Titlebook: Measuring Business Cycles in Economic Time Series; Regina Kaiser,Agustín Maravall Book 2001 Springer Science+Business Media New York 2001

晚间

ARIMA Models and Signal Extraction,because, in general, the polynomial Ψ(.) will contain an infinite number of parameters. Therefore we use a rational approximation of the type . where .(.) and .(.) are finite polynomials in . of order . and ., respectively. Then we can write

Accommodation

Detrending and the Hodrick-Prescott Filter, e.g., Otnes and Enochson (1978)). The filters are typically expressed by means of the sine or tangent functions. For the sine-type case, the filter is represented, in the frequency domain, by its gain function which, for the two-sided filter, is given by

幻影

Some Basic Limitations of the Hodrick-Prescott Filter,of information that provides the final estimator, the latter cannot be less efficient. Besides, concurrent estimators, obtained with a one-sided filter, induce phase effects that distort the timing of events and harm early detection of turning points.

图表证明

Improving the Hodrick-Prescott Filter,or for the last quarters implies, in turn, a poor performance in early detection of turning points. Furthermore, as was just mentioned, direct inspection of Figure 5.3 shows another limitation of the HP filter: the cyclical signal it provides seems rather uninformative. Seasonal variation has been r

贵族

hypnotic

情感脆弱

https://doi.org/10.1007/978-1-4613-0129-5Stochastic Processes; calculus; correlation; time series; time series analysis

Offstage

Hodrick-Prescott Filtering Within a Model-Based Approach,What we have suggested in the previous section is to estimate the cycle in steps. First, the AMB method is used to obtain the trend-cycle estimator . (i.e., the noise-free SA series). In a second step, the HP filter is applied to ..

否认

上腭

Detrending and the Hodrick-Prescott Filter, e.g., Otnes and Enochson (1978)). The filters are typically expressed by means of the sine or tangent functions. For the sine-type case, the filter is represented, in the frequency domain, by its gain function which, for the two-sided filter, is given by