how to calculate which leading which?
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Less about whether NQ leads ES or vice versa and more of a factor of intraday shifts of whether the SP futures lead the cash index and SPY at one time and then the SPY or cash index shows a lead over the futures at another due to arbitrage related correlation.
One reason it's helpful to have the ES, SPX, and SPY on screen at the same time with their respective intraday SRs to help see the bigger picture.
One reason it's helpful to have the ES, SPX, and SPY on screen at the same time with their respective intraday SRs to help see the bigger picture.
The scientific way to test for leading or lagging behavior is to calculate a lagged correlation.
For example, to test if the ES follows the NQ with a 1 minute lag, then you would take a sample of ES and NQ minute-by-minute prices, compute the change from one minute to the next, lag the NQ series (add 1 minute to each of the times), and then compute the correlation between the two series.
If, when the NQ goes up one minute, the ES goes up the next minute, you will get a positive correlation.
For example, to test if the ES follows the NQ with a 1 minute lag, then you would take a sample of ES and NQ minute-by-minute prices, compute the change from one minute to the next, lag the NQ series (add 1 minute to each of the times), and then compute the correlation between the two series.
If, when the NQ goes up one minute, the ES goes up the next minute, you will get a positive correlation.
As Foz said, lagged correlation is a very good way to measure what leads what. One trick is to perform the lagged correlation at a number of different lags to ensure that the results aren't corrupted by differential volatility. Also, if one uses this technique, it is important to use total least squares (rather than regular LS) to avoid biased estimates of the coefficients. Regular LS assumes that one of the time series is totally devoid of noise -- an assumption that is untrue when looking at two financial time series.
One can also tackle the problem in phase-space -- taking a difference of the phase values at each frequency after doing an Fourier Transform on the two time series. The delta-phase (in radians) times the period length of the frequency is an estimate of the timing difference between the two signals at that frequency. These delta-phase measurements will probably only be meaningful for moderate and lower frequencies -- the higher frequency components of the Fourier Transform will be too disturbed by phase wrapping and differences in volatility in the two price series.
Happy leading,
Traden4Alpha
One can also tackle the problem in phase-space -- taking a difference of the phase values at each frequency after doing an Fourier Transform on the two time series. The delta-phase (in radians) times the period length of the frequency is an estimate of the timing difference between the two signals at that frequency. These delta-phase measurements will probably only be meaningful for moderate and lower frequencies -- the higher frequency components of the Fourier Transform will be too disturbed by phase wrapping and differences in volatility in the two price series.
Happy leading,
Traden4Alpha