Understanding the Lomb–Scargle Periodogram

Bootstrapping the log-periodogram regression

Semiparametric estimation of the memory parameter in economic time series raises the problem of the small sample size and the poor approximation of the asymptotic distribution to the finite sample counterpart. This paper considers the bootstrap to improve the finite sample distribution of the popular log peridogram regression and shows that it can significantly reduce the error in the coverage ...

The Periodogram at the Fourier Frequencies 1

In the time series literature one can often nd the claim that the periodogram ordinates of an iid sequence at the Fourier frequencies behave like an iid standard exponential sequence. We review some results about functions of these periodogram ordinates, including the convergence of extremes, point processes, the empirical distribution function and the empirical process. We show when the analog...

Significance Tests for Periodogram Peaks

We discuss methods currently in use for determining the significance of peaks in the periodograms of time series. We discuss some general methods for constructing significance tests, false alarm probability functions, and the role played in these by independent random variables and by empirical and theoretical cumulative distribution functions. We also discuss the concept of “independent freque...

Detecting non-sinusoidal periodicities in observational data using multi-harmonic periodograms

We address the problem of assessing the statistical significance of candidate periodicities found using the so-called ‘multi-harmonic’ periodogram, which is being used for detection of non-sinusoidal signals, and is based on the least-squares fitting of truncated Fourier series. The recent investigation (Baluev 2008) made for the LombScargle periodogram is extended to the more general multi-har...

Log-periodogram regression in asymmetric long memory