Convolution‐based filtering and forecasting: An application to WTI crude oil prices

Abstract

We introduce new methods of filtering and forecasting for the causal-noncausal convolution model. This model represents the dynamics of stationary processes with local explosions, such as spikes and bubbles, which characterize the time series of commodity prices, cryptocurrency exchange rates, and other financial and macroeconomic variables. The convolution model is a structural mixture of independent latent causal and noncausal component series. We propose an algorithm that recovers the latent components by evaluating the filtering density of one component, conditional on the observed past, present, and future values of the time series. Forecasts of the observed time series are obtained as a combination of filtered causal and noncausal component forecasts. The new filtering and forecasting methods are illustrated in a simulation study and compared with the results obtained from the mixed causal-noncausal autoregressive MAR model in application to WTI crude oil prices.

Forecasting bubbles with mixed causal-noncausal autoregressive models

“…Although commodities are a competitive market with many buyers and sellers, there is evidence that their dynamics can be explained with noncausal autoregressive models. Hecq and Voisin (2021) found evidence of noncausality in monthly Nickel prices, Gourieroux, Jasiak, and Tong (2021); Hecq and Voisin (2019) in crude oil monthly prices, Karapanagiotidis (2014) in 25 commodity futures price, including soft, precious metals, energy, and livestock sectors and Lof and Nyberg (2017) in the exchange rates of commodity exporters. All series do not share the same trend, but they appear to be affected by similar shocks.…”

A short term credibility index for central banks under inflation targeting: an application to Brazil

“…(and not only weak white noise) non-Gaussian to ensure the identifiability of the causal and the noncausal part (Breidt et al, 1991). There is a increasing literature making use of MAR models; see among others Karapanagiotidis (2014), Hencic and Gouriéroux (2015), Gouriéroux and Jasiak (2016), Lof and Nyberg (2017), Hecq and Sun (2021), Bec et al (2020), Gourieroux et al (2021b), Gourieroux et al (2021a).…”

Modelling and forecasting economic time series with mixed causal-noncausal models

“…There is a increasing literature making use of MAR models; see among others Karapanagiotidis (2014), Hencic and Gouriéroux (2015), , Lof and Nyberg (2017), Hecq and Sun (2021), Bec, Nielsen, and Saïdi (2020a), Gourieroux, Jasiak, and Tong (2021), Gourieroux, Hencic, and Jasiak (2021).…”

“…The increasing interest in MAR models and their numerous empirical applications in the literature demonstrate their versatility and the benefits of using these models in many areas of applications. MAR models have proven to provide a better fit than purely causal models for inflation rates (Lanne and Saikkonen, 2011), Bitcoin prices (Hencic and Gouriéroux, 2015), crude oil prices (Gourieroux, Jasiak, and Tong, 2021) and many other commodity prices and financial times series (see among others Hecq, Lieb, and Telg, 2016;Fries and Zakoïan, 2019a). However, the literature employing and analysing MAR models for prediction purposes is still very limited.…”