Characterizing Cycles
3 important questions on Characterizing Cycles
What about the autocorrelation function?
Normalized or standardized by the standard deviations. Therefore superior interpretability of correlations. This is obtained by dividing the Y(t) by the Y(0), i.e. just the variance.
What about a lag operator?
Operates on a serie by lagging itself. Usually written with a polynominal in the lag operator (to the power). The polynomial number states the displacement/lagged time. Actually, delta is a first-order polynomial in the lag operator.
Basically the function becomes a weighted sum or distributed lag of current and past values. Infinite-order polynomial are very important. Maybe weird as that implies infinite parameters in a finite sample. They are however very central in modelling an forecasting. Which is explained by WOLD theorem.
Basically the function becomes a weighted sum or distributed lag of current and past values. Infinite-order polynomial are very important. Maybe weird as that implies infinite parameters in a finite sample. They are however very central in modelling an forecasting. Which is explained by WOLD theorem.
What about rational distributed lags?
Infinite polynomial B(L) can be a ratio of finite-order polynomials Those are called rational polynomials and the distributed lags constructed from them are rational distributed lags. Via this way there are not infintely many free paramters in the B(L) polynomial. What if approximately rational? That will be an approximation of the WOLD representation using rational distributed lags, just like ARMA and ARIMA.
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