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Oversampling of stochastic processes
No full textDiscrete-time ARMA processes can be placed in a one-to-one correspondence with a set of continuous-time processes that are bounded in frequency by the Nyquist value of ð radians per sample period. It is well known that, if data are sampled from a continuous process of which the maximum frequency exceeds the Nyquist value, then there will be a problem of aliasing. However, if the sampling is too rapid, then other problems will arise that will cause the ARMA estimates to be severely biased. The paper reveals the nature of these problems and it shows how they may be overcome.Stochastic Differential Equations, Band-Limited Stochastic Processes, Oversampling
Investigating Economic Trends And Cycles
Get PDFMethods are described for extracting the trend from an economic data sequence and for isolating the cycles that surround it. The latter often consist of a business cycle of variable duration and a perennial seasonal cycle. There is no evident point in the frequency spectrum where the trend ends and the business cycle begins. Therefore, unless it can be represented by a simple analytic function, such as an exponential growth path, there is bound to be a degree of arbitrariness in the definition of the trend. The business cycle, however defined, is liable to have an upper limit to its frequency range that falls short of the Nyquist frequency, which is the maximum observable frequency in sampled data. This must be taken into account in fitting an ARMA model to the detrended data.
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