Determination of Relevant Frequencies and Modeling Varying Amplitudes of Harmonic Processes

Abstract

When a process is dominated by few important frequencies the observations of this process can be modelled by a harmonic process (Bloomfield (2000)). If the amplitudes of these dominating frequencies vary over time their dominance may not be apparent during the whole process. To discriminate between frequencies relevant for such a process we determine the distribution of the periodogram ordinates, and use this distribution to derive a procedure to assess the relevance of the frequencies. This procedure uses the standardized median (Gather and Schultze (1999)) to determine the variance of the error process. In a simulation study we show that this procedure is very efficient even under difficult conditions such as a low signal-to-noise ratio or AR(1) disturbances. Furthermore, we show that the necessary transformation to estimate the amplitudes from periodogram ordinates leads to a good normality approximation which makes it especially easy to model the development of the amplitudes from these estimates.