On the Validity of Granger Causality for Ecological Count Time Series
Abstract
:1. Introduction
2. Materials and Methods
2.1. Vector Autoregressive Models and Granger Causality
2.2. Simulations
2.3. Applications
3. Results
3.1. Simulations
3.2. Applications
4. Discussion
4.1. Practical Implications
- Tools of quantitative (numerical) analysis can indeed be applied to variables that take only a minimum of count values, for example 0, 1. For Granger causality, the shortcoming of having time series of few counts can be balanced by having long time series.
- Based on the latter result, it is suggested to rather use a small sampling time in the observation of ecological populations than aggregating the data in longer sampling times to produce bigger counts, and then use tools developed for continuous-valued data. Data aggregation, which is often the common practice, reduces the length of the time series and may have considerable effects (estimation accuracy, undetected seasonality or periodicity, occurrence of instantaneous causality). Indeed, it was shown in the simulation study that Granger causality is less accurately estimated with short time series.
- The present study suggests that the data precision can be relaxed at the cost of accuracy in the estimation of Granger causality. However, this cost can be compensated for by increasing the time series length, so that in the cases where high-quality data collection is difficult or costly, low-resolution observations may be adequate if the time series is long enough. For example, the abundance of the Common Eider species was rounded to hundreds of Eiders, and the same Granger causality relationships were estimated by counting the abundance in 10 classes of Eiders from 0 to 9 (0 for no Eiders). Some abiotic factors could easily be collected directly from the observers of Eiders, during their work, in similar classes. For instance, the temperature could have been classified in a scale from 0 to 9 (0 for temperatures close to the area’s minimum temperature for the season of observations).
4.2. Theoretical Implications
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
References
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Pair | CGCI (VAR) | FDR (VAR) | CGCI (DVAR) | FDR (DVAR) |
---|---|---|---|---|
X1 → X2 | 0.1906 | 18 | 0.1848 | 19 |
X2 → X1 | 0.8900 | 890 | 0.3924 | 118 |
X1 → X3 | 0.7560 | 781 | 1.0750 | 320 |
X3 → X1 | 0.1922 | 16 | 0.1762 | 11 |
X1 → X4 | 0.1847 | 19 | 0.1859 | 10 |
X4 → X1 | 0.1868 | 17 | 0.1988 | 9 |
X2 → X3 | 0.5097 | 419 | 0.1974 | 15 |
X3 → X2 | 0.1885 | 20 | 0.1964 | 12 |
X2 → X4 | 0.1925 | 18 | 0.1927 | 8 |
X4 → X2 | 0.7879 | 830 | 0.3985 | 140 |
X3 → X4 | 0.1864 | 25 | 0.1932 | 13 |
X4 → X3 | 0.1905 | 18 | 0.1916 | 14 |
K = 2 | N = 25 | N = 50 | N = 100 | N = 1000 | ||||
Relation | GCI | FDR | GCI | FDR | GCI | FDR | GCI | FDR |
X1 → X2 | 0.051 | 55 | 0.024 | 49 | 0.012 | 65 | 0.001 | 80 |
X2→ X1 | 2.580 | 850 | 0.740 | 973 | 0.552 | 998 | 0.508 | 1000 |
K = 3 | N = 25 | N = 50 | N = 100 | N = 1000 | ||||
Relation | CGCI | FDR | CGCI | FDR | CGCI | FDR | CGCI | FDR |
X1 → X2 | 0.059 | 54 | 0.026 | 46 | 0.012 | 46 | 0.001 | 55 |
X2→ X1 | 1.008 | 749 | 0.521 | 961 | 0.488 | 1000 | 0.461 | 1000 |
X1 → X3 | 0.047 | 23 | 0.021 | 31 | 0.011 | 37 | 0.001 | 26 |
X3→ X1 | 0.758 | 602 | 0.342 | 844 | 0.311 | 985 | 0.286 | 1000 |
X2 → X3 | 0.048 | 31 | 0.024 | 35 | 0.011 | 30 | 0.001 | 45 |
X3→ X2 | 1.687 | 689 | 0.469 | 907 | 0.424 | 994 | 0.403 | 1000 |
X1 → X2 | 0.059 | 54 | 0.026 | 46 | 0.012 | 46 | 0.001 | 55 |
K = 4 | N = 25 | N = 50 | N = 100 | N = 1000 | ||||
Relation | CGCI | FDR | CGCI | FDR | CGCI | FDR | CGCI | FDR |
X1 → X2 | 0.066 | 42 | 0.027 | 53 | 0.013 | 37 | 0.001 | 49 |
X2→ X1 | 0.714 | 770 | 0.547 | 976 | 0.497 | 1000 | 0.462 | 1000 |
X1 → X3 | 0.068 | 42 | 0.026 | 41 | 0.011 | 38 | 0.001 | 37 |
X3→ X1 | 0.493 | 550 | 0.357 | 864 | 0.326 | 992 | 0.299 | 1000 |
X1 → X4 | 0.052 | 23 | 0.022 | 36 | 0.010 | 32 | 0.001 | 34 |
X4→ X1 | 0.382 | 416 | 0.232 | 686 | 0.206 | 931 | 0.183 | 1000 |
X2 → X3 | 0.136 | 46 | 0.025 | 47 | 0.012 | 39 | 0.001 | 47 |
X3→ X2 | 1.239 | 732 | 0.526 | 945 | 0.493 | 1000 | 0.457 | 1000 |
X2 → X4 | 0.132 | 37 | 0.023 | 36 | 0.010 | 30 | 0.001 | 50 |
X4→ X2 | 1.056 | 563 | 0.342 | 828 | 0.307 | 982 | 0.286 | 1000 |
X3 → X4 | 0.132 | 28 | 0.026 | 44 | 0.012 | 36 | 0.001 | 38 |
X4→ X3 | 1.905 | 643 | 0.537 | 886 | 0.429 | 994 | 0.402 | 1000 |
X1 → X2 | 0.066 | 42 | 0.027 | 53 | 0.013 | 37 | 0.001 | 49 |
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Papaspyropoulos, K.G.; Kugiumtzis, D. On the Validity of Granger Causality for Ecological Count Time Series. Econometrics 2024, 12, 13. https://doi.org/10.3390/econometrics12020013
Papaspyropoulos KG, Kugiumtzis D. On the Validity of Granger Causality for Ecological Count Time Series. Econometrics. 2024; 12(2):13. https://doi.org/10.3390/econometrics12020013
Chicago/Turabian StylePapaspyropoulos, Konstantinos G., and Dimitris Kugiumtzis. 2024. "On the Validity of Granger Causality for Ecological Count Time Series" Econometrics 12, no. 2: 13. https://doi.org/10.3390/econometrics12020013
APA StylePapaspyropoulos, K. G., & Kugiumtzis, D. (2024). On the Validity of Granger Causality for Ecological Count Time Series. Econometrics, 12(2), 13. https://doi.org/10.3390/econometrics12020013