Ec821: Time Series Econometrics Spring 2003 Notes Section 10 Part 1
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0 0 t t t t t = + ()cos () + () sin () 1. Spectral analysis Y , Y Y Y t. Y Y Y Y ω ωt dω ω ωt dω Y. Our focus thus far has been on considering how the timeseries reacts to a sequence of innovations and the implications of the relationship between and for the covariance (or correlation) between and at distinct dates and We speak of this as analysing the properties of in the time domain. We might also consider the timeseries behavior in the frequency domain, where is described as a weighted sum of periodic (sine and cosine) functions: (1.1) This is known as the spectral representation of the timeseries, and its study is known as spectral analysis. The goal will be to determine how important cycles of different frequencies are in accounting for the behavior of The two types of analysis (time-domain and frequency-domain modelling) are not mutually exclusive. Any CS process has both a time-domain representation and a frequency-domain representation, and any feature of the data that can be described by one representation can be equally well described by the other representation. For some features, the time-domain description may be simpler or more convenient to work with, while for other features the frequency-domain representation may be simpler.
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تاریخ انتشار 2003