median | 0.380 | not per stock |
Log periodogram regression estimates of the fractional integration parameter for log realised volatility. Currency estimates use 514 low frequency ordinates on 30 minute returns across 3,045 days from 1 December 1986 to 30 June 1999. Equity estimates use five minute returns on thirty index constituents across 1,366 trading days from 2 January 1993 to 29 May 1998, with an asymptotic standard error of 0.074 reported at a different bandwidth and no per stock standard errors in the table.
Fractional integration estimates for log realised volatility run from 0.387 to 0.430 across three currency pairs and have a median of 0.349 across thirty US stocks. The same estimates fall by about 0.15 when applied to realised standard deviation instead.
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