# Assessing the Time-Frequency Co-Movements among the Five Largest Engineering Consulting Companies: A Wavelet-Base Metrics of Contagion and VaR Ratio

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### Wavelet Analysis

## 3. Empirical Exercise

#### 3.1. Data and Descriptive Statistics

#### 3.2. Results

## 4. Conclusions and Suggestions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Heston, S.L.; Rouwenhorst, K.G. Does industrial structure explain the benefits of international diversification? J. Financ. Econ.
**1994**, 46, 111–157. [Google Scholar] [CrossRef] - Bekaert, G.; Hodrick, R.J.; Zhang, X. International stock return co-movements. J. Financ.
**2009**, 64, 2591–2626. [Google Scholar] [CrossRef] [Green Version] - Graham, M.; Kiviaho, J.; Nikkinen, J. The rise in co-movement across national stock markets: Market integration or IT bubble? J. Empir. Financ.
**2004**, 11, 659–680. [Google Scholar] - Rua, A.; Nunes, L.C. International co-movement of stock market returns: A wavelet analysis. J. Empir. Financ.
**2009**, 16, 632–639. [Google Scholar] [CrossRef] [Green Version] - Graham, M.; Kiviaho, J.; Nikkinen, J. Integration of 22 emerging stock markets: A three-dimensional analysis, Glob. Financ. J.
**2012**, 23, 34–47. [Google Scholar] [CrossRef] - Conlon, T.; Cotter, J.; Gençay, R. Commodity futures hedging, risk aversion and the hedging horizon. Eur. J. Financ.
**2016**, 22, 1534–1560. [Google Scholar] [CrossRef] - Das, D.; Kannadhasan, M.; Tiwari, A.K.; Al-Yahyaee, K.H. Has co-movement dynamics in emerging stock markets changed after global financial crisis? New evidence from wavelet analysis. Appl. Econ. Lett.
**2018**, 25, 1447–1453. [Google Scholar] - Chakrabarty, A.; De, A.; Gunasekaran, A.; Dubey, R. Investment horizon heterogeneity and wavelet: Overview and further research directions. Phys. A Stat. Mech. Appl.
**2015**, 429, 45–61. [Google Scholar] [CrossRef] - Aguiar-Conraria, L.; Martins, M.M.; Soares, M.J. Estimating the Taylor rule in the time-frequency domain. J. Macroecon.
**2018**, 57, 122–137. [Google Scholar] [CrossRef] [Green Version] - Matos, P.; da Silva, C.; dos Santos, D.; Reinaldo, L. Credit, default, financial system and development. Q. Rev. Econ. Financ.
**2020**, 79, 281–289. [Google Scholar] [CrossRef] - Diebold, F.X.; Yilmaz, K. Better to give than to receive: Predictive directional measurement of volatility spillovers. Int. J. Forecast.
**2012**, 28, 57–66. [Google Scholar] [CrossRef] [Green Version] - Kang, S.H.; McIver, R.; Yoon, S.M. Dynamic spillover effects among crude oil, precious metal, and agricultural commodity futures markets. Energy Econ.
**2017**, 62, 19–32. [Google Scholar] [CrossRef] - Akhtaruzzaman, M.; Boubaker, S.; Sensoy, A. Financial contagion during COVID–19 crisis. Financ. Res. Lett.
**2021**, 38, 101604. [Google Scholar] [CrossRef] - Gamba-Santamaria, S.; Gomez-Gonzalez, J.E.; Hurtado-Guarin, J.L.; Melo-Velandia, L.F. Stock market volatility spillovers: Evidence for Latin America. Financ. Res. Lett.
**2017**, 20, 207–216. [Google Scholar] [CrossRef] [Green Version] - Jiang, Z.; Yoon, S.M. Dynamic co-movement between oil and stock markets in oil-importing and oil-exporting countries: Two types of wavelet analysis. Energy Econ.
**2020**, 90, 104835. [Google Scholar] [CrossRef] - Pal, D.; Mitra, S.K. Oil price and automobile stock return co-movement: A wavelet coherence analysis. Econ. Model.
**2019**, 76, 172–181. [Google Scholar] [CrossRef] - Wu, K.; Zhu, J.; Xu, M.; Yang, L. Can crude oil drive the co-movement in the international stock market? Evidence from partial wavelet coherence analysis. N. Am. J. Econ. Financ.
**2020**, 101194. [Google Scholar] [CrossRef] - Choi, S.-Y. Industry volatility and economic uncertainty due to the COVID-19 pandemic: Evidence from wavelet coherence analysis. Financ. Res. Lett.
**2020**, 37, 101783. [Google Scholar] [CrossRef] [PubMed] - Goodell, J.W.; Goutte, S. Diversifying with cryptocurrencies during COVID-19 Finance research letters. Available SSRN
**2020**. forthcoming. [Google Scholar] [CrossRef] - Matos, P.; Costa, A.; da Silva, C. COVID-19, stock market and sectoral contagion in US: A time-frequency analysis. Res. Int. Bus. Financ.
**2021**, 57, 101400. [Google Scholar] [CrossRef] [PubMed] - Kim, S.; In, F. The relationship between stock returns and inflation: New evidence from wavelet analysis. J. Empir. Financ.
**2005**, 12, 435–444. [Google Scholar] [CrossRef] - Reboredo, J.C.; Rivera-Castro, M.A. Wavelet-based evidence of the impact of oil prices on stock returns. Int. Rev. Econ. Financ.
**2014**, 29, 145–176. [Google Scholar] [CrossRef] - Lin, F.L.; Yang, S.Y.; Marsh, T.; Chen, Y.F. Stock and bond return relations and stock market uncertainty: Evidence from wavelet analysis. Int. Rev. Econ. Financ.
**2018**, 55, 285–294. [Google Scholar] [CrossRef] - Mink, M. Measuring stock market contagion: Local or common currency returns? Emerg. Mark. Rev.
**2015**, 22, 18–24. [Google Scholar] [CrossRef] - Dong, M.; Chang, C.P.; Gong, Q.; Chu, Y. Revisiting global economic activity and crude oil prices: A wavelet analysis. Econ. Model.
**2019**, 78, 134–149. [Google Scholar] [CrossRef] - Sun, Q.; Tong, H.S. Risk and January effect. J. Bank. Financ.
**2010**, 34, 965–974. [Google Scholar] [CrossRef] - Khaled, M.S.; Keef, S.P. A note on the turn of the month and year effects in international stock returns. Eur. J. Financ.
**2012**, 18, 597–602. [Google Scholar] [CrossRef] - Fang, L.; Bessler, D.A. Is it China that leads the Asian stock market contagion in 2015? Appl. Econ. Lett.
**2018**, 25, 752–757. [Google Scholar] [CrossRef]

**Figure 1.**Accumulated return for the five largest consulting engineering companies in the world. Notes: Data from 9 January 2014 to 9 December 2020. Source: Investing.com (accessed on 11 December 2020).

**Figure 2.**Time series (

**a**), wavelet power spectrum (

**b**) and global wavelet power spectrum (GWPS) (

**c**) of the five largest engineering consulting companies. Notes: Data from 9 January 2014 to 9 December 2020. Source: Investing.com (accessed on 11 December 2020). (

**a**) Time series, (

**b**) wavelet power spectrum, (

**c**) global wavelet power spectrum (GWPS). In (

**a**) the color code ranges from blue (low volatility) to red (high volatility). The black (grey) contour marks significance at 5% (10%) level. Black dashed lines: cone of influence (indicates the region affected by edge effects).

**Figure 3.**Partial wavelet coherency among the five largest consulting engineering companies. Notes: The cone of influence is shown as the black curve. The 5% significance level contours are in black, the 10% significance level contours are in gray. The significance level was derived from Monte Carlo Simulations with 1000 runs. Data from 9 January 2014 to 9 December 2020. Source: Investing.com (accessed on 11 December 2020) and Federal Reserve Bank of St. Louis.

**Figure 4.**Ratio between the value at risk (VaR) of the five largest consulting engineering companies portfolio with and without co-movement. Notes: Data from 9 January 2014 to 9 December 2020. Source: Investing.com (accessed on 11 December 2020).

Aecom | Arcadis | Jacobs | SNC | WSP | |
---|---|---|---|---|---|

Mean | 0.050% | 0.042% | 0.049% | −0.020% | 0.100% |

Standard Deviation | 2.124% | 2.382% | 1.778% | 2.359% | 1.512% |

Skewness | −0.403 | −0.437 | −0.038 | −0.595 | 0.197 |

Kurtosis | 9.829 | 11.286 | 6.734 | 24.044 | 10.401 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Albuquerque Junior, M.; Filipe, J.A.; Jorge Neto, P.d.M.; Silva, C.d.C.d.
Assessing the Time-Frequency Co-Movements among the Five Largest Engineering Consulting Companies: A Wavelet-Base Metrics of Contagion and VaR Ratio. *Mathematics* **2021**, *9*, 504.
https://doi.org/10.3390/math9050504

**AMA Style**

Albuquerque Junior M, Filipe JA, Jorge Neto PdM, Silva CdCd.
Assessing the Time-Frequency Co-Movements among the Five Largest Engineering Consulting Companies: A Wavelet-Base Metrics of Contagion and VaR Ratio. *Mathematics*. 2021; 9(5):504.
https://doi.org/10.3390/math9050504

**Chicago/Turabian Style**

Albuquerque Junior, Marcos, José António Filipe, Paulo de Melo Jorge Neto, and Cristiano da Costa da Silva.
2021. "Assessing the Time-Frequency Co-Movements among the Five Largest Engineering Consulting Companies: A Wavelet-Base Metrics of Contagion and VaR Ratio" *Mathematics* 9, no. 5: 504.
https://doi.org/10.3390/math9050504