Harmonic Regression Models: A Comparative Review with Applications

Abstract

Strongly periodic series occur frequently in many disciplines. This paper reviews one specific approach to analyzing such series viz. the harmonic regression approach.In this paper the five major methods suggested under this approach are critically reviewed and compared, and their empirical potential highlighted via two applications. The out-of-sample forecast comparisons are made using the Superior Predictive Ability test, which specifically guards against the perils of data snooping. Certain tentative conclusions are drawn regarding the relative forecasting ability of the different methods.

Analysis of long-term fluctuations in stream flow time series: An application to Litani River, Lebanon

“…A further flexible approach to analyse nonstationary time series is based on the Dynamic Harmonic Regression of unobserved components, which is particularly useful for adaptive seasonal adjustment, signal extraction and interpolation over gaps, as well as forecasting and backcasting (Young et al 1999). A deep and extensive review of the all these methods is given by Artis et al (2007). In this study we use the Singular Spectrum Analysis (SSA), which is a method used to identify and quantify the temporal behaviour of a time series, like oscillations, cyclic events, scaling, as well as to identify any anomalous patterns that may exist according to a certain background or reference signal level.…”

Periodicity Detection Method for Small-Sample Time Series Datasets

“…When the data can be modeled by n harmonics, the number of parameters that are optimized by the fitting method is 3 n + 1,3 which is too many parameters for small datasets 4…”

“…The basic method is to calculate the power spectra by using the discrete Fourier transform (DFT) or the autocovariance matrix, and then to test the significance of each spectrum of a harmonic by outlier detection methods 3. A simple method uses quantiles of spectra to detect outliers.…”

Time frequency analysis of functional MR images

“…Absence of roots near the unit cycle prevents time-series from mistakenly being labeled as being generated by a non-stationary process [18]. Location of complex roots near the unit cycle may also result in Priestley's P (ω) test being less effective in forecasting the future values of process, as required in some meteorological and econometric applications, as shown by [108]; at the same time it has been applied successfully for harmonic analysis by [3,9,97] in meteorology and econometric applications. considered with confidence level below 99%.…”

“…Temporal correlation in noise also affects its variance and hence the signal to noise ratio (SNR) values. 3 We have used the variance σ 2 z instead of σ ǫ 2 to calculate the SNR of signal affected with temporally correlated noise. The experiments were performed at two levels of signal-to-noise ratios, SNR = 0.9 and 1.2.…”