One-dimensional series of data

1) Choose a one-dimensional series of data, from either the dataset you described in the midterm, or from the temperature data I gave you in class.

2) Plot the whole series, using any computer plotting tool you wish.

3) Answer the question: Is it appropriate to take the variability about a mean value for this data set? The answer will be no if it includes an abrupt transition across which the behavior changes drastically. In this case you may break the series into two pieces on the sides of the transition. The answer will be no also if the data is dominated by a trend. In this case, you would need to find the trend by performing a linear fit (using linear regression or a degree-one polynomial fit) to the data, so that you can remove the trend.

4) After taking care of item 3, compute the mean, standard deviation, and find the power spectrum of the series, and/or at least two of the subseries if the set needs to be so divided. The best way of doing the power spectrum is to take the Fourier transform of the autocovariance function. (I described the autocovariance in class; there is a tool in numpy that does this that I have given you in the example I posted.) If the autocovariance is too difficult for some reason, you have permission to simply take the Fourier transform of the series; however, the spectra obtained by taking longer and longer series of data will not converge.

5) Try to identify and interpret one or more peaks in the data.

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