Palgrave Handbook of Econometrics: Applied Econometrics

392 Structural Time Series Models notice that this is 1 at the zero frequency and decreases monotonically to zero asω approaches ...

Tommaso Proietti 393 using a three-year window, i.e.,K= 3 s, as a valid rule of thumb for macroeconomic time series. They also c ...

394 Structural Time Series Models which also expresses the gain of the filter. The latter is monotonically decreasing withλ; it ...

Tommaso Proietti 395 roots of the AR polynomial are a pair of complex conjugates with modulusρ−^1 and phase&; correspondingl ...

396 Structural Time Series Models We estimate this model for the US GDP series using the sample period 1947:1– 2006:4. For compa ...

Tommaso Proietti 397 Table 9.1 Frequency domain ML estimation results for quarterly US real GDP, 1947:1–2006:4 ARIMA MNZ Clark φ ...

398 Structural Time Series Models 1960 1980 2000 –2 0 2 4 US GDP growth rates 100 Δ yt –1.0 –0.5 0.0 0.5 1.0 –317.0 –316.5 –316. ...

Tommaso Proietti 399 1960 1980 2000 –5.0 –2.5 0.0 2.5 5.0 Real-time cyclical component 1960 1980 2000 –5.0 –2.5 0.0 2.5 5.0 Smoo ...

400 Structural Time Series Models The first expression shows that the weights for the extraction of the cycle sum to zero. Since ...

Tommaso Proietti 401 two orthogonal stationary processes as follows: ξt= ( 1 +L)rζt+( 1 −L)mκt φ(L) , (9.15) whereζtandκtare two ...

402 Structural Time Series Models parameterλ 1 andλ 2 , determined according to (9.7). Obviouslyλ 1 >λ 2. The trend- cycle de ...

Tommaso Proietti 403 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 0.2 0.4 0.6 0.8 1.0 BK Ideal Bandpass m = ...

404 Structural Time Series Models 1960 1980 2000 8 9 US GDP trend Series Trend – ARIMA(2,1,2) 1960 1980 2000 –0.025 0.025 US GDP ...

Tommaso Proietti 405 of periodicity that goes from one and a half years (6 quarters) to eight years (32 quarters). The gain of t ...

406 Structural Time Series Models 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0. ...

Tommaso Proietti 407 leakage from the non-stationary component. Moreover, the filter seriously distorts the evidence for the com ...

408 Structural Time Series Models that the sum of the AR coefficients on lagged inflation is unity,δ(L)=δ∗(L), where δ∗(L)is a ...

Tommaso Proietti 409 whereFtis the information set at timet. Basistha and Nelson (2007) estimate a bivariate model of output and ...

410 Structural Time Series Models This will be referred to as the GM specification. We shall consider two cases: (i) the sequenc ...

Tommaso Proietti 411 Table 9.2 ML estimation results for bivariate models of quarterly US log GDP (yt) and the consumer price in ...