Time for action - analysing the exchange rate

1. 1. Assume that we have loaded the currency exchange rate data into a variable curr and that we have 230 data points. The month index is given by:

octave:39> m_index = [0:229];

1. 2. The increasing trend is given by the end-points in the data:

octave:40> a = (curr(230)-curr(1))/229; b = curr(1);

1. 3. Subtracting the trend from the data:

octave:41> curr1 = curr a*m_index b;

1. 4. To ensure a data set with zero-mean, we use:

octave:42> curr2 = curr1-mean(curr1);

1. 5. We can then perform a Fourier analysis on the "trend-free" data using the ordinary frequency f = ω / 2π:

octave:43> N=230; n=[-N/2:N/2]; n(N+1) = []; freq = n./N;
octave:44> acurr = abs( fftshift( fft(curr2) ) );

1. 6. To plot the result, we use:

octave:45> plot(freq, acurr)

• The result is shown below for positive frequencies. Note that we may have an aliasing problem!

1. 7. Now the ordinary frequency of the main mode is:

octave:46> i = find( acurr==max(accur) ); freq(i)
ans = 0.030434...