Identifying the frequency and connectivity dynamics of the US economy

Tessmann, Mathias Schneid; Passos, Marcelo de Oliveira; Khodr, Omar Barroso; Lima, Alexandre Vasconcelos; Fontana, Pedro Henrique Pontes Article Identifying the frequency and connectivity dynamics of the US economy Economies Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Tessmann, Mathias Schneid; Passos, Marcelo de Oliveira; Khodr, Omar Barroso; Lima, Alexandre Vasconcelos; Fontana, Pedro Henrique Pontes (2024) : Identifying the frequency and connectivity dynamics of the US economy, Economies, ISSN 2227-7099, MDPI, Basel, Vol. 12, Iss. 6, pp. 1-20, https://doi.org/10.3390/economies12060149 This Version is available at: https://hdl.handle.net/10419/329075 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Citation: Tessmann, Mathias Schneid, Marcelo De Oliveira Passos, Omar Barroso Khodr, Alexandre Vasconcelos Lima, and Pedro Henrique Pontes Fontana. 2024. Identifying the Frequency and Connectivity Dynamics of the US Economy. Economies 12: 149. https://doi.org/10.3390/ economies12060149 Academic Editor: Robert Czudaj Received: 16 January 2024 Revised: 6 March 2024 Accepted: 13 March 2024 Published: 12 June 2024 Copyright: © 2024 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 (https:// creativecommons.org/licenses/by/ 4.0/). economies Article Identifying the Frequency and Connectivity Dynamics of the US Economy Mathias Schneid Tessmann 1,*, Marcelo De Oliveira Passos 2, Omar Barroso Khodr 3, Alexandre Vasconcelos Lima 1and Pedro Henrique Pontes Fontana 1 1Economics and Management School, Brazilian Institute of Education Development and Research (IDP), Brasília 70750-600, DF, Brazil; alexandr[email protected] (A.V.L.); [email protected] (P.H.P.F.) 2 Organizations and Markets Graduate Program, Universidade Federal de Pelotas, Pelotas 96010-610, RS, Brazil; [email protected] 3Essex Business School, University of Essex, Colchester C04 3SQ, UK; khodr.omar[email protected] *Correspondence: [email protected] Abstract: This paper seeks to investigate the connectivity of the US economy through the dynamics of the transmission of volatility in sectoral indices. For this, we use daily asset data and two methodologies. The first creates a spillover index that measures market connectivity and the second partitions this index into different frequency bands that denote periods. We found results that show significant transmissions of volatility among the 64 analyzed assets. Notably, the DJIA, Wilshire 5000, and S&P 500 showed significant volatility and were the main drivers of volatility for the other sectors and indices. Results also indicated that sectors that transferred volatility were influenced by three key factors: periods of economic uncertainty, socioeconomic circumstances resulting from post-crisis events, and the impact of economic and financial news on market sentiment. Additionally, we found that global returns and price changes in market indices sent considerable volatility into commodity assets. Our results are potentially useful for investors, portfolio managers, financial economists, financial advisors, financial market regulators, and policymakers. Keywords: volatility transmission; spillover index; frequency decomposition; post-crisis volatility JEL Classification: E30; E44; G01; G10 1. Introduction Volatility repercussions, in the view of Chan et al. (1991), can be seen as proxies for assessments of the intensity and quality of economic and financial information flows. In this sense, it is a common practice in financial markets to analyze how information and its consequent volatility transmissions flow from one asset to another, from one sector to another, or even from one market to another. Such analyses are useful for financial market regulators, policymakers, activating circuit-breakers on stock exchanges, analysts and investment managers, investors, hedgers, traders, and commodity producers. Assessing the existing connections in an economy and its intersectoral relationships is an important contribution that empirical economics can bring because, through these identifications, measures to mitigate systemic risks can be taken. Likewise, one of the most recurrent research topics in the field of financial economics is the verification of the existence of links that may exist between financial and nonfinancial assets traded in the market. Thus, presenting empirical evidence of how markets interact and how their assets react to changes in expectations and macroeconomic variations makes the measurement of volatility transmissions and interdependencies between sectoral financial assets important. In this sense, we intend to investigate the patterns and dynamics of the transmission of volatility in a series of sectoral assets of the US economy, including the main indices of Economies 2024,12, 149. https://doi.org/10.3390/economies12060149 https://www.mdpi.com/journal/economies Economies 2024,12, 149 2 of 20 the US stock market, the Select Sector SPDR index funds, the Commodity Research Bureau index, and the prices of WTI and Brent oil, as well as US Treasury bond returns. Our study covers a period from 22 December 1998 to 12 July 2021, providing a dataset of 5547 price observations for each asset. Therefore, we use two econometric methodologies in this paper: the spillover index proposed by Diebold and Yilmaz (2012) and the frequency decompositions method of Baruník and Krehlík(2018). The first method measures interactions and interdependencies based on the decomposition of variances, which allowed us to quantify the extent of volatility transmission and determine overall market connectivity. The second details these interactions and connectivity relationships across different frequency bands, which helped us in the separate analysis of short-term and long-term dynamics. With the spillover indices, we partitioned their effects into three different frequencies: overnight (1 day), very short term (1 to 4 days), short term (4 to 30 days), and medium/long term (more than 30 days), which provided us with information about frequency band dependent connections. This highlighted the strength of the shocks in these different periods that, without this methodology, could be neglected; that is, more precise evidence that considers the effects over time would be absent. When we examine the results, we see a pattern that indicates that volatility transmissions were significant across the 64 included assets. Notably, the DJIA, Wilshire 5000, and S&P 500 exhibited high levels of volatility and functioned as significant volatility transmitters for various sectors and market indices. Specifically, the transport, energy, health, industrial, and technology sectors stood out as the most exposed to volatility transmissions. The same happened with the main market indices, such as the S&P 500, Nasdaq, and Wilshire 5000. Several works dealt with the repercussions of volatility, such as Nazlioglu et al. (2013), who examined volatility transmissions between oil and agricultural commodity returns in pre-crisis and post-crisis periods. The authors found distinct patterns and variations between the two periods. The research by Barunik et al. (2015) investigated the asymmetries in the repercussions between different sectors, finding results for the consumer, telecommunication, and health sectors that presented greater asymmetries in the repercussions when compared to the financial, information technology, and energy sectors. From the perspective of Mensi et al. (2021), there is evidence that the diesel and gas sectors were net transmitters of volatility to other markets since asymmetric repercussions occurred. Our findings suggest that the sectors that recorded the most intense volatility transmissions were those influenced by three factors. First, circumstances arising from economic instability, uncertainty, and post-crisis factors (global financial crisis, European crisis, and COVID-19 pandemic). Second, financial news affected “market sentiment” and, in effect, increased the repercussions of volatility in the assets and sectors considered. Third, returns and changes in market index prices provoked reactions in raw material assets. Thus, by making some patterns of connectivity and interdependence explicit, we believe we provide a less distorted view of the dynamics of interactions between assets, indices, and sectors, which, we hope, can be useful for policymakers in the finance and design of policies for financial markets that mitigate systemic risk and promote market stability, for investors and portfolio managers, as well as for the general population benefiting from economic stability. The paper is structured in four more sections. The second section provides a brief theoretical reference about the sectoral connectivity of the economy, and in Section 3, we define the database, detailing its elaboration process, as well as the methodology used in the empirical analysis. In Section 4, we present and discuss the results, and in Section 5, we make the final considerations. 2. Review of Empirical Literature Several authors also point out that the circumstances brought about by the post-crisis periods influenced volatility transmissions and connectivity effects (Costa et al. 2022;Umar Economies 2024,12, 149 3 of 20 et al. 2021;Bouri et al. 2017;Vardar et al. 2018). The literature also explored the direct and indirect impacts that financial news had on intraand cross-sector volatility (Hassan and Malik 2007;Malik and Ewing 2009) across selected sectors and assets and at different frequencies. In this sense, our purpose is, in addition to what has already been mentioned, to contribute to the understanding of some aspects not directly measurable (some of a qualitative nature) that influence the volatility links between and inside assets and sectors. Ewing et al. (2002) calculated the transmission of volatility between the oil and natural gas markets from a sample of daily returns data. They produced evidence that suggested continued volatility in both markets. Therefore, they found that returns exhibited fluctuations over time in the volatility series. They suggested that volatility in natural gas returns was more persistent than that in oil returns, stating that this may indicate a greater “window of profit opportunities” for investors in natural gas than in oil. Hughes et al. (2006) empirically tested the volatility patterns of American Treasury bonds (Treasury bills or T-bills) between January 1983 and December 2000. They analyzed the daily returns for bonds with different maturities of 13; 26; and 52 weeks, examining trading periods starting from the first half hour of active New York trading, which begins at 8:30 a.m. and proceeds until the close at 4 p.m., as well as the overnight period lasting from 4 p.m. to 9 a.m. (on the next day of negotiations). According to the authors, the night period includes the volatility effect of relevant macroeconomic announcements that take place until 8:30 a.m. The authors investigated variations in standard deviations every 1 h throughout the day. The results for the different bonds (with and without coupons) suggest that the intraday volatility of 13-week bonds was higher compared to bonds maturing in 26 and 52 weeks. For them, in practical terms, there is no daily opening and closing day in trading sessions. This dynamic works according to local (or domestic) trading compared to global trading, which operates 24 h a day. In New York, volatility was concentrated at the beginning and end of Treasury bond trading hours. The literature also suggests similar parameters, presented by Cyree et al. (2014) and Baillie and Bollerslev (1991), who conclude that empirical results in the 24-h foreign exchange markets and the 24-h Eurodollar market confirm that volatility is greatest at the beginning and end of the workday, even in the absence of market closing. Hassan and Malik (2007) investigated volatility repercussions and shocks among the main sectoral indices in the United States, based on daily data from 1 January 1992 to 6 June 2005 . The sectors investigated were financial, industrial, consumer, health, energy, and technology. In a broad sense, both authors achieved results that show significant occurrences among the second moments of these indices. They concluded that there is a transmission of relevant shocks and volatility between all the mentioned sectors. Kumiega et al. (2011) studied the factors that increased the returns on the US stock markets in 2007 and early 2010. This period presented specific trends in the prices of energy and raw materials, in addition to indications that it was affected by the crisis of important institutions’ financial and insurance conditions, in addition to high volatility followed by the resumption of activity in the global market. The authors developed an opinion regarding the returns on ETFs in the S&P 500 sector with statistically independent signals and used the independent component analysis method, concluding that there were two sets of overall market betas during the period, combined with a dominant factor for the energy and materials sector. They also demonstrated that the EGARCH model, which deals with asymmetric responses between returns and volatility, adjusted to significant levels of variance during an international financial crisis. They found that the estimated correlations reduced greatly when raw material prices rose. However, they rose sharply again after the fall of the S&P 500, in the last months of 2008. Finally, the authors found that the three main factors were a factor of energy and materials, another stock market standard, and a factor dominated by finance. Nazlioglu et al. (2013) estimated the volatility connections present between oil prices and the prices of some specific agricultural commodities (wheat, corn, soybeans, and sugar). They used the recently developed causality-in-variance test and computed impulse Economies 2024,12, 149 4 of 20 response functions within a sample with daily observations from 1 January 1986 to 21 March 2011. By identifying the effect of the shock of the crisis on food prices, they separated the observations into two subsamples: the period before the shock (1 January 1986 to 31 December 2005) and the period after (1 January 2006 to 21 March 2011). The variance causality test concluded that the volatility of the oil market extends to agricultural markets—excluding the sugar market—in the post-shock period, even though there was no risk connectivity between oil and agricultural products in the pre-shock period. Regarding the impulse response functions, they also showed that a shock in oil price volatility had repercussions on agricultural markets only in the period after the shock. With this, the authors concluded that there is a transition in the dynamics of volatility transmission after a food price shock when volatility transmission emerges differently in the risk interconnections between energy and agricultural markets. Bouri et al. (2017) examined the effects of commodity volatility on sovereign credit default swap (CDS) spreads in emerging and frontier markets, based on a sample of daily observations from seventeen emerging countries and six frontier countries. They documented a relevant transmission of volatility from commodity markets to sovereign CDS spreads in both emerging and frontier markets. Despite finding a significant effect for most countries in that sample, the authors found that their results vary over time and depending on the country. They also found evidence of a greater transmission effect of volatility from the energy and precious metals sectors. Vardar et al. (2018) used a VAR-BEKK GARCH model to study the shock transmission and volatility spillover (STVS) effects among daily stock market indices from the US, the UK, France, Germany, Japan, Turkey, China, South Korea, South Africa, and India. The five most relevant raw material prices were added to these indices: natural gas, crude oil, platinum, gold, and silver. The period analyzed was from 5 July 2005 to 14 October 2016. Thus, the months before, during, and after the crisis that led to the Great Recession were examined. In the sample period, developed and emerging countries exhibited bidirectional STVS effects between stock and commodity returns. However, the authors concluded that there were less unilateral effects of the STVS present in commodity returns on stocks, but also clear unilateral effects of the STVS of stock returns on commodity returns, in both developed and emerging countries. They also discovered other instances of relevant STVS effects across commodity and stock markets across countries during the crisis and post-crisis periods vis-à-vis the pre-crisis period. The authors stated that the effects of the STVS are the new normal for stock and commodity markets, despite the work of monetary authorities in the post-global crisis period. Finally, they stated that resource allocation choices between stocks and commodities could be made while considering analyzing the direction of the effects of STVS in some stock/commodity markets and also throughout the economic cycles of the world economy. Umar et al. (2021) investigated the repercussions of volatility in shocks in oil and agricultural commodity prices. Using a sample starting from January 2002 and proceeding to July 2020, that is, within a period covering the global financial crisis, the European sovereign debt crisis, and the COVID-19 pandemic, the authors ran Granger–Newbold causality tests and computed static and dynamic connection indices, producing evidence that indicates that oil price shocks were caused, in the Granger–Newbold sense, by changes in the prices of grains, live cattle, and wheat. The Granger supply shock causes variations in grain prices. The authors also highlighted that livestock was the largest transmitter and lean pork was the largest receiver, whether for price or volatility connectivity and based on a static connection approach. However, considering the dynamic perspective, they concluded that the connection increased during the period of the financial crisis. Farid et al. (2021) studied the ex ante and ex post periods of the COVID-19 outbreak in the US economy, focusing on critical structural changes and variable patterns of volatility connectivity between stocks and metal and energy commodities such as oil, gold, silver, and natural gas. They investigated 5-min high-frequency trading data from the most traded US ETFs to model a volatility connectivity network, computing intraday volatility estimates Economies 2024,12, 149 5 of 20 using the MCS-GARCH model. After this procedure, they adopted the Diebold and Yilmaz (2012) index methodology to measure volatility transmissions among financial markets. The authors concluded that there was a significant impact of the COVID-19 pandemic on the aforementioned connections among financial markets. Volatility repercussions among different assets reached a peak during the most critical moments of the pandemic. Mensi et al. (2021) estimated the dynamic connectivity of asymmetric volatility among ten US stock sectors (consumer goods, consumer services, finance, healthcare, materials, oil and gas, technology, telecommunications, real estate investment trusts (REITs), and utilities). They also adopted the indices of Diebold and Yilmaz (2012,2014) and the realized semivariances introduced by Baruník et al. (2017) for five-minute data. The authors found variable repercussions over time in the sectors that are part of the US stock markets. Such repercussions were more intense when significant economic, energy, and geopolitical events occurred. Furthermore, the repercussions of bad volatility tend to predominate over the repercussions of good volatility. This supports the evidence of asymmetric volatilities. Financials, materials, oil and gas, REITs, technology, telecommunications, and utilities were net recipients of good volatility (positive semivariance) transmissions. On the other hand, oil and gas transmitted bad volatility (negative semivariance), with the connectivity network among sectors showing asymmetric behavior. Costa et al. (2022) analyzed volatility transmissions involving 11 sectoral indices in the US. Using daily data from 1 January 2013 to 31 December 2020, the three authors estimated indices from Diebold and Yilmaz (2009,2012,2014), noticing changes in the degrees of connections among sectors and finding specifically stylized facts for sectors throughout the COVID-19 pandemic. This work reached several conclusions, including the existence of a substantial increase in total connectivity, from the initial period of the pandemic until the end of July 2020. Furthermore, there were significant changes in connectivity between pairs of sectors. 3. Methodology 3.1. Data We use daily closing prices from major US stock market indices; Select Sector SPDR index funds (in US dollars); the Commodity Research Bureau index; the futures market, in US dollars, of continuous contracts; contracts for WTI and Brent crude oil prices; and, finally, the US Treasury. The period covered is from 22 December 1998 to 12 July 2021, totaling 5547 price observations for each data frame. Table 1details the assets considered, and Table 2presents descriptive statistics on closing prices and returns. Table 1. Assets considered. Number Codes Assets: Indices, Funds and Bonds Description 1 CRB Commodity Research Bureau Index The Commodity Research Bureau (CRB) index is a representative indicator of the global commodity markets. 2 IRX CBOE 13 Week Treasury Bill Yield Index Some of the best-known yield-based options follow the yields of the most recently issued 13-week Treasury bills, 5-year Treasury notes, 10-year Treasury notes, and 30-year Treasury bonds. 3 DGS10 Market Yield on US Treasury Securities at 10-Year Constant Maturity Quoted on an investment basis. 4 DGS2 Market Yield on US Treasury Securities at 2-Year Constant Maturity Quoted on an investment basis. 5 DGS30 Market Yield on US Treasury Securities at 30-Year Constant Maturity Quoted on an investment basis. Economies 2024,12, 149 6 of 20 Table 1. Cont. Number Codes Assets: Indices, Funds and Bonds Description 6 DGS5 Market Yield on US Treasury Securities at 5-Year Constant Maturity Quoted on an investment basis. 7 XLB Materials Select Sector SPDR Fund Composed of companies involved in such industries as chemicals, construction materials, containers and packaging, metals and mining, and paper and forest products. 8 Brent Crude Oil Crude Oil Brent blend is a light crude oil (LCO), though not as light as West Texas Intermediate (WTI). 9 WTI Crude Oil Crude Oil West Texas Intermediate (WTI) crude oil is a specific grade of crude oil. 10 DJIA DJIA—Dow Jones Industrial Average An index of 30 blue-chip stocks of US industrial companies. 11 DJTA DJTA—Dow Jones Transportation Average A price-weighted average of 20 transportation stocks traded in the United States. In addition to railroads, the index includes airlines, trucking, marine transportation, delivery services, and logistics companies. 12 DJUA DJUA—Dow Jones Utility Average A Dow Jones index group that tracks the performance of several well-established utility companies. DJUA companies must be US-based and incorporated with most of their revenues generated within the US. 13 XLE Energy Select Sector SPDR Fund Energy companies in this index primarily develop and produce crude oil and natural gas, and provide drilling and other energy-related services. 14 XLF S&P Financial Select Sector A wide array of diversified financial service firms, insurance companies, banks, capital markets, and consumer finance and thrift companies are featured in this index. 15 XLV S&P Health Care Select Sector Companies in this sector primarily include healthcare equipment and supplies, healthcare providers and services, and biotechnology, and pharmaceutical industries. 16 XLI S&P Industrial Select Sector Industries in this index include aerospace and defense, building products, construction and engineering, electrical equipment, conglomerates, machinery, commercial services and supplies, air freight and logistics, airlines, marine, road and rail, etc. 17 Nasdaq NDQ—Nasdaq Composite An index that measures the performance of over 2500 common equities listed on the Nasdaq stock exchange. 18 SPX SPX—S&P 500 Composite Stock Price Index A capitalization-weighted index of 500 stocks intended to be a representative sample of leading companies in major sectors of the US economy. 19 XLK S&P Technology Select Sector Stocks primarily covering products developed by internet software and service companies, IT consulting services, and semiconductor equipment, computers, and peripherals are included in this index. Economies 2024,12, 149 7 of 20 Table 1. Cont. Number Codes Assets: Indices, Funds and Bonds Description 20 XLU S&P Utilities Select Sector The utilities index primarily provides companies that produce, generate, transmit, or distribute electricity or natural gas. 21 Wilshire 5000 Wilshire 5000 Total Market Index An index that measures the performance of the entire US stock market. Source: elaborated by authors. Table 2. Descriptive statistics of the analyzed indices. Closing Prices Returns Mean Std. Dev. Minimum Maximum Mean Std. Dev. Minimum Maximum S&P 500 1693.2930 747.5181 676.5300 4384.6300 0.0002 0.0124 −0.1277 0.1042 Nasdaq Composite 3967.5080 2736.3610 1114.1100 14,733.2400 0.0003 0.0160 −0.1315 0.1325 Dow Jones Industrial Average 14,881.2600 6303.3170 6547.0500 34,996.1800 0.0002 0.0118 −0.1384 0.1033 Dow Jones Transportation Average 5843.0840 3051.6690 1942.1900 15,943.3000 0.0003 0.0157 −0.1640 0.0896 Dow Jones Utility Average 487.3838 181.9854 167.5700 960.8900 0.0002 0.0125 −0.1175 0.1277 Wilshire 5000 70.1798 41.6704 24.5800 218.3000 0.0003 0.0125 −0.1306 0.0984 Materials Select Sector 38.1431 14.3355 16.6300 88.6800 0.0002 0.0154 −0.1325 0.1186 Energy Select Sector 54.7083 20.3556 19.8000 101.2900 0.0001 0.0185 −0.2249 0.1537 Financial Select Sector 20.6623 5.9894 5.0203 38.4700 0.0001 0.0190 −0.1807 0.1524 Industrial Select Sector 43.1685 19.6372 15.3600 105.5300 0.0003 0.0137 −0.1204 0.1013 Technology Select Sector 39.6322 26.8948 11.5800 151.3200 0.0003 0.0164 −0.1487 0.1493 Consumer Staples Select Sector 35.9272 14.3787 17.8200 71.5200 0.0001 0.0185 −0.2249 0.1537 Utilities Select Sector 38.0688 11.9984 15.2300 70.9800 0.0002 0.0234 −0.2814 0.1277 Healthcare Select Sector 48.9630 26.4922 21.8800 128.9800 0.0003 0.0329 −0.1038 2.5759 Consumer Discretionary Select Sector 55.7172 36.9693 16.1100 183.7400 0.0005 0.0190 −0.3514 0.1537 30−Year Treasury Bond 4.0043 1.2482 0.9900 6.7500 − 0.0001 0.0167 −0.2332 0.2569 10−Year Treasury Note 3.3704 1.4023 0.5200 6.7900 − 0.0001 0.0234 −0.3151 0.3417 5−Year Treasury Note 2.7563 1.6036 0.1900 6.8300 − 0.0002 0.0329 −0.3567 0.3145 2−Year Treasury Note 2.1419 1.8238 0.0900 6.9300 − 0.0004 0.0465 −0.3514 0.3483 13−Week Treasury Bill 1.6575 1.8286 −0.1050 6.2200 − 0.0011 0.2473 −4.0073 2.5759 WTI Crude Oil 58.9245 26.7146 −36.9800 145.1600 0.0005 0.0274 −0.2814 0.4258 Brent Crude Oil 61.4961 30.3102 9.1200 143.6800 0.0005 0.0254 −0.2564 0.4120 Commodity Research Bureau Index 240.2832 70.1056 106.2929 473.5200 0.0001 0.0109 −0.0794 0.0742 Source: elaborated by the authors. 3.2. Diebold–Yilmaz Method As presented in Tessmann et al. (2021), the Diebold and Yilmaz (2012) method uses a variance decomposition associated with autoregressive vectors, VAR, estimated using the Economies 2024,12, 149 8 of 20 Akaike criterion for lag selection. To calculate the total spillover index, the decomposition of the error variance is estimated H steps forward by θg ij(H): Sg(H)= ∑N i,j=0 i=j ϑg ij(H) ∑N i,j=1ϑg ij(H)100 = ∑N i,j=1 i=j ϑg ij(H) N100 (1) where Σ is the variance matrix for the error vector ε , each iand jare a different sector of the US economy, σjj is the standard deviation of the error term for the equation jth, and ei is the selection vector, with one as the ith element and zeros otherwise. Measure the directional repercussions of volatility received by the US economy sector ifrom all other sectors jas in Equation (2). The same applies to measuring the directional repercussions of volatility transmitted by sector index ito all other sector indices jby inverting the relationship ij by ji in the numerator. Sg i.(H)= ∑N j=1 j=i ϑg ij(H) ∑N i,j=1ϑg ij(H)100 = ∑N j=1 j=i ϑg ij(H) N100 (2) 3.3. Baruník–Krehlík Refinement As in Tessmann et al. (2021), the total spillover index that measures the transmission of volatility between the US economy sectors is divided into overnight (1 day), very short-term (1 to 4 days), short-term (4 to 30 days) and medium/long term (more than 30 days) using the method developed by Baruník and Krehlík(2018) that measures connectivity frequency dynamics through the spectral representation of variance decompositions. The measure of connectivity is based on impulse response functions, defined in the time domain, and when defining the generalized decompositions of staggered error variance in the frequency bands d=(a,b) : a , b∈(−π,π)a<b , the frequency connection in frequency band d is then defined as CF d=100  ∑θ∼ d)j,k ∑θ∼ ∞)j,k −Trθ∼ d ∑θ∼ ∞)j,k (3) The internal connection in frequency band d is then defined as in Equation (4). The internal connection denotes the connection effect that the frequency connection breaks down the original connection into distinct parts which, in short, provide the original connection measurement C∞. Cw d=100 1−Trθ∼ d ∑(θ∼ d)j,k!(4) 4. Results The Diebold–Yilmaz Spillover Index shows the extent to which volatility is transmitted across reported assets. The index can be interpreted as a percentage varying from zero to one hundred. Its output provides an overview of asset-to-asset, asset-to-market, and market-to-asset volatility, as well as total market connectivity. Figure 1depicts the total connectivity of US assets along the years 1998 to 2021. During this period, that is, from 22 December 1998 to 12 July 2021, several significant peaks of volatility occurred in financial markets. Our research began after the Asian financial crisis in 1997. This crisis generated considerable volatility in Asian economies and in other emerging markets. However, this event did not affect the beginning of our study period. In 2000, the bursting of the dot-com bubble resulted in a significant market correction, in Economies 2024,12, 149 15 of 20 of the Wilshire 5000 index for the entire market. This last index is a stock market index that tracks the performance of (nearly) the entirety of the publicly traded US equity market. Table A5 displays the results of medium/long-term impacts (i.e., greater than thirty days). In it, we observe a distinct pattern with significant volatility among the 64 assets involved. The DJIA, Wilshire 5000, and S&P 500 were the assets that transmitted the most volatility for the various sectors and market indices. Overall, the sectors most affected by volatility connections from others were transport, energy, healthcare, industry, and technology. Market indices such as the S&P 500, Nasdaq, and Wilshire 5000 also received considerable levels of volatility. We also emphasize that the cell at the intersection of the last column and the bottom row of each table represents the total connectivity of the market. In this sense, total connectivity tends to smooth out as time increases. For example, in Table 4, said intersection cell shows a total connectivity of 29.42 in the period of 1 day (overnight). However, when we look at Table A1, where the period considered is 1 to 4 days, we see a small increase to 30.89. However, this trend is reversed in Table A2, which evaluates the period from 4 to 30 days (short term), as connectivity decreases to 14.95. Finally, in the period of 30 days or more (medium/long term), connectivity reaches its lowest point: 2.02. Economies 2024,12, 149 16 of 20 Table A1. Total spillover indices. CRB IRX DGS10 DGS2 DGS30 DGS5 XLB DCOIL BRENTEU DCOIL WTICO X.DJI X.DJT X.DJU XLE XLF XLV XLI NASDAQ COM X.SPX XLK XLU WIL 5000 FROM CRB 29.88 0.25 1.51 0.48 1.72 1.13 4.09 11.90 18.69 2.41 1.57 1.38 9.91 1.59 0.92 2.42 1.71 2.83 1.44 1.12 3.03 3.34 IRX 0.51 88.99 0.36 0.77 0.36 0.38 0.55 0.30 0.59 0.71 0.37 0.45 1.20 1.08 0.23 0.47 0.37 0.76 0.33 0.43 0.79 0.52 DGS10 1.12 0.07 22.04 9.26 19.01 18.30 2.47 0.99 0.79 3.06 2.65 0.53 2.59 2.52 1.65 3.01 1.91 2.83 1.80 0.54 2.85 3.71 DGS2 0.54 0.29 13.69 33.06 9.03 19.78 1.66 0.36 0.38 2.52 2.18 0.45 1.63 2.37 1.32 2.39 1.64 2.42 1.51 0.41 2.39 3.19 DGS30 1.44 0.10 21.48 6.88 24.92 15.38 2.58 1.11 1.17 2.94 2.44 0.42 2.87 2.53 1.54 2.88 1.76 2.74 1.60 0.45 2.78 3.58 DGS5 0.90 0.11 19.51 14.24 14.52 23.52 2.11 0.71 0.57 2.84 2.48 0.45 2.18 2.47 1.53 2.79 1.76 2.63 1.61 0.44 2.63 3.64 XLB 1.80 0.08 1.54 0.70 1.41 1.24 13.66 0.63 0.77 8.89 7.76 3.53 6.60 6.47 5.18 9.08 5.32 8.50 4.82 3.51 8.49 4.11 DCOIL BRENTEU 16.79 0.44 1.63 0.40 1.66 1.10 2.08 37.55 17.47 1.56 0.81 0.93 8.37 1.08 0.51 1.39 1.00 1.76 0.89 0.68 1.88 2.97 DCOIL WTICO 22.76 0.25 1.26 0.41 1.69 0.88 2.04 15.07 36.41 1.36 0.63 0.58 8.49 0.76 0.49 1.27 0.97 1.63 0.87 0.43 1.75 3.03 X.DJI 0.84 0.08 1.48 0.83 1.24 1.29 6.93 0.40 0.43 10.67 6.88 3.91 5.07 7.49 6.55 8.76 6.86 9.95 6.70 4.01 9.64 4.25 X.DJT 0.68 0.05 1.65 0.91 1.33 1.45 7.74 0.26 0.25 8.85 13.58 3.02 4.48 7.40 5.39 9.81 6.49 8.85 5.65 3.14 9.02 4.12 X.DJU 0.86 0.07 0.58 0.31 0.41 0.47 5.19 0.47 0.37 7.39 4.42 19.80 5.72 4.98 4.99 5.75 3.62 7.48 3.49 16.53 7.10 3.82 XLE 5.07 0.21 1.79 0.77 1.75 1.43 7.53 2.98 3.61 7.38 5.09 4.50 15.58 5.39 3.96 6.83 3.88 7.48 3.41 3.92 7.46 4.02 XLF 0.72 0.15 1.53 0.96 1.35 1.41 6.44 0.31 0.31 9.53 7.30 3.39 4.74 13.51 5.41 8.31 6.20 9.87 5.39 3.45 9.71 4.12 XLV 0.49 0.03 1.13 0.62 0.93 1.00 5.75 0.21 0.25 9.29 5.95 3.76 3.86 5.99 15.12 7.74 7.59 9.78 6.77 4.14 9.61 4.04 XLI 0.91 0.06 1.58 0.85 1.33 1.38 7.68 0.38 0.42 9.53 8.32 3.35 5.08 7.10 5.93 11.55 6.60 9.23 6.09 3.43 9.20 4.21 NASDAQ COM 0.71 0.05 1.14 0.67 0.92 1.00 5.12 0.29 0.35 8.49 6.24 2.35 3.33 6.05 6.65 7.52 13.09 10.48 11.93 2.63 10.97 4.14 X.SPX 0.95 0.08 1.32 0.76 1.12 1.16 6.37 0.42 0.48 9.56 6.61 3.80 4.94 7.46 6.65 8.16 8.14 10.27 7.65 3.97 10.15 4.27 XLK 0.64 0.05 1.14 0.65 0.89 0.97 4.95 0.29 0.33 8.84 5.78 2.43 3.14 5.61 6.32 7.38 12.70 10.50 13.93 2.86 10.61 4.10 XLU 0.64 0.07 0.54 0.26 0.40 0.42 5.07 0.32 0.27 7.43 4.53 16.33 4.92 4.98 5.43 5.81 3.95 7.65 4.00 19.72 7.26 3.82 WIL 5000INDFC 1.01 0.08 1.33 0.75 1.14 1.16 6.38 0.45 0.51 9.29 6.76 3.62 4.94 7.36 6.54 8.15 8.54 10.17 7.76 3.77 10.27 4.27 TO 2.83 0.12 3.63 1.97 2.96 3.40 4.42 1.80 2.29 5.80 4.23 2.82 4.48 4.32 3.68 5.23 4.33 6.07 3.99 2.85 6.06 77.28 Source: elaborated by the authors. Table A2. Volatility spillovers in the overnight period (one day only). CRB 13-Week Treasury Bill 10-Years Treasury Note 2-Year Treasury Note 30-Year Treasury Bond 5-Year Treasury Note XLB Brent Oil WTI Oil DJI DJT DJU XLE XLF XLV XLI NDQ SPX XLK XLU WILSHIRE 5000 FROM CRB 10.32 0.02 0.56 0.15 0.56 0.40 0.89 3.99 6.55 0.50 0.28 0.23 2.50 0.31 0.19 0.51 0.31 0.58 0.26 0.15 0.62 0.93 IRX 0.20 38.18 0.23 0.29 0.21 0.20 0.35 0.16 0.19 0.38 0.21 0.30 0.61 0.59 0.15 0.25 0.21 0.43 0.20 0.28 0.44 0.28 DGS10 0.44 0.01 7.74 3.26 6.68 6.47 0.94 0.42 0.36 1.34 1.03 0.28 1.12 1.02 0.78 1.20 0.82 1.23 0.80 0.29 1.23 1.42 DGS2 0.25 0.08 5.45 14.29 3.70 7.81 0.67 0.15 0.18 1.05 0.86 0.20 0.71 1.02 0.56 0.96 0.68 1.02 0.64 0.20 1.01 1.30 DGS30 0.54 0.01 7.35 2.54 8.57 5.54 0.95 0.45 0.49 1.29 0.93 0.21 1.21 1.02 0.72 1.14 0.74 1.17 0.70 0.24 1.18 1.35 DGS5 0.37 0.01 7.26 5.06 5.52 8.79 0.80 0.31 0.24 1.20 0.93 0.23 0.91 0.98 0.69 1.10 0.74 1.11 0.70 0.23 1.11 1.40 XLB 0.72 0.01 0.61 0.27 0.53 0.50 4.97 0.23 0.36 3.25 2.74 1.36 2.41 2.31 1.96 3.25 1.97 3.16 1.80 1.33 3.14 1.52 Brent Crude Oil 2.70 0.06 0.56 0.12 0.45 0.34 0.27 10.94 2.80 0.25 0.12 0.19 1.17 0.12 0.11 0.22 0.12 0.26 0.12 0.11 0.27 0.49 Economies 2024,12, 149 17 of 20 Table A2. Cont. CRB 13-Week Treasury Bill 10-Years Treasury Note 2-Year Treasury Note 30-Year Treasury Bond 5-Year Treasury Note XLB Brent Oil WTI Oil DJI DJT DJU XLE XLF XLV XLI NDQ SPX XLK XLU WILSHIRE 5000 FROM WTI Crude Oil 8.07 0.08 0.38 0.11 0.44 0.23 0.51 4.90 13.00 0.38 0.16 0.19 2.36 0.20 0.15 0.34 0.22 0.43 0.21 0.11 0.46 0.95 DJIA 0.41 0.02 0.67 0.35 0.54 0.58 2.76 0.17 0.22 4.34 2.68 1.67 2.15 3.01 2.68 3.45 2.79 4.08 2.73 1.71 3.94 1.74 DJTA 0.31 0.01 0.68 0.36 0.52 0.59 2.85 0.10 0.14 3.43 4.93 1.24 1.78 2.82 2.14 3.62 2.50 3.45 2.20 1.27 3.50 1.60 DJUA 0.41 0.03 0.36 0.17 0.26 0.29 2.22 0.20 0.22 3.31 1.90 7.54 2.36 2.18 2.25 2.42 1.71 3.37 1.67 6.52 3.19 1.67 XLE 1.96 0.04 0.68 0.28 0.61 0.54 2.81 1.10 1.42 2.94 1.87 1.82 5.86 2.11 1.65 2.55 1.55 3.01 1.38 1.58 2.97 1.57 XLF 0.37 0.04 0.63 0.36 0.53 0.57 2.65 0.14 0.18 3.88 2.78 1.48 2.08 5.37 2.28 3.27 2.52 4.03 2.20 1.49 3.96 1.69 XLV 0.26 0.01 0.54 0.27 0.43 0.47 2.25 0.10 0.15 3.52 2.17 1.57 1.63 2.20 5.61 2.91 2.69 3.65 2.46 1.65 3.58 1.55 XLI 0.40 0.01 0.65 0.32 0.54 0.56 2.77 0.14 0.21 3.57 2.94 1.35 1.94 2.54 2.26 4.24 2.44 3.47 2.28 1.36 3.44 1.58 Nasdaq 0.33 0.01 0.52 0.28 0.40 0.45 2.03 0.13 0.17 3.44 2.40 1.05 1.48 2.47 2.70 2.96 4.88 4.15 4.44 1.14 4.31 1.66 SPX 0.46 0.02 0.60 0.32 0.49 0.53 2.57 0.18 0.25 3.91 2.57 1.62 2.12 3.01 2.72 3.23 3.23 4.18 3.04 1.67 4.12 1.75 XLK 0.30 0.01 0.52 0.29 0.39 0.45 2.00 0.12 0.16 3.65 2.25 1.11 1.45 2.34 2.62 2.97 4.81 4.24 5.27 1.27 4.25 1.68 XLU 0.30 0.03 0.32 0.13 0.24 0.25 2.08 0.13 0.16 3.15 1.86 6.28 1.98 2.06 2.33 2.34 1.73 3.25 1.75 7.84 3.08 1.59 Wilshire 5000 0.47 0.02 0.60 0.32 0.49 0.52 2.51 0.19 0.26 3.73 2.57 1.52 2.08 2.92 2.63 3.16 3.29 4.05 3.00 1.56 4.06 1.71 TO 0.92 0.03 1.39 0.73 1.12 1.30 1.66 0.63 0.70 2.29 1.58 1.14 1.62 1.68 1.50 1.99 1.67 2.39 1.55 1.15 2.37 29.42 Source: elaborated by the authors. Table A3. Volatility spillovers in the very short term: one to four days. CRB 13-Week Treasury Bill 10-Year Treasury Note 2-Year Treasury Note 30-Year Treasury Bond 5-Year Treasury Note XLB Brent Oil WTI Oil DJI DJT DJU XLE XLF XLV XLI NDQ SPX XLK XLU WILSHIRE 5000 FROM CRB 12.31 0.12 0.63 0.21 0.73 0.48 1.85 4.94 7.65 1.10 0.72 0.65 4.36 0.74 0.43 1.09 0.79 1.30 0.66 0.54 1.39 1.45 IRX 0.21 34.40 0.12 0.33 0.12 0.14 0.17 0.10 0.25 0.24 0.12 0.13 0.43 0.37 0.06 0.16 0.12 0.25 0.11 0.13 0.26 0.18 DGS10 0.45 0.04 9.02 3.79 7.80 7.48 1.00 0.39 0.31 1.18 1.06 0.19 1.01 0.99 0.62 1.20 0.75 1.10 0.70 0.19 1.11 1.49 DGS2 0.20 0.13 5.44 12.52 3.56 7.85 0.66 0.14 0.14 0.99 0.87 0.17 0.63 0.91 0.52 0.95 0.65 0.95 0.59 0.16 0.94 1.26 DGS30 0.59 0.05 8.81 2.77 10.23 6.21 1.05 0.45 0.47 1.14 0.98 0.15 1.13 1.00 0.59 1.15 0.70 1.07 0.63 0.16 1.09 1.44 DGS5 0.36 0.06 7.89 5.86 5.84 9.48 0.86 0.28 0.23 1.11 1.01 0.17 0.86 0.99 0.59 1.12 0.70 1.03 0.63 0.16 1.04 1.47 XLB 0.69 0.04 0.61 0.28 0.56 0.49 5.55 0.25 0.28 3.60 3.18 1.42 2.67 2.65 2.09 3.71 2.15 3.44 1.95 1.42 3.44 1.66 Brent Crude Oil 7.96 0.21 0.66 0.17 0.69 0.46 0.95 16.09 8.28 0.70 0.36 0.42 3.89 0.52 0.22 0.61 0.45 0.80 0.39 0.31 0.85 1.38 WTI Crude Oil 9.18 0.09 0.52 0.18 0.73 0.39 0.89 6.27 14.70 0.59 0.27 0.25 3.63 0.33 0.21 0.55 0.43 0.71 0.38 0.19 0.76 1.26 DJIA 0.29 0.03 0.56 0.32 0.47 0.49 2.72 0.15 0.14 4.17 2.73 1.51 1.94 2.94 2.56 3.47 2.68 3.88 2.62 1.55 3.76 1.66 DJTA 0.24 0.02 0.64 0.37 0.52 0.57 3.12 0.10 0.08 3.52 5.52 1.18 1.75 2.96 2.14 3.97 2.59 3.51 2.25 1.24 3.59 1.64 DJUA 0.29 0.02 0.19 0.11 0.13 0.15 1.97 0.17 0.11 2.76 1.67 7.89 2.18 1.88 1.87 2.20 1.32 2.80 1.28 6.52 2.65 1.44 XLE 1.98 0.09 0.70 0.31 0.71 0.57 2.98 1.19 1.40 2.87 2.03 1.76 6.21 2.12 1.53 2.71 1.50 2.91 1.32 1.54 2.91 1.58 XLF 0.24 0.07 0.60 0.40 0.54 0.56 2.52 0.12 0.10 3.75 2.93 1.30 1.81 5.36 2.10 3.31 2.45 3.88 2.12 1.33 3.82 1.62 XLV 0.17 0.01 0.43 0.25 0.35 0.38 2.32 0.08 0.07 3.75 2.44 1.49 1.51 2.45 6.15 3.15 3.13 3.97 2.75 1.66 3.91 1.63 XLI 0.33 0.02 0.62 0.35 0.52 0.54 3.12 0.15 0.14 3.83 3.40 1.32 2.02 2.90 2.38 4.68 2.66 3.71 2.45 1.36 3.70 1.69 Economies 2024,12, 149 18 of 20 Table A3. Cont. CRB 13-Week Treasury Bill 10-Year Treasury Note 2-Year Treasury Note 30-Year Treasury Bond 5-Year Treasury Note XLB Brent Oil WTI Oil DJI DJT DJU XLE XLF XLV XLI NDQ SPX XLK XLU WILSHIRE 5000 FROM Nasdaq 0.25 0.02 0.43 0.26 0.35 0.38 2.02 0.11 0.12 3.33 2.49 0.89 1.26 2.37 2.61 2.98 5.25 4.13 4.79 1.01 4.34 1.63 SPX 0.34 0.03 0.50 0.30 0.43 0.44 2.50 0.16 0.16 3.73 2.63 1.47 1.89 2.93 2.60 3.23 3.21 4.01 3.02 1.54 3.97 1.67 XLK 0.23 0.02 0.43 0.26 0.34 0.37 1.94 0.11 0.11 3.45 2.30 0.91 1.17 2.18 2.47 2.91 5.10 4.12 5.58 1.08 4.18 1.60 XLU 0.22 0.02 0.18 0.10 0.13 0.14 1.96 0.12 0.08 2.84 1.75 6.50 1.90 1.92 2.08 2.26 1.49 2.93 1.52 7.78 2.78 1.47 Wilshire 5000 0.36 0.03 0.50 0.30 0.44 0.44 2.52 0.17 0.17 3.64 2.70 1.40 1.90 2.91 2.57 3.24 3.39 4.00 3.08 1.47 4.05 1.68 TO 1.17 0.05 1.45 0.80 1.19 1.36 1.77 0.73 0.97 2.29 1.70 1.11 1.81 1.72 1.44 2.09 1.73 2.40 1.58 1.12 2.40 30.89 Source: elaborated by the authors. Table A4. Spillovers in the short term: four to thirty days. CRB 13-Week Treasury Bill 10-Year Treasury Note 2-Year Treasury Note 30-Year Treasury Bond 5-Year Treasury Note XLB Brent Oil WTI Oil DJI DJT DJU XLE XLF XLV XLI NDQ SPX XLK XLU WILSHIRE 5000 FROM CRB 6.39 0.09 0.29 0.10 0.38 0.21 1.19 2.61 3.94 0.71 0.50 0.44 2.68 0.48 0.27 0.72 0.54 0.84 0.45 0.37 0.90 0.84 IRX 0.08 14.49 0.02 0.14 0.02 0.04 0.03 0.03 0.13 0.08 0.03 0.02 0.14 0.11 0.01 0.05 0.03 0.07 0.03 0.02 0.08 0.05 DGS10 0.20 0.02 4.65 1.94 3.99 3.83 0.48 0.16 0.11 0.48 0.50 0.06 0.41 0.45 0.22 0.54 0.30 0.45 0.27 0.05 0.45 0.71 DGS2 0.08 0.07 2.48 5.51 1.56 3.63 0.29 0.06 0.06 0.42 0.39 0.06 0.26 0.39 0.21 0.42 0.27 0.39 0.24 0.05 0.39 0.56 DGS30 0.27 0.03 4.68 1.38 5.38 3.20 0.51 0.18 0.18 0.45 0.47 0.05 0.47 0.45 0.21 0.52 0.28 0.44 0.24 0.05 0.45 0.69 DGS5 0.15 0.04 3.84 2.92 2.78 4.62 0.40 0.11 0.09 0.47 0.48 0.05 0.36 0.44 0.22 0.51 0.28 0.43 0.25 0.04 0.43 0.68 XLB 0.34 0.03 0.28 0.13 0.28 0.22 2.76 0.13 0.13 1.79 1.63 0.67 1.35 1.33 1.00 1.87 1.06 1.68 0.94 0.67 1.68 0.82 Brent Crude Oil 5.38 0.15 0.36 0.10 0.46 0.26 0.76 9.24 5.61 0.53 0.30 0.29 2.91 0.39 0.15 0.48 0.38 0.61 0.33 0.23 0.67 0.97 WTI Crude Oil 4.84 0.07 0.31 0.11 0.47 0.23 0.56 3.43 7.67 0.35 0.17 0.12 2.20 0.20 0.11 0.34 0.28 0.43 0.25 0.11 0.47 0.72 DJIA 0.13 0.02 0.22 0.13 0.20 0.20 1.27 0.07 0.06 1.91 1.30 0.64 0.87 1.36 1.16 1.62 1.23 1.76 1.19 0.67 1.71 0.75 DJTA 0.11 0.02 0.29 0.17 0.25 0.26 1.56 0.05 0.03 1.68 2.75 0.53 0.84 1.43 0.99 1.96 1.23 1.66 1.06 0.55 1.7 0.78 DJUA 0.14 0.01 0.03 0.02 0.02 0.02 0.88 0.08 0.04 1.16 0.75 3.84 1.05 0.81 0.77 0.99 0.52 1.16 0.48 3.07 1.11 0.63 XLE 0.99 0.06 0.35 0.15 0.38 0.28 1.52 0.60 0.69 1.38 1.05 0.81 3.09 1.03 0.69 1.37 0.73 1.38 0.63 0.70 1.40 0.77 XLF 0.99 0.04 0.27 0.18 0.25 0.25 1.12 0.05 0.03 1.68 1.39 0.53 0.76 2.45 0.91 1.52 1.09 1.73 0.94 0.55 1.71 0.72 XLV 0.05 0.01 0.15 0.09 0.13 0.13 1.05 0.03 0.02 1.77 1.018 0.62 0.64 1.18 2.96 1.48 1.56 1.90 1.36 0.74 1.87 0.76 XLI 0.16 0.02 0.27 0.16 0.24 0.24 1.58 0.08 0.06 1.88 1.74 0.59 0.99 1.46 1.13 2.32 1.32 1.81 1.20 0.62 1.81 0.83 Nasdaq 0.11 0.01 0.17 0.11 0.15 0.14 0.95 0.05 0.05 1.53 1.19 0.37 0.53 1.07 1.19 1.39 2.60 1.93 2.38 0.43 2.05 0.75 SPX 0.14 0.02 0.19 0.12 0.18 0.17 1.15 0.07 0.07 1.69 1.24 0.63 0.82 1.34 1.17 1.50 1.50 1.83 1.41 0.67 1.82 0.76 XLK 0.10 0.01 0.17 0.10 0.14 0.14 0.89 0.05 0.05 1.54 1.08 0.36 0.47 0.95 1.09 1.32 2.47 1.89 2.71 0.44 1.92 0.72 XLU 0.11 0.01 0.03 0.02 0.03 0.02 0.91 0.06 0.03 1.27 0.81 3.13 0.92 0.88 0.90 1.06 0.64 1.30 0.65 3.62 1.24 0.67 Wilshire 5000 0.16 0.02 0.20 0.12 0.18 0.17 1.19 0.08 0.07 1.69 1.31 0.61 0.85 1.36 1.18 1.54 1.64 1.87 1.48 0.65 1.90 0.78 TO 0.65 0.04 0.70 0.39 0.58 0.65 0.87 0.38 0.54 1.07 0.83 0.50 0.93 0.81 0.65 1.01 0.83 1.13 0.75 0.51 1.14 14.95 Source: elaborated by the authors. Economies 2024,12, 149 19 of 20 Table A5. Spillovers in the medium/long term: more than thirty days. CRB 13-Week Treasury Bill 10-Year Treasury Note 2-Year Treasury Note 30-Year Treasury Bond 5-Year Treasury Note XLB Brent Oil WTI Oil DJI DJT DJU XLE XLF XLV XLI NDQ SPX XLK XLU WILSHIRE 5000 FROM CRB 0.87 0.01 0.04 0.01 0.05 0.03 0.17 0.36 0.54 0.10 0.07 0.06 0.37 0.07 0.04 0.10 0.08 0.12 0.06 0.05 0.13 0.12 IRX 0.01 1.92 0.00 0.02 0.00 0.00 0.00 0.00 0.02 0.01 0.00 0.00 0.02 0.01 0.00 0.01 0.00 0.01 0.00 0.00 0.01 0.01 DGS10 0.03 0.00 0.63 0.26 0.54 0.52 0.06 0.02 0.01 0.06 0.07 0.01 0.05 0.06 0.03 0.07 0.04 0.06 0.03 0.01 0.06 0.10 DGS2 0.01 0.01 0.33 0.74 0.21 0.49 0.04 0.01 0.01 0.06 0.05 0.01 0.03 0.05 0.03 0.06 0.04 0.05 0.03 0.01 0.05 0.07 DGS30 0.04 0.00 0.64 0.19 0.74 0.44 0.07 0.02 0.02 0.06 0.06 0.01 0.06 0.06 0.03 0.07 0.04 0.06 0.03 0.01 0.06 0.09 DGS5 0.02 0.00 0.52 0.40 0.38 0.62 0.05 0.01 0.01 0.06 0.06 0.01 0.05 0.06 0.03 0.07 0.04 0.06 0.03 0.01 0.06 0.09 XLB 0.05 0.00 0.04 0.02 0.02 0.04 0.03 0.38 0.02 0.24 0.22 0.09 0.18 0.18 0.13 0.25 0.14 0.23 0.13 0.09 0.23 0.11 Brent Crude Oil 0.75 0.02 0.05 0.01 0.06 0.04 0.11 1.28 0.79 0..08 0.04 0.04 0.41 0.05 0.02 0.07 0.05 0.09 0.05 0.03 0.10 0.14 WTI Crude Oil 0.66 0.01 0.04 0.01 0.07 0.03 0.08 0.47 1.05 0.05 0.02 0.02 0.31 0.03 0.02 0.05 0.04 0.06 0.04 0.01 0.07 0.10 DJIA 0.02 0.00 0.03 0.02 0.03 0.03 0.17 0.01 0.01 0.26 0.18 0.09 0.12 0.18 0.15 0.22 0.17 0.24 0.16 0.09 0.23 0.10 DJTA 0.01 0.00 0.04 0.02 0.03 0.03 0.21 0.01 0.00 0.23 0.37 0.07 0.11 0.19 0.13 0.27 0.17 0.22 0.14 0.07 0.23 0.11 DJUA 0.02 0.00 0.00 0.00 0.00 0.00 0.12 0.01 0.00 0.15 0.10 0.52 0.14 0.11 0.10 0.13 0.07 0.15 0.06 0.41 0.15 0.08 XLE 0.14 0.01 0.5 0.02 0.05 0.04 0.21 0.08 0.09 0.19 0.14 0.11 0.42 0.14 0.09 0.19 0.10 1.19 0.09 0.09 0.19 0.10 XLF 0.01 0.00 0.04 0.02 0.03 0.03 0.15 0.01 0.00 0.22 0.19 0.07 0.10 0.33 0.12 0.20 0.15 0.23 0.13 0.07 0.23 0.10 XLV 0.01 0.00 0.02 0.01 0.02 0.02 0.14 0.00 0.00 0.24 0.16 0.08 0.08 0.16 0.40 0.20 0.21 0.26 0.18 0.10 0.25 0.10 XLI 0.02 0.00 0.04 0.02 0.03 0.03 0.21 0.01 0.01 0.26 0.24 0.08 0.13 0.20 0.15 0.31 0.18 0.24 0.16 0.08 0.25 0.11 Nasdaq 0.02 0.00 0.02 0.01 0.02 0.02 0.13 0.01 0.01 0.20 0.16 0.05 0.07 0.14 0.16 0.19 0.35 0.26 0.32 0.06 0.28 0.10 SPX 0.02 0.00 0.03 0.02 0.02 0.02 0.15 0.01 0.01 0.23 0.17 0.08 0.11 0.18 0.16 0.20 0.20 0.25 0.19 0.09 0.24 0.10 XLK 0.01 0.00 0.02 0.01 0.02 0.02 0.12 0.01 0.01 0.21 0.14 0.05 0.06 0.13 0.15 0.18 0.33 0.25 0.37 0.06 0.26 0.10 XLU 0.01 0.00 0.00 0.00 0.00 0.00 0.12 0.01 0.00 0.17 0.11 0.42 0.13 0.12 0.12 0.14 0.09 0.17 0.09 0.49 0.17 0.09 Wilshire 5000 0.02 0.00 0.03 0.02 0.02 0.02 0.16 0.01 0.01 0.23 0.18 0.08 0.11 0.18 0.16 0.21 0.22 0.25 0.20 0.09 0.26 0.11 TO 0.09 0.01 0.09 0.05 0.08 0.09 0.12 0.05 0.08 0.14 0.11 0.07 0.13 0.11 0.09 0.14 0.11 0.15 0.10 0.07 0.15 2.02 Source: elaborated by the authors. Economies 2024,12, 149 20 of 20 References Baillie, Richard T., and Tim Bollerslev. 1991. Intra-day and inter-market volatility in foreign exchange rates. Review of Economic Studies 58: 565–85. [CrossRef] Baruník, Jozef, and Tomáš Krehlík. 2018. Measuring the frequency dynamics of financial connectedness and systemic risk. Journal of Financial Economics 16: 271–96. [CrossRef] Barunik, Jozef, Evzen Kocenda, and Lukas Vacha. 2015. Volatility Spillovers Across Petroleum Markets. William Davidson Institute Working Paper 1093. Available online: https://ssrn.com/abstract=2600204 (accessed on 12 March 2024). Baruník, Jozef, Evžen Koˇcenda, and Lukáš Vácha. 2017. Asymmetric Volatility Connectedness on the Forex Market. Journal of International Money and Finance 77: 39–56. [CrossRef] Bouri, Elie, Maria E. De Boyrie, and Ivelina Pavlova. 2017. Volatility transmission from commodity markets to sovereign CDS spreads in emerging and frontier countries. International Review of Financial Analysis 49: 155–65. [CrossRef] Chan, Louis K. C., Yasushi Hamao, and Josef Lakonishok. 1991. Fundamentals and Stock Returns in Japan. Journal of Finance 46: 1739–64. [CrossRef] Costa, Antonio, Paulo Matos, and Cristiano da Silva. 2022. Sectoral Connectedness: New Evidence from US Stock Market during COVID-19 Pandemics. Finance Research Letters 45: 102124. [CrossRef] [PubMed] Cox, John C., Jonathan E. Ingersoll, and Stephen A. Ross. 1985. A Theory of the Term Structure of Interest Rates. Econometrica 53: 385–407. [CrossRef] Cyree, Ken B., Mark D. Griffiths, and Drew B. Winters. 2014. An Empirical Examination of the Intraday Volatility in Euro–Dollar Rates. The Quarterly Review of Economics and Finance 44: 44–57. [CrossRef] Diebold, Francis X., and Kamil Yilmaz. 2009. Measuring Financial Asset Return and Volatility Spillovers, with Application to Global Equity Markets. The Economic Journal 119: 158–71. [CrossRef] Diebold, Francis X., and Kamil Yilmaz. 2012. Better to give than to receive: Predictive directional measurement of volatility spillovers. International Journal of Forecasting 28: 57–66. [CrossRef] Diebold, Francis X., and Kamil Yilmaz. 2014. On the Network Topology of Variance Decompositions: Measuring the Connectedness of Financial Firms. Journal of Econometrics 182: 119–34. [CrossRef] Ewing, Bradley T., Farooq Malik, and Ozkan Ozfidan. 2002. Volatility transmission in the oil and natural gas markets. Energy Economics 24: 525–38. Farid, Saqib, Ghulam Mujtaba Kayani, Muhammad Abubakr Naeem, and Syed Jawad Hussain Shahzad. 2021. Intraday volatility transmission among precious metals, energy, and stocks during the COVID-19 pandemic. Resources Policy 72: 102101. [CrossRef] Hassan, Syed Aun, and Farooq Malik. 2007. Multivariate GARCH modeling of sector volatility transmission. The Quarterly Review of Economics and Finance 47: 470–80. [CrossRef] Hughes, Michael P., Stanley D. Smith, and Drew B. Winters. 2006. An empirical examination of intraday volatility in on-the-run US Treasury bills. Journal of Economics and Business 59: 487–99. [CrossRef] Kumiega, Andrew, Thaddeus Neururer, and Ben Van Vliet. 2011. Independent component analysis for realized volatility: Analysis of the stock market crash of 2008. The Quarterly Review of Economics and Finance 51: 292–302. [CrossRef] Malik, Farooq, and Bradley T. Ewing. 2009. Volatility transmission between oil prices and equity sector returns. International Review of Financial Analysis 3: 95–100. [CrossRef] Mensi, Walid, Ramzi Nekhili, Xuan Vinh Vo, Tahir Suleman, and Sang Hoon Kang. 2021. Asymmetric volatility connectedness among US stock sectors. The North American Journal of Economics and Finance 56: 101327. [CrossRef] Nazlioglu, Saban, Cumhur Erdem, and Ugur Soytas. 2013. Volatility spillover between oil and agricultural commodity markets. Energy Economics 36: 658–65. [CrossRef] Passos, Marcelo de Oliviera, Mathias Schneid Tessmann, Régis Augusto Ely, Daniel Uhr, and Marcio Taceli Taveira. 2020. Effects of volatility among commodities in the long term: Analysis of a complex network. Annals of Financial Economics 15: 2050014. [CrossRef] Tessmann, Mathias Schneid, Régis Augusto Ely, and Mario Durante Canever. 2021. Volatility transmissions between commodity futures contracts in the short, medium and long term. International Journal of Financial Markets and Derivatives 8: 79–99. [CrossRef] Umar, Zaghum, Mariya Gubareva, Muhammad Naeem, and Ayesha Akhter. 2021. Return and volatility transmission between oil price shocks and agricultural commodities. PLoS ONE 16: e0246886. [CrossRef] [PubMed] Vardar, Gülin, Yener Co¸skun, and Tezer Yelkenci. 2018. Shock transmission and volatility spillover in stock and commodity markets: Evidence from advanced and emerging markets. Eurasian Economic Review 8: 231–88. [CrossRef] Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.