By averaging over a number of periodogram
values (using Hamming weights in our case), a smoother energy spectrum can be obtained (Fig.
max] in the region of alpha band 8-13 Hz was estimated calculating the power spectral density of the recorded EEG signal by means of Welch's averaged periodogram
Since the sine and cosine functions are orthogonal, their squared coefficients can be added for each frequency to produce a periodogram
where this periodogram
value can be interpreted in variance terms at a given frequency.
The power spectral density (PSD) for each segment was estimated using the periodogram
method (Proakis and Manolakis, 1996).
was calculated by the periodogram
method, which is the windowed discrete Fourier transform (DFT) of the biased estimate of autocorrelation sequence.
The results of the Fourier analysis showed that the higher value of the periodogram
and the higher spectral density corresponded to a period between 7 days and 8 days (Fig.
9) Smoothed periodogram
for growth rate of real premiums exhibits a significant peak, suggesting the same length of the dominant cycle (around 8.
2005): "A Spectral Analysis of the Sunspot Time Series Using the Periodogram
," ECE: 538, Statistical Signal Processing 1, Portland State University.
Figure 3 shows the periodogram
of the frequency analysis.
To test the null hypothesis that a series follows white-noise series, I fitted exponential distribution to periodogram
distribution (Kolmogorov-Smirnov test).
c]-selected model involved the following steps: 1) verification of the resemblance of residuals to white noise (ACF plots, Ljung-Box test, cumulative periodogram
test); 2) tests on the normality of residuals (Jarque-Bera and Shapiro-Wilks tests); and 3) confirmation of model stationarity, invertibility, and parameter redundancy (Shapiro et al.
Geweke and Porter-Hudak (1983) showed that using a periodogram
estimate, the least squares estimate of d using the above regression is distributed in large samples if the number of observations [n.