Exercise 8

This is an exercise in data analysis. It requires a computer and some appropriate data analysis program (IDL, Mathlab, ...). Two data sets should be analyzed. The first data set is generated by the Ornstein-Uhlenbeck process:

dx = - a x dt + dB (1)

where dB is a Gaussian white noise process.

The second data set is a part of the d¹8O record from the GRIP ice-core drilling in Greenland. The data points are 5.2 years averages,
beginning at present going backward in time. Both sets contain n = 17000 data points.

Estimate the drift coefficient a from the data realization of the Ornsein-Uhlenbeck process..

Highpass filter the data with a highpass running in octaves: $\omega_{cut} = 2^{-m} \omega_N$, where $m=0, ...,\log(n)/\log(2)$. (The Nyquist frequency is the maximum frequency, $\omega_N=\pi /\Delta T$)

Plot the highpass. For each highpass calculate the flatness factor $(f=\langle x^4\rangle /\langle x^2\rangle^2)$. Plot f as a function of m.

Are any of the two sets intermittent ?
 
 
 

1998-11-08