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Volume 3, Issue 3 2011 Article 2 Journal of Time Series Econometrics Noncausal Autoregressions for Economic Time Series Markku Lanne, University of Helsinki Pentti Saikkonen, University of Helsinki Recommended Citation: Lanne, Markku and Saikkonen, Pentti (2011) "Noncausal Autoregressions for Economic Time Series," Journal of Time Series Econometrics: Vol. 3: Iss. 3, Article 2. DOI: 10.2202/1941-1928.1080 ©2011 De Gruyter. All rights reserved. Noncausal Autoregressions for Economic Time Series Markku Lanne and Pentti Saikkonen Abstract This paper is concerned

with the computation of the generalized impulse response function. Empirical results are reported in Section 4. Finally, Section 5 concludes. 2 Noncausal autoregression The starting point of our analysis is the noncausal AR model of Lanne and Saikkonen (2011) that can be described as follows. 2 An alternative formulation is proposed by Breidt et al. (1991). However, as Lanne and Saikkonen (2011) point out, their model has the advantages that it is straightforward to test for the specified number of leads and lags and inference on the autoregressive parameters is

future and past errors, implying that future errors are predictable given the realized observations of the variable in question. An early discussion of noncausal autoregressions is provided by Breidt et al. (1991). Recently, Lanne and Saikkonen (2011b) introduced a useful reparametrization of the noncausal AR process allowing for explicit dependence on both leads and lags of the variable in question. A stationary noncausal AR( r,s ) process y t , depending on r lags and s leads (with r and s both positive integers), is defined by: with ϕ ( L )=1– ϕ 1 L – … ϕ