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# Spectral analysis time series

Spectral analysis time series

In Time series analysis, spectral analysis implies a statistical technique applied in the characterizing and analysing the sequenced data. These sequenced data are the data, which have been taken in one or more in more than one dimensional space and time. Examples of such data includes the population density on the roads, or the observations of the daily births on the roads. Therefore, the spectral analysis in time series implies the decomposition of the sequential data in to oscillations of different lengths or scales. There are two basic reasons for decomposition. First is that it makes the manipulation of data easy when it is in spectral domain. Second, the decomposition reveals have necessary statistical descriptions of the data, which may indicate the important factors that affect or produce such data.

Roles of Spectral Analysis in Time Series

There are several roles prayed by spectral analysis in the time series analysis. These include (1) estimation, (2) hypothesis testing and hypothesis suggestion (3) description and reduction of data. In any field of study, where the phenomena being studied could be characterised according to its behaviour of the frequency domain, there is need to estimate the spectral density function and other spectral properties, which are associated with the stationary multiple time series. In addition, spectral analysis in time series is also applied in testing the fitness of the various models. This implies the goodness of fit of various models which could be discussed by the use of various sample spectra of the fitted model residuals. As a result, suggests the possible fitted model, including the explanatory variable and mechanism to fit in the time series using the suggested spectra.

Tests done in spectral analysis

The spectral analysis transforms the time series data in to its coordinates in space frequencies, and then analyses these characteristics in isolated space. The coordinates makes it possible to extract the magnitudes and the phase. It is possible to develop the representation of the spectral density and the periodogram. By studying the spectral density, it is possible to identify the seasonal components and the noise components. In this case, the spectral density corresponds to the transformation of a continuous time series, which implies that there is only a little number of the equally spaced data. This implies that there is need to obtain the discrete frontier coordinates and the periodogram. The pereiodogram is then applied to obtain the spectral density estimates, which best estimated the spectrum.