Optimal Forecasting of Noncausal Autoregressive Time Series

Abstract

In this paper, we propose a simulation-based method for computing point and density forecasts for univariate noncausal and non-Gaussian autoregressive processes. Numerical methods are needed to forecast such time series because the prediction problem is generally nonlinear and no analytic solution is therefore available. According to a limited simulation experiment, the use of a correct noncausal model can lead to substantial gains in forecast accuracy over the corresponding causal model. An empirical application to U.S. inflation demonstrates the importance of allowing for noncausality in improving point and density forecasts.JEL Classification: C22, C53, C63

Autoregression-based estimation of the new Keynesian Phillips curve

“…where b f and b b are the ML estimates, and E t t+1 can be computed as a forecast from the estimated AR(r, s) as shown by Lanne et al (2010). Neither the marginal cost variable x t nor the coe¢ cient as such are not, of course, identi…able, but the time series of x t are informative about the properties of the implied drivers of the in ‡ation series.…”

Has US inflation really become harder to forecast?

“…Therefore, following Lanne and Saikkonen (2008), we specify Student's t-distribution for t . In addition to these authors, also Lanne et al (2009Lanne et al ( , 2010 have shown this distribution to …t U.S. in ‡ation series well.…”

“…In addition to the univariate causal and noncausal AR models, random walk forecasts of Atkeson and Ohanian (2001) and moving average forecasts are consid- we only consider iterated multistep forecasts that SW found quantitatively quite similar to their direct forecasts. Lanne and Saikkonen (2008) propose a model selection procedure that was employed in forecasting by Lanne et al (2010). However, in this paper all noncausal forecasts are based on the recursively estimated …xed AR(0,4) model that should be adequate for quarterly data.…”

“…Speci…cally, they claim that before 1983, PC models were superior to the univariate autoregressive (AR) model, but after 1984, the situation has reversed.We argue that SW's benchmark model is not the appropriate univariate model, especially in the 1970-1983 period, but, in fact, in ‡ation dynamics are better captured by a noncausal, instead of a conventional causal AR model. This claim is backed up by the …ndings of Lanne and Saikkonen (2008) and Lanne et al (2009) for the CPI in ‡ation and Lanne et al (2010) for the GDP price in ‡ation.…”

“…However, as shown by Lanne and Saikkonen (2008), and Lanne et al (2009Lanne et al ( , 2010, the errors of AR models estimated for U.S. in ‡ation series are not well characterized as Gaussian, but exhibit excess kurtosis. In those papers, Student's t-distribution is assumed for the errors and it turns out to provide a good …t.…”