Testing for Granger causality with mixed frequency data

Ghysels, Eric; Hill, Jonathan B.; Motegi, Kaiji

doi:10.1016/j.jeconom.2015.07.007

Cited by 87 publications

(120 citation statements)

References 52 publications

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“…(). Earlier analogous references include the works by Coates and Diggle () and Diggle () who modelled the log‐ratio of two spectral densities by a quadratic function. Given G unknown spectral density functions, say f j (·), let

log \{\frac{f_{j} (ω)}{f_{G} (ω)}\} = a_{j}^{normalT} Z false(italicω false) - π < ω < π,

for j =1,2,…, G −1 where a j =( a j 0 , a j 1 ,…, a jp ) T is a ( p +1)‐dimensional vector of unknown parameters and Z ( ω )=(1,2 cos ( ω ),2 cos (2 ω ),…,2 cos ( pω )) T .…”

Section: Discussion On the Paper By Nason Powell Elliott And Smithmentioning

confidence: 99%

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Should we Sample a time Series more Frequently?: Decision Support via Multirate Spectrum Estimation

Nason

Powell

Elliott

et al. 2016

Journal of the Royal Statistical Society Series A: Statistics in Society

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Summary. Suppose that we have a historical time series with samples taken at a slow rate, e.g. quarterly. The paper proposes a new method to answer the question: is it worth sampling the series at a faster rate, e.g. monthly? Our contention is that classical time series methods are designed to analyse a series at a single and given sampling rate with the consequence that analysts are not often encouraged to think carefully about what an appropriate sampling rate might be. To answer the sampling rate question we propose a novel Bayesian method that incorporates the historical series, cost information and small amounts of pilot data sampled at the faster rate. The heart of our method is a new Bayesian spectral estimation technique that is capable of coherently using data sampled at multiple rates and is demonstrated to have superior practical performance compared with alternatives. Additionally, we introduce a method for hindcasting historical data at the faster rate. A freeware R package, regspec, is available that implements our methods. We illustrate our work by using official statistics time series including the UK consumer price index and counts of UK residents travelling abroad, but our methods are general and apply to any situation where time series data are collected.

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log \{\frac{f_{j} (ω)}{f_{G} (ω)}\} = a_{j}^{normalT} Z false(italicω false) - π < ω < π,

for j =1,2,…, G −1 where a j =( a j 0 , a j 1 ,…, a jp ) T is a ( p +1)‐dimensional vector of unknown parameters and Z ( ω )=(1,2 cos ( ω ),2 cos (2 ω ),…,2 cos ( pω )) T .…”

Section: Discussion On the Paper By Nason Powell Elliott And Smithmentioning

confidence: 99%

“…() and Götz and Hauzenberger (), and for assessing Granger causality in Ghysels et al . (,b). A recent overview of models for mixed frequency data is given by Foroni and Marcellino ().…”

Section: Introductionmentioning

confidence: 99%

Should we Sample a time Series more Frequently?: Decision Support via Multirate Spectrum Estimation

Nason

Powell

Elliott

et al. 2016

Journal of the Royal Statistical Society Series A: Statistics in Society

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show abstract

“…The notation in this section follows Ghysels, Hill, and Motegi (). We denote the low‐ frequency (quarterly) export target variable by y L ( τ ) and the high‐frequency (monthly) indicator variable by z H ( τ , j ) where τ = 1,..., T indicates the quarterly periods with sample size T .…”

Section: Empirical Methodologymentioning

confidence: 99%

PMIs: Reliable indicators for exports?

Grossmann

Scheufele

2019

Rev International Economics

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Foreign economic activity is a major determinant of export developments. However, foreign GDP figures are published too late to be useful for short‐term forecasting. This paper presents a number of indicators based on the widely available PMI surveys that provide very early signals of foreign activity. Using MIDAS models we analyze the in‐ and out‐of‐sample performance of these and related indicators for two very trade‐exposed countries (Germany and Switzerland). We find that the monthly indicators based on foreign PMIs are strongly correlated with quarterly export growth. The forecast comparison shows that PMI‐based indicators perform very well relative to other benchmark models.

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“…Particularly the latter model class, MF‐VAR models, has received a lot of attention recently, predominantly in two related fields of application: forecasting (Schorfheide and Song, ; Götz and Hauzenberger, , among others) and Granger causality (GC) testing (Ghysels et al, ; ; Götz et al, ). Both topics are of immense interest to practitioners at, for example, central banks, who routinely forecast key variables like the gross domestic product (GDP) using a variety of, usually higher‐frequent, indicators, or investigate causal patterns between the time series they monitor.…”

Section: Introductionmentioning

confidence: 99%

“…Under this definition, GC testing in fact boils down to testing a set of zero restrictions on the parameters of the respective system. The three articles mentioned above cover different aspects of such GC testing within a MF‐VAR: Ghysels et al () discuss the general theory of associated hypothesis tests in detail, which – while asymptotically valid – suffer from size distortions and a loss of power in case the number of HF observations is large relative the low‐frequency (LF) period. Götz et al () and Ghysels et al () then introduce various ways to overcome these implications of the curse of dimensionality .…”

Section: Introductionmentioning

confidence: 99%

Granger Causality Testing in Mixed‐Frequency VARs with Possibly (Co)Integrated Processes

Goetz

Hecq

2019

Journal Time Series Analysis

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We analyze Granger causality (GC) testing in mixed-frequency vector autoregressions (MF-VARs) with possibly integrated or cointegrated time series. It is well known that conducting inference on a set of parameters is dependent on knowing the correct (co)integration order of the processes involved. Corresponding tests are, however, known to often suffer from size distortions and/or a loss of power. Our approach works for MF variables that are stationary, integrated of an arbitrary order, or cointegrated. As it only requires the estimation of a MF-VAR in levels with appropriately adjusted lag length, after which GC tests can be conducted using simple standard Wald tests, it is of great practical appeal. In addition, we show that the presence of non-stationary and trivially cointegrated high-frequency regressors leads to standard distributions when testing for causality on a subset of parameters, sometimes even without any need to augment the VAR order. Monte Carlo simulations and two applications involving the oil price and consumer prices as well as GDP and industrial production in Germany illustrate our approach.1 Unfortunately, the name of said researcher as well as the conference he presented at slipped the authors' memories; as if choosing the adjective 'young' was not enough for proving that one grew older. 2 There exists a multitude of sub-variants of each model class, for example, hybrid versions of MIDAS LASSO (Siliverstovs, 2017), Markov-switching MF models (Foroni et al., 2015a) and MF-VARs with time-varying parameters and stochastic volatility Hauzenberger, 2018 or Cimadomo andD'Agostino, 2016), among many others. GC IN POSSIBLY (CO)INTEGRATED MF-VARS 915Particularly the latter model class, MF-VAR models, has received a lot of attention recently, predominantly in two related fields of application: forecasting (Schorfheide and Song, 2015; Götz and Hauzenberger, 2018, among others) and Granger causality (GC) testing 2018;Götz et al. 2016). Both topics are of immense interest to practitioners at, for example, central banks, who routinely forecast key variables like the gross domestic product (GDP) using a variety of, usually higher-frequent, indicators, or investigate causal patterns between the time series they monitor. We will focus on GC testing, generally introduced in Granger (1969), whereby both concepts are obviously related when defining GC as predictability of one series conditional on past observations of the other (Dufour and Renault, 1998). Under this definition, GC testing in fact boils down to testing a set of zero restrictions on the parameters of the respective system. The three articles mentioned above cover different aspects of such GC testing within a MF-VAR: Ghysels et al. (2016) discuss the general theory of associated hypothesis tests in detail, which -while asymptotically valid -suffer from size distortions and a loss of power in case the number of HF observations is large relative the low-frequency (LF) period. Götz et al. (2016) and Ghysels et al. (2018) then introduce various wa...

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Testing for Granger causality with mixed frequency data

Cited by 87 publications

References 52 publications

Should we Sample a time Series more Frequently?: Decision Support via Multirate Spectrum Estimation

Should we Sample a time Series more Frequently?: Decision Support via Multirate Spectrum Estimation

PMIs: Reliable indicators for exports?

Granger Causality Testing in Mixed‐Frequency VARs with Possibly (Co)Integrated Processes

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