Abstract
This paper introduces the notion of common non-causal features and proposes tools to detect them in multivariate time series models. We argue that the existence of co-movements might not be detected using the conventional stationary vector autoregressive (VAR) model as the common dynamics are present in the non-causal (i.e. forward-looking) component of the series. We show that the presence of a reduced rank structure allows to identify purely causal and non-causal VAR processes of order P>1 even in the Gaussian likelihood framework. Hence, usual test statistics and canonical correlation analysis can be applied, where either lags or leads are used as instruments to determine whether the common features are present in either the backward- or forward-looking dynamics of the series. The proposed definitions of co-movements are also valid for the mixed causal—non-causal VAR, with the exception that a non-Gaussian maximum likelihood estimator is necessary. This means however that one loses the benefits of the simple tools proposed. An empirical analysis on Brent and West Texas Intermediate oil prices illustrates the findings. No short run co-movements are found in a conventional causal VAR, but they are detected when considering a purely non-causal VAR.
| Original language | English |
|---|---|
| Pages (from-to) | 697-715 |
| Number of pages | 19 |
| Journal | Oxford Bulletin of Economics and Statistics |
| Volume | 81 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1 Jun 2019 |
| Externally published | Yes |
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Detecting Co-Movements in Non-Causal Time Series. / Cubadda, Gianluca; Hecq, Alain; Telg, Sean.
In: Oxford Bulletin of Economics and Statistics, Vol. 81, No. 3, 01.06.2019, p. 697-715.Research output: Contribution to Journal › Article › Academic › peer-review
TY - JOUR
T1 - Detecting Co-Movements in Non-Causal Time Series
AU - Cubadda, Gianluca
AU - Hecq, Alain
AU - Telg, Sean
PY - 2019/6/1
Y1 - 2019/6/1
N2 - This paper introduces the notion of common non-causal features and proposes tools to detect them in multivariate time series models. We argue that the existence of co-movements might not be detected using the conventional stationary vector autoregressive (VAR) model as the common dynamics are present in the non-causal (i.e. forward-looking) component of the series. We show that the presence of a reduced rank structure allows to identify purely causal and non-causal VAR processes of order P>1 even in the Gaussian likelihood framework. Hence, usual test statistics and canonical correlation analysis can be applied, where either lags or leads are used as instruments to determine whether the common features are present in either the backward- or forward-looking dynamics of the series. The proposed definitions of co-movements are also valid for the mixed causal—non-causal VAR, with the exception that a non-Gaussian maximum likelihood estimator is necessary. This means however that one loses the benefits of the simple tools proposed. An empirical analysis on Brent and West Texas Intermediate oil prices illustrates the findings. No short run co-movements are found in a conventional causal VAR, but they are detected when considering a purely non-causal VAR.
AB - This paper introduces the notion of common non-causal features and proposes tools to detect them in multivariate time series models. We argue that the existence of co-movements might not be detected using the conventional stationary vector autoregressive (VAR) model as the common dynamics are present in the non-causal (i.e. forward-looking) component of the series. We show that the presence of a reduced rank structure allows to identify purely causal and non-causal VAR processes of order P>1 even in the Gaussian likelihood framework. Hence, usual test statistics and canonical correlation analysis can be applied, where either lags or leads are used as instruments to determine whether the common features are present in either the backward- or forward-looking dynamics of the series. The proposed definitions of co-movements are also valid for the mixed causal—non-causal VAR, with the exception that a non-Gaussian maximum likelihood estimator is necessary. This means however that one loses the benefits of the simple tools proposed. An empirical analysis on Brent and West Texas Intermediate oil prices illustrates the findings. No short run co-movements are found in a conventional causal VAR, but they are detected when considering a purely non-causal VAR.
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U2 - 10.1111/obes.12281
DO - 10.1111/obes.12281
M3 - Article
VL - 81
SP - 697
EP - 715
JO - Oxford Bulletin of Economics and Statistics
JF - Oxford Bulletin of Economics and Statistics
SN - 0305-9049
IS - 3
ER -