Monthly 200304 201911 ru4 industrial production index

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Monthly 2003:04 – 2019:11 RU4 Industrial Production Index Monthly 2006:04 – 2020:01 RU5 Passenger Car Sales (Imported Plus Domestic) Monthly 2006:04 – 2020:01 South Africa SA1 Real GDP Quarterly 1980:II – 2019:III SA2 Volume of production (manufacturing) Monthly 1980:04 – 2019:012 SA3 Merchandixe exports Monthly 1980:04 – 2020:01 SA4 New vehicules sold Monthly 1980:04 – 2019:12 SA5 Electricity production Monthly 1985:02 – 2019:12 United Kingdom UK1 Real GDP Quarterly 1980:II – 2019:IV UK2 Index of industrial production Monthly 1980:04 – 2019:12 UK3 Exports: value goods in Pounds Monthly 1980:04 – 2019:12 UK4 Passenger Car Registration Monthly 1980:04 – 2020:01 UK5 MFG Order Books Monthly 1980:04 – 2020:02 United States US1 Real GDP Quarterly 1947:II – 2019:IV US2 Industrial production index Monthly 1947:04 – 2020:01 US3 All employees, total nonfarm Monthly 1947:04 – 2020:01 US4 Real personal income excluding current transfer receipts Monthly 1959:04 – 2020:01 US5 Real manufacturing and trade industries sales Monthly 1967:04 – 2019:12 Note: The table reports the list of variables used in the models fitted to each economic region, along with frequency and coverage period. ECB Working Paper Series No 2381 / March 2020 36
A Online Appendix A.1 Full specification of the model The common factor f t affects all the observed variables; it evolves according to the following rule: f t = μ 0 (1 - s t ) + μ 1 s t + s t x t + e f,t , e f,t ∼ N (0 , σ 2 f ) . (A.1) The indicator s t ∈ { 0 , 1 } equals one whenever there is an abnormal episode; it is a two-state Markov-switching process whose evolution is summarized by p = Pr( s t = 1 | s t - 1 = 1) and q = Pr( s t = 0 | s t - 1 = 0). In case of an abnormal episode ( s t = 1), the common factor is augmented by an unobserved variable x t , which evolves as follows: x t = s t x t - 1 + (1 - s t ) v t , v t ∼ N (0 , σ 2 v ) . (A.2) Whenever there is an abnormal episode, the common factor is augmented by x t , which takes a random value at the beginning of the episode and then remains constant for the duration of the episode. Each monthly variable is assumed to be a combination of the common factor f t and an individual component u i,t : y m i,t = γ i f t + u i,t . (A.3) Each individual component is assumed to have P lags: u i,t = ψ i, 1 u i,t - 1 + ... + ψ i,P u i,t - P + e i,t , e i,t ∼ N (0 , σ 2 i ) . (A.4) In addition, following Mariano and Murasawa ( 2003 ), the growth rate of a variable observed with quarterly frequency (such as the GDP) can be expressed as a combination of its monthly unobserved growth rates as follows: y q j,t = 1 3 y m j,t + 2 3 y m j,t - 1 + y m j,t - 2 + 2 3 y m j,t - 3 + 1 3 y m j,t - 4 . (A.5) In turn, the monthly growth rates have the same decomposition as described in equation ( A.3 ), so that we can express each quarterly growth rate as a combination of the common factor and ECB Working Paper Series No 2381 / March 2020 37
the individual component, as follows: y q j,t = 1 3 γ j f t + 2 3 γ j f t - 1 + γ j f t - 2 + 2 3 γ j f t - 3 + 1 3 γ j f t - 4 + + 1 3 u j,t + 2 3 u j,t - 1 + u j,t - 2 + 2 3 u j,t - 3 + 1 3 u j,t - 4 . (A.6) As for the individual components of the quarterly series, they have the same structure as those described by equation ( A.4 ) for the monthly series.

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