Palgrave Handbook of Econometrics: Applied Econometrics

412 Structural Time Series Models 1950 1960 1970 1980 1990 2000 –5 0 5 Output gap 1950 1960 1970 1980 1990 2000 0 1 2 3 4 CPI qu ...

Tommaso Proietti 413 τ=(τ 1 ,...,τn), and: θ 1 = ⎛ ⎝θ− 01 +^1 στη^2 (i−^1 ) ∑ t χtχ′t ⎞ ⎠ − 1 , mφ 1 =φ 1 ⎛ ⎝θ− 01 mφ 0 +^1 ...

414 Structural Time Series Models 1950 1960 1970 1980 1990 2000 –5 0 5 1.0 0.5 0.0 –0.5 Output gap 0.0 0.2 0.4 0.6 0.8 1.0 Trend ...

Tommaso Proietti 415 The filtered probabilities,P(St|ηt,κt,), are obtained by the following discrete filter: (i) The filter is ...

416 Structural Time Series Models (g) GenerateT 11 (i),T 10 (i)= 1 −T 11 (i)andT 00 (i),T 01 (i)= 1 −T 00 (i)from the posterior: ...

Tommaso Proietti 417 1950 1960 1970 1980 1990 2000 –5 0 5 10 Output gap 1950 1960 1970 1980 1990 2000 0.5 1.0 Posterior probabil ...

418 Structural Time Series Models the International Monetary Fund (DeMasi, 1997), the Congressional Budget Office (2001), and th ...

Tommaso Proietti 419 of the unemployment rate, using a terminology due to Rünstler, 2002), is the first-order Taylor approximati ...

420 Structural Time Series Models Only a systematic sample of the cumulator variableYτcis available; in particular, the end of q ...

Tommaso Proietti 421 1950 1960 1970 1980 1990 2000 0 1 Monthly GDP and trend 1950 1960 1970 1980 1990 2000 –0.05 0.00 0.05 Month ...

422 Structural Time Series Models and Rossi (2004) and Proietti, Musso and Westermann (2007). The implications of the uncertaint ...

Tommaso Proietti 423 predictive validity, as possible bias would emerge. This criterion is adopted by a number of authors; e.g., ...

424 Structural Time Series Models The sources (ii) and (iii) typically arise because the individual components are unobserved an ...

Tommaso Proietti 425 and thephase Ph(ω)=arctan(−wI(ω)/wR(ω)). The former measures the amplitude effect of the filter, so that if ...

426 Structural Time Series Models and the corresponding detrending filters are: ψ ̃t|∞= λ|^1 −L| 4 1 +λ| 1 −L|^4 yt, ψ ̃t|t= θ(L ...

Tommaso Proietti 427 9.7.1 The augmented Kalman filter The Kalman filter (KF) is a fundamental algorithm for the statistical tre ...

428 Structural Time Series Models 9.7.3 Smoothing Smoothing deals with the estimation of the components and the disturbances bas ...

Tommaso Proietti 429 the joint posterior density: f(ς 0 ,...,ςn|Yn)=f(ςn|y) n∏− 1 t= 0 f(ςt|ςt+ 1 ,...,ςn;Yn). Conditional rando ...

430 Structural Time Series Models Apel, M. and P. Jansson (1999) A theory-consistent system approach for estimating potential ou ...

Tommaso Proietti 431 Doornik, J.A. (2006) Ox: An Object-Oriented Matrix Programming Language. London: Timberlake Consultants Pre ...