An innovative MS-VAR model with integrated financial knowledge for measuring the impact of stock market bubbles on financial security

Zheng, Chao Article An innovative MS-VAR model with integrated financial knowledge for measuring the impact of stock market bubbles on financial security Journal of Innovation & Knowledge (JIK) Provided in Cooperation with: Elsevier Suggested Citation: Zheng, Chao (2022) : An innovative MS-VAR model with integrated financial knowledge for measuring the impact of stock market bubbles on financial security, Journal of Innovation & Knowledge (JIK), ISSN 2444-569X, Elsevier, Amsterdam, Vol. 7, Iss. 3, pp. 1-20, https://doi.org/10.1016/j.jik.2022.100207 This Version is available at: https://hdl.handle.net/10419/327177 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. 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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-nc-nd/4.0/ An innovative MS-VAR model with integrated financial knowledge for measuring the impact of stock market bubbles on financial security Chao Zheng a, * a School of Economics, Shandong Normal University, Address: No.1, University Road, Science Park, Changqing District, Jinan, Shandong, 250358, P.R. China ARTICLE INFO Article History: Received 13 February 2022 Accepted 24 May 2022 Available online 1 June 2022 ABSTRACT In the modern financial system, division of labor and close cooperation between different departments are determinants of risk contagion. The risk resulting from the volatility of the stock market can easily spread to other industries and departments, leading to systemic financial and economic crises. Previous research has mostly examined financial security from the lens of macro currency security, and the security of the banking system, but has ignored its micro-basic problems, such as the bounded rationality of investors due to the lack of financial knowledge. The study analyzes the behavior of micro-investors, price fluctuations in the meso‑stock market, and the macro-financial security in a unified framework. First, we use the comprehensive analysis method to superimpose some basic values and investor behavior characteristics, such as the stock price fluctuation index, and then construct the ultimate stock price bubble index; second, the principal component method is used to establish a financial security index that is in line with basic economic reality and consistent with previous studies; the innovative MS-VAR model is used to analyze whether the stock price bubble will affect financial security, and the rhythm and correlation of the two parties under different regimes are summarized. The results show that the stock market bubble level istheGrangercauseoffinancial security, the stock market bubble index is the leading indicator of the financial security index, and the relevant parameters of the model are significant and have obvious economic significance. This study has important implications for scientific market regulation. © 2022 The Author(s). Published by Elsevier España, S.L.U. on behalf of Journal of Innovation & Knowledge. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Keywords: Stock price bubble index Financial security index Financial knowledge Innovative MS-VAR model JEL Codes: D830 G100 G410 Introduction Finance, which is the core of the modern economy, is not only an important tool for resource allocation and macro-control, but also an important force to promote economic and social development. Financial safety and stability are the basis of a country's steady and healthy economic development. Stock market risk has a micro-foundation, with some participants lacking financial knowledge and information interpretation ability. Moreover, due to the arbitrariness of transactions, irrational investors follow the trend blindly and chase sell in stock market. When stock prices rise from its basic level to the level of support, price bubbles are created, and when these bubbles reach a certain stage, they burst, and then stock prices fall rapidly, leading to sharp fluctuations in the stock market and risks in the capital market. Therefore, due to the COVID-19 pandemic, and the accelerated development of economic globalization, it is essential to improve investors’financial knowledge, guard against capital market risks, and maintain financial security. This study mainly analyzes the behavior of micro-investors, price fluctuations in the meso‑stock market, and macro-financial security in a unified framework, that is, the bounded rational decision-making behavior of investors due to the lack of financial knowledge at the micro level causes the excessive volatility risk of the stock market at the meso level, and the contagion effect of the risk will lead to the financial security at the macro level. The rest of this paper is organized as follows. Section 2 introduces the relevant literature and proposes hypotheses. Section 3 describes the mechanism of stock market bubbles affecting financial security. Section 4 builds a bubble index with multiple indicators that reflect the company's underlying value and market sentiment. Section 5 constructs the financial security index. Section 6 uses the innovative MSVAR model to empirically study the impact of China's stock price bubble index on the financial security index. Section 7 presents the conclusions and makes recommendations. Literature review Research on stock market bubbles The basic logic of a right-tailed unit root test (Sup ADF or SADF) and generalized right-tailed unit root test (Generalized SADF or GSADF) is to capture the nonlinear characteristics of stock prices and * Corresponding author: Chao Zheng, Institution: School of Economics, Shandong Normal University, No.1, University Road, Science Park, Changqing District, Jinan, Shandong, P.R. China, 250358. E-mail address: [email protected] https://doi.org/10.1016/j.jik.2022.100207 2444-569X/© 2022 The Author(s). Published by Elsevier España, S.L.U. on behalf of Journal of Innovation & Knowledge. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Journal of Innovation & Knowledge 7 (2022) 100207 Journal of Innovation &Knowledge https://www.journals.elsevier.com/journal-of-innovation-and-knowledge determine the critical value of statistics through rolling regression and forward recursion. Phillips et al. (2011) proposed SADF, which is better than ADF in the detection of periodic bubble bursts. Phillips et al.(2015) , further put forward the GSADF test method, which is better suited for sequences with multiple bubbles in the sample period. Fantazzini (2016) pointed out that there was a negative bubble in the oil market in 2014−2015 by combining the GSADF method and log-periodic power model. Kraussl et al. (2016) used sup-ADF to study asset price bubbles in the art market. Liu et al. (2017) used recursive sup-ADF to study the speculative bubble of China's consumer price index from 2006 to 2014. Guo (2018) used the BSADF method to study periodic bubbles in China's stock and real estate markets, and the results showed that periodic bubbles appeared frequently during the research period. Zhang et al. (2018) used SADF and GSADF, and found that there were multiple bubbles in China's real estate market. Ding (2021) analyzed the heterogeneity and impact of the ''herding behavior'' of various institutional investors under different market conditions and found that the ''herding behavior'' of securities investment funds and securities companies exacerbated the volatility of the stock market. Based on the monthly data for interest rates, money supply, and stock prices, Sun and Zhu (2021) studied the dynamic impact effect of price and quantity monetary policy on stock price using the MCMC method and TVP-SV-VAR model under the Bayesian framework and found that the impact of interest rates on stock prices is greater than that of money supply. Wang (2021) confirmed that the impact of monetary policy on stock asset prices is greater and lasts longer when the investor sentiment variables are included. Research on financial security Wang (2010) believed that capital financing secured financial security. Fredrish (2012) analyzed the types of financial systems in which financial security can be guaranteed. Emrah et al. (2013) studied the influence of financial opening on economic and financial security. The potential risks of the capital market have an impact on financial security (Zhu & Zhang, 2017). Liang (2018) analyzed the mechanism of systemic financial risks from the theoretical level and evaluated China'sfinancial security from both macro and micro perspectives. A sovereign credit rating is related to a country'sfinancial security and stability (Li, 2019). Zhao (2020) proposed the principles of effective supervision of legal digital currency risks, active maintenance of financial security, promotion of financial innovation, and development of regulatory technology. Excessive debt can easily lead to systemic risks, which is not conducive to maintaining financial security (Li & Ning, 2020). Miao and Run (2020) studied and proposed prevention suggestions based on three aspects, namely, the measurement method of systemic financial risk, risk contagion effect, and selection of regulatory tools. The impact of interest rate shocks and interest rate fluctuations on financial security is strongest during an economic crisis and weak during the period of the economic new normal (Liu et al., 2021). Research on financial knowledge Noctor et al. (1992) first proposed the concept of financial knowledge, which is defined as people's ability to make wise judgments and effective decisions in the use and management of funds. Lusardi et al. (2014) defined financial knowledge as the information related to people's handling of economic and financial affairs and the making of reasonable decisions in terms of wealth accumulation, financial planning, debt planning, investment management, and so on. Wu (2015) believed that the popularization of financial knowledge was an effective way to improve the breadth and depth of financial product investment. Xiang and Guo (2019) found that financial knowledge can change investors'risk attitudes. Jia (2020) found that popularizing financial knowledge helped to reduce the ratio of retail investors in China's stock market and promote the development of institutional investors. Gong et al. (2021) studied the interaction between heterogeneous traders and their impact on price discovery by establishing a futures market pricing model and found that behavioral factors, such as risk appetite, rationality, and market liquidity had a comprehensive impact on stability conditions. Xie (2021) believed that increasing the popularity of financial knowledge can significantly improve the level of human capital accumulation, restrain financial risks, and subsequently reduce the distortion of market factors. Luo (2021) found that financial knowledge can boost household consumption spending by improving the structure of household financial asset allocations. Mechanism of stock market bubbles affecting financial security Impact of investor behavior on stock price (1) Influence of investors'bounded rationality on stock price Given the influencing factors of stock price, Fama (1970) presented the efficient market hypothesis (EMH), which holds that from the perspective of information economics, the stock price is determined by and responds to information. The EMH theory is only a theoretical abstraction and simplification of the real price determination process because information cannot automatically affect the price and because investors, a key factor, are ignored. The premise for the information to work is that there are investors in the market who receive and interpret relevant information to form good and bad expectations regarding fluctuations in stock price. Under this expectation, buy and sell decisions are formed, and the purchase and sale orders of all investors in the whole market are gathered to form the equilibrium price of the stock at a certain time. As shown in Fig. 1, the stock price formation process can be described as follows: investors classify all information (historical, public, and private information) into two types: fundamental and technical information. Then, they interpret it as good or bad news regarding the corresponding stocks and form stock price expectations through the investor utility function. Subsequently, purchase and sale decisions are made, and finally, stock prices are determined. From a dynamic point of view, the newly formed stock price directly affects investors'expectations and is considered new historical information, becoming the basis for further analysis by investors. Considering investors as the research object may more truly reflect the trading situation in the stock market and the stock price decision process. Moreover, investors’bounded rationality and investor sentiment have naturally appeared in the field of vision as new research dimensions. In the traditional rational person hypothesis, investors'processing of all kinds of information is unbiased and costfree. If we ignore this hypothesis, that is, investors are limited rationally and cannot interpret all kinds of information accurately, the biased behavior of investors will evolve into market sentiment, resulting in investors making too optimistic or pessimistic judgments about stock price. The stock market is prone to price bubbles as they are greatly affected by investors'behavior bias. Therefore, investor behavior is one of the important factors that determine stock price. (1) Influence of financial knowledge on stock market investment Investors'bounded rationality will be manifested in various belief and behavior deviations, including loss aversion, regret avoidance, overconfidence, lack of self-confidence, and herding behavior. C. Zheng Journal of Innovation & Knowledge 7 (2022) 100207 2 Generally, the bounded rational behaviors of these investors accumulate in the stock market, resulting in a high stock turnover rate, soaring stock prices, and other phenomena, which can be summarized as the emotional factors that determine stock price. Financial knowledge affects investor participation in the stock market in many aspects. First, investors with financial knowledge can identify the risks and benefits of various stock products and reduce the threshold for entering the stock market. Second, with improvements in investors'financial knowledge, their acceptability of risk will also be enhanced, and their interest in investing in the stock market and choosing high-risk investment types, such as stocks will also be greatly promoted. Third, when investors have rich financial knowledge, it is not easy to produce cognitive biases, such as overconfidence. They focus more on allocation to different kinds of assets in accordance with their risk preference to ensure that they do not blindly pursue high returns and put all their assets in risky investments such as stocks, leading to the emergence of stock price bubbles (SPBs). Finally, further improvements in financial knowledge enable investors to reduce transaction costs and hold a more reasonable and effective portfolio. Analysis of the concept of financial security and its influencing factors (1) Definition of financial security Financial security is mainly defined from three angles: the financing security of monetary funds, the security of national interests, and the security concept of financial risk and crisis. Considering the literature, we define financial security as the state of healthy, stable, and orderly development of the financial industry. In this state, financial risks are controllable and do not accumulate above the threshold, resulting in no financial crises. The security status of the financial system can be described as a three-zone system, as shown in Fig. 2: Financial security (green), indicating that the risk of the financial system is controllable and operates well; Financial insecurity (mild, yellow) means that there is some accumulation of financial risks, and if the risk continues to accumulate it will threaten the stability of the financial system. Regulatory authorities need to deal with it in a timely and correct manner, to reduce financial security risks, or to at least maintain a mild state of financial insecurity and prevent further deterioration. In a state of financial insecurity (serious, red light), there will generally be a financial crisis, and once the risk breaks out, regulatory authorities need to take measures to deal with it quickly. (1) Definition of financial security The financial system is complex and huge, and according to the current supervision mode of China'sfinancial industry, it includes at least the following three subsystems, as shown in Fig. 3: Banking and insurance subsystem, securities subsystem, and currency subsystem. At the same time, from a broader perspective, the financial system is also a subsystem of the economic system, and the security of economic operations is essential for the security of the financial system. Therefore, the influencing factors of financial security can be analyzed from four dimensions: economic system security, banking and insurance system security, capital market security, and monetary security. Path analysis of stock market bubbles affecting financial security From the analysis in the previous section, it is evident that banking and insurance industry security, capital market security, and money market security are the three subsystems of the national financial security system. The security and stability of the stock market directly affect the security and stability of the capital market which subsequently affects financial security. The periodic expansion and rupture of stock market bubbles are typically unsafe events in the capital market, especially when stock prices collapse due to the Fig. 1. Information, investor expectations, stock price transmission chain. Fig. 2. Schematic diagram of the security status of the financial system. C. Zheng Journal of Innovation & Knowledge 7 (2022) 100207 3 bubbles bursting, and the effect of the collapse is transmitted and spread through the mechanism of the enterprise/family balance sheet effect. This leads to corporate liquidity risks and banking and currency crises, which ultimately affect financial security. The mechanism of the stock market bubble's impact on financial security can be divided into the family balance sheet effect and enterprise balance sheet effect, and after superimposing the principle of the financial accelerator, the corresponding impact effect is amplified. (1) Household balance sheet effect In the SPB expansion stage, individual investors with limited rationality will constantly revise their expectations, their emotions will become increasingly more optimistic, the effect of virtual wealth will be stronger, the level of consumption will improve, and consumption expenditure will be increased by mortgage. Thus, in the bubble burst and stock price collapse stage, the effect of wealth deflation will be significant, the shrinking of virtual wealth in the hands of investors will inhibit consumption expenditure, reduce total social demand, and slow economic growth. Some investors with leveraged consumption will default due to cash flow problems, and the crisis will extend to banks and other financial sectors. (1) Enterprise balance sheet effect The decline of the stock market worsens the balance sheet of enterprises, as the value of assets decline but the value of liabilities do not. To alleviate the debt pressure, enterprises usually need to sell equity in the secondary market, which further causes a decline in the stock market. If the debt type of the enterprise is an equity pledge, the decline in share price will lead to an insufficient value of the equity pledge, and financial institutions, such as banks or securities companies, will require an increase in the pledge. When the enterprise cannot take out the full amount of the pledge, the pledged equity may be sold, resulting in a sharp decline in share price and the demonstration effect of the decline. Severely insolvent enterprises will go bankrupt and liquidate, and the existence of mutual guarantee mechanisms for enterprise financing from banks will simultaneously lead to continuous debt default, which will induce the risk of asset losses in banks and other financial sectors, and the crisis will continue to spread, ultimately affecting financial security. (1) Principle of the financial accelerator There is a negative correlation between the agency cost of external financing and the borrower's net asset value. Therefore, if the borrower's net asset value changes positively with the economic cycle (e.g., when enterprises’profit and asset price increase with the economic cycle), the agency cost of external financing will change inversely with the economic cycle. Especially in periods of economic recession, the external financing cost of enterprises continues to rise, resulting in the contraction of enterprises'investment, expenditure, and production activities, and the contraction further triggers a new round of adverse shocks, which continue to strengthen and cause an economic recession. This impact amplification effect is the principle of the ''financial accelerator''. It can be said that the superimposition of the financial accelerator effect and balance sheet effect is the internal mechanism of the diffusion of most financial crises in various social and economic sectors (Bernanke & Ben, 1983;Bernanke & Gertler, 1989;Bernanke et al., 1996). Construction of the stock market bubble index Tobin's Q value method and K bubble coefficient method are characterized by a single index, which is simple but the degree of disclosure is not enough from the consistency of research methods and practicality perspective. The GSADF method simply studies the existence of bubbles from the stock price perspective itself but does not accommodate basic factors and investor sentiment factors. However, due to the comprehensive consideration of the basic value and emotional indicators, the price bubble index obtained by the principal component method is more appropriate to reveal the degree of the market bubble. Therefore, this research method is adopted in the analysis of the impact of bubbles on financial security. Basic models (1) Principal component model The core idea of principal component analysis lies in dimensionality reduction to simplify the problem, which can help to extract most of the information regarding the original variables when performing multivariate analysis where correlation exists and the information is Fig. 3. Schematic diagram of the factors affecting the financial security system. C. Zheng Journal of Innovation & Knowledge 7 (2022) 100207 4 not duplicated (Dai & Deng, 2018). The key to principal component analysis is to determine the loadings of the original variables on the plural principal components. y1¼a11x1þa12x2þ... þa1pxp y2¼a21x1þa22x2þ... þa2pxp ... yp¼ap1x1þap2x2þ... þappxp 8 > > > < > > > : ð1Þ Where, ai1;ai2 ...aijði¼1;2;...pÞrepresent the eigenvector corresponding to the eigenvalue of the covariance matrix of variable. x; x1;x2;...;xprepresent the value of the original variable after standardization. The standardization of original variables is due to the inconsistency of the original data index units, and there is a biased influence of the dimensions on the statistical analysis results. Therefore, standardization is needed to eliminate dimensional factors and ensure that the analysis results are accurate. Determination principle of coefficient aij: First, yiand yj(i6¼j; i, j=1,2,..., m) are independent of each other. Second, y1has the largest variance in all linear combinations of x1,x2;...,xp;and y2has the largest variance in all linear combinations of x1;x2;...,xpnot related to y1;yphas the largest variance among all linear combinations of x1;x2;...;xpthat are not related to y1;y2...; ym1The new variable index y1;y2;...;ypis called the first, second, ....and P principal components of the original variable index x1;x2;...;xp. (2) State-space model and the Kalman filter algorithm State-space models arise from the analysis of smooth time series and portray the dynamic change process of variables. The Kalman filter algorithm is a data processing technique of removing noise to restore real data and is easy to implement programmatically. It was initially used in engineering and is now increasingly used in the analysis of economic problems. The linear factor spatial state model is established based on relevant variables: Xtþ1¼AXtþwt Yt¼BXtþet ð2Þ Where wt»Nð0;QÞis the process noise, et»Nð0;RÞis the measurement noise, Xtis the state variable, Ytis the output vector, A is the transfer matrix, B is the output matrix, and the initial state of the system is X0, the mean value is m0, variance is S0, and the covariance is COV0. In the state-space model of dynamic systems, the system state vector X1:n¼½X1;X2;...;Xnis unobservable, and the observable measurements are vector Y1:n¼½Y1;Y2;...;Ynand parameter set Q¼½A;B;Q;R;m0;COV0, the Kalman filter method is used to estimate X1:nwhich is based on known Y1:nand Q. Assuming that the noise obeys the normal distribution, the mean Xtjt¼EðXtjY1:tÞand covariance COVt;tjt¼COVðXt;XtjY1:tÞof the probability estimation at time t can be estimated by the parameters Xt1jt1and COVt1;t1jt1at time t-1. According to Thomas (2005), the main results are as follows: Xtjt1¼AXt1jt1 COVt;tjt1¼ACOVt1;t1jt1ATþwt Xtjt¼Xtjt1þKtYtBXtjt1  COVt;tjt¼COVt;tjt1þKtBCOVt;tjt1 COVt;t1jt¼IKtBðÞACOVt1jt1 Kt¼COVt;tjt1BTBCOVt;tjt1BTþR  1 ð3Þ Indicator selection The results of indicator selection and its basic logic are: (1) Average price-to-earnings ratio (P/E) of SSE A-shares (2) Total market capitalization-weighted monthly market turnover ratio (TTR) (3) Stock turnover amount (R): The absolute value of the turnover amount is more ambitious, and the current month's year-on-year data is used here (4) Number of shares traded (M): This indicator also uses month-onmonth data (5) Total stock market capitalization on SSE (N): Using month-onmonth data To eliminate the effect of dimensionality, the stock volume is unitized and a total of five variables, PE, TTR, R, M, and N, are used. The original data are monthly data except for GDP, which is quarterly data. In this study, the cubic-match last method provided by EViews software is used to increase the frequency of GDP data. Descriptive statistics Fig. 4 shows the sequence diagram of five basic variables. These indicators have a certain collinearity, which is suitable for analysis using the principal component method. According to the results of descriptive statistics (Table 1), it can be found that the mean, maximum and minimum values of the stock market turnover ratio, P/E ratio, M, R, and market trading volume all vary widely, which shows that the stock market in China changes more drastically, and this unstable characteristic can easily create a bubble in the stock market. The skewness of each indicator is greater than 0, which is rightskewed, and the largest Kurtosis value is the series R. However, the remaining indicators are not seen below 7, which shows that the probability distribution expressed by the sample data slightly deviates from the normal distribution and is positively skewed (or rightskewed) and has a fat-tailed distribution. Principal component analysis method The five variables are standardized and the principal components are selected by a principal component analysis (Table 2). The cumulative contribution of the first two principal components is 85.55%, which exceeds the standard level of 85%, and the gravel plot (Fig. 5) produces a visible turn at the second point. Therefore, the first two principal components are selected as representatives of the market bubble level and used to construct the stock bubble index. Based on the extracted principal component common factors, the SPB coefficient can be constructed as shown in Fig. 6. Kalman filter algorithm To remove the influence of clutter, the SPB index is optimized by constructing a state-space model and using the Kalman filtering algorithm. First, the spatial state model of the five indicators and the stock bubble index is established, the dependent variable is denoted as PAC, the fixed regression coefficient variable is C, the five indicators are all regression variables with AR (1) random coefficients, and the underlying variance structure is a general diagonal matrix (diagonal). The established measurement equations and state equations are: Measurement equation: PAC ¼Cð1ÞþSV1TTR þSV2PE þSV3R þSV4MþSV5Nþvar ¼expðCð2ÞÞ½ ð4Þ 5 C. Zheng Journal of Innovation & Knowledge 7 (2022) 100207 Equation of state: SV1¼Cð4ÞþCð5ÞSV1ð1Þþ var ¼expðCð3ÞÞ½ SV2¼Cð7ÞþCð8ÞSV2ð1Þþ var ¼expðCð6ÞÞ½ SV3¼Cð10ÞþCð11ÞSV3ð1Þþ var ¼expðCð9ÞÞ½ SV4¼Cð13ÞþCð14ÞSV4ð1Þþ var ¼expðCð12ÞÞ½ SV5¼Cð16ÞþCð17ÞSV5ð1Þþ var ¼expðCð15ÞÞ½ ð5Þ Second, estimating the state-space model using the Kalman filter algorithm requires specifying the initial values of the unknown parameters (hyperparameters). The initial values of c(1), and c(2) can be obtained by establishing the following regression equations. PAC ¼cð1Þþcð2ÞTTR þcð3ÞPE þcð4ÞRþcð5ÞMþcð6ÞN ¼1:9758 þ3:3059 TTR þ3:3369 PE þ0:2700 Rþ0:5808 Mþ0:3399 N ð6Þ The intercept term C (1) of the reference regression equation is 1.9758, and the parameter C (1) of the set state equation is also taken as this value. The residual sum of squares (RSS/T) of the equation is taken as an estimate of the variance, and its logarithm is obtained as C (2) = LOG (143 1019/174) = 19.08521321. The valuation of C (3)-C (15) is estimated as follows. By modeling state space with each of the five indicators, a regression equation is established and the two unknown parameters of the measurement equation are estimated according to the intercept term and residual sum of squares. According to Gao et al. (2016), the three unknown parameters of the state equation can be first assigned as 0.1, 0.9, and 9. Then, the estimated values of the two parameters of the above measurement equation and the initial values of the three parameters of the state equation are inputted using the param command, and the state vector obeying AR (1) is predicted. Finally, the three unknown parameters of the state equation are determined by building the estimated coefficients of the AR (1) model of the state vector and the residual sum-of-squares estimation, where C(3n) =log (RSS/T), n=1,2...5. After the above optimization of the SPB index by applying the Kalman filter algorithm, the SPBF index (Fig. 7) can be obtained as the final measure of the size of the stock market bubble. Fig. 7 shows that China's stock market has experienced severe bubbles during the four periods of 2007, 2009−2010, 2014−2015, and 2017, which is consistent with the actual market trend. Moreover, the bubble index shows that the bubble level of the stock market during the 2014−2015 period is higher than that of the 2006 −2007 period, which reveals the actual situation of the A-share bull market in the 2014−2015 period. Thus, the index of the constructed SPBs not only synchronizes with the sharp rise and fall of the stock market, but also reveals the extent of support of the real economy in a rising stock market, and further confirms that the selected principal component index can better measure the size of the stock market bubble. Construction of the financial security index In this section, we discuss the construction of China'sfinancial security index based on principal component analysis. He and Fig. 4. Sequence diagram of five basic variables. Table 1 Data descriptive statistics. M N PE R TTR Mean 0.354963 0.591828 0.211805 0.895911 0.187488 Median 0.10705 0.16355 0.17665 0.10335 0.162498 Maximum value 3.8421 7.422 0.6964 10.3485 0.649182 Minimum value 0.629 0.8959 0.0976 0.7839 0.041519 Standard deviation 0.840133 1.288658 0.112101 2.04715 0.109258 Skewness 2.440913 2.199361 2.02122 2.458817 1.835588 Kurtosis 8.79661 9.086048 7.150209 9.483288 7.311311 Table 2 Results of principal component analysis. Eigenvalues: (sum= 5, mean= 1) Number Value Difference Proportion Cumulative Value Cumulative Proportion 1 2.988553 1.699787 0.5977 2.988553 0.5977 2 1.288766 0.794237 0.2578 4.277319 0.8555 3 0.494529 0.341064 0.0989 4.771848 0.9544 4 0.153465 0.078778 0.0307 4.925313 0.9851 5 0.074687 —0.0149 5 1 6 C. Zheng Journal of Innovation & Knowledge 7 (2022) 100207 Lou (2012) selected 26 indicators for principal component analysis from four dimensions: micro-financial institution security, meso‑financial-market security, macroeconomic operation security, and international external risk impact. Jia and Li (2015), and Liang (2016) selected 16 indicators from the 2 dimensions of the macroeconomic environment and financial industry evaluation for principal component analysis. Liang et al. (2018) selected 23 indicators from the 4 dimensions of the macro economy, capital market, money market, and foreign exchange market for principal component analysis. Guo et al. (2018) used the factor analysis method based on panel data to construct China's regional financial security index by region and identified the status of China's regional financial security in different periods based on the MS-VAR model. Xu and Zhou (2019) used principal component analysis to estimate the financial security index from 2000 to 2016 and analyzed the impact effect of macroeconomic fluctuations on financial security. Gu et al. (2020) constructed a financial security assessment system based on the three perspectives of macro-level, fiscal level, and financial level, and analyzed China's overall financial security and the financial security of the four economic regions by using the entropy method. Zhou et al. (2021) selected 22 mixing sample data composed of annual, quarterly, and monthly frequencies, estimated them using the newly constructed mixing layered dynamic factor model, and measured China's mixing financial security index system. In the literature, the principal component method is the main method used to construct the financial security index. The idea is to simplify multiple interrelated basic indexes into a few comprehensive indexes through dimension reduction technology. Moreover, these few comprehensive indexes are not related to each other, and they can provide most of the information of the original indexes. With the process of principal component analysis, the weight of each principal component is generated automatically, which largely offsets the interference of human factors in the evaluation process. Therefore, the comprehensive evaluation theory based on principal components can better ensure the objectivity of the evaluation results and truthfully reflect the actual problems. Fig. 6. Schematic diagram of the stock price bubble coefficient trend. Fig. 5. The scree plot of principal component analysis. C. Zheng Journal of Innovation & Knowledge 7 (2022) 100207 7 Design ideas of the financial security index (1) Design ideas The financial industry has its particularity in product supply and pricing of mainly virtual assets, where the prices are highly volatile. The influencing factors of financial system security can be analyzed from four dimensions: economic system security, banking, and insurance system security, capital market security, and currency security. Among them, economic security is the macro background of financial security. Banking and insurance security, capital market security, and currency security are subsystems of financial security. This division standard completely covers all the influencing fields of financial security. Therefore, following this logic, in this section we take these four dimensions as the first-level indexes, and establish the second-level and third-level indexes accordingly, to construct a more reasonable and reliable financial security index. The availability of data should be considered in the construction of indexes, as shown in Table 3. The first-level index to describe the degree of financial security should be referred to by the four systems, namely, the macroeconomic system, banking and insurance system, capital market system, and monetary system. Each first-level index is divided into secondlevel indexes that can describe its basic operation status. For example, the macroeconomic system can take economic operation status and financial policy status as second-level indexes; the banking and insurance system can be naturally decomposed into two second-level indexes: the operation status of banking and insurance; the capital market consists of the stock market, bond market and derivatives market. Considering the market scale and influence, only the stock market is introduced as the second-level index; the money market considers the internal and external value of money as second-level indexes. In terms of third-level indexes, the economic operation of the macroeconomic environment can be tracked by the GDP growth rate, fixed asset investment growth rate of the whole society, and the macroeconomic prosperity leading index; financial policy can be represented by the year-on-year growth rate of M2; the third-level indexes of banking operation can include the non-performing loan ratio of commercial banks and the monthly standard deviation of the interbank 7-day lending rate; the third-level indexes of the insurance industry include the growth rate of insurance assets and the growth rate of insurance total compensation; the monthly standard deviation of the Shanghai Composite Index is introduced to measure the thirdlevel indexes of the stock market; indexes of currency security include the CPI and the monthly standard deviation of exchange rates between the US dollar and RMB. There are 11 economic indexes. (1) Description of indicators ①GDP growth rate: The GDP index is the background of the whole financial security problem; hence, it must be selected. Fig. 7. Schematic diagram of the stock price bubble coefficient optimized by Kalman filter. Table 3 Alternative indicators of financial security index construction. First-level Index Second-level Index Third-level Index Macroeconomic System Economic Operation GDP growth rate, Fixed-asset investment growth rate of the whole society, Macroeconomic prosperity leading index Financial Policy The year-on-year growth rate of M2 Banking and Insurance System Banking System Non-performing loan ratio of commercial banks, Monthly standard deviation of interbank 7-day lending rate Insurance System The growth rate of insurance assets, the Growth rate of insurance total compensation Capital Market System Stock Market Monthly standard deviation of the exchange rate between the US dollar and RMB, Monthly standard deviation of the Shanghai Composite Index Monetary System Internal Value CPI External Value Monthly standard deviation of the exchange rate between the US dollar and RMB Note: the volatility index of the real effective exchange rate is replaced by the monthly standard deviation of the exchange rate between the US dollar and the RMB. C. Zheng Journal of Innovation & Knowledge 7 (2022) 100207 8 regime), that is, maintaining a safe and unsafe (serious) state is 0.565, the probability of transforming from Reg. 1 to Reg. 2 is 0.435, and the probability of directly transforming from Reg. 1 to Reg. 3 is close to 0. This shows that the state of Reg. 1 is unstable, and the probability of switching to other regimes is the highest, which reflects that the probability of the financial market switching from a severe financial insecurity extreme state to a general risk state is very high, and the financial system will not always be in a state of financial crisis. China's financial system is in Reg. 2, that is, the probability of maintaining financial insecurity (mild) is 0.7901, which is much better than that in Reg. 1, indicating that Reg. 2 is relatively stable. The probability of changing from Reg. 2 to Reg. 1 is 0.1272, and the probability of changing to Reg. 3 is 0.08269, that is, the probability of changing to financial security is slightly higher, which also shows that China'sfinancial system as a whole is relatively healthy. The probability of China's financial system remaining in Reg. 3, that is, the financial security state is 0.7827, which is also relatively stable. The probability of changing from Reg. 3 to Reg. 2 is 0.2172. The probability of changing to Reg. 1 is close to 0. Table 15 presents the count of the probability and duration of maintaining the state of a regime. The probability of China'sfinancial market remaining in the state of Reg. 1 is 0.1749 and the duration is 2.3 months; the probability of Reg. 2 is 0.5977 and the duration is 4.76 months; the probability of Reg. 3 is 0.2274, and the duration is 4.6 months. The data show that China'sfinancial market is in a state of financial insecurity (mild) and financial security for more than 4 months, which is a long time. The duration of financial insecurity (severe) is only half that of other states, and its probability is low. Furthermore, this result is also consistent with the generally held view in finance that financial crises always break out quickly and violently. However, after all parties, especially the regulatory authorities, respond quickly, the crisis can usually be alleviated quickly and effectively. (1) Correlation statistics under different regimes As can be seen from Table 16, the correlation coefficient between the stock market bubble index and the financial security index is 0.6657 under Reg. 1, which has a significant positive correlation. This shows that the bigger the stock market bubble index, the bigger the financial security index. Thus, under the condition of financial insecurity (serious), the stock market bubble bursts or is at a low level, which is generally accompanied by a stock market plunge. In this case, the existence of an appropriate stock market bubble is beneficial to the improvement of financial security. The correlation coefficient between the stock market bubble index and the financial security index decreases from 0.1915 to 0.271 under Reg. 2 and 3, and the negative correlation gradually increases, which indicates that an increase in the stock market bubble will bring about a decline in the degree of financial security when the actual financial market security situation is good. This is an interesting result found in this study, as it Fig. 10. Innovative MSIH (3)-VAR (3) probability map of model area system. Table 14 Regime switching probability matrix. Reg. 1 Reg. 2 Reg. 3 Reg. 1 0.565 0.435 6.10E-07 Reg. 2 0.1272 0.7901 0.08269 Reg. 3 0.0001374 0.2172 0.7827 Table 15 Regime status and duration. Sample size Probability Duration Reg. 1 30.5 0.1749 2.3 Reg. 2 101.2 0.5977 4.76 Reg. 3 38.3 0.2274 4.6 Table 16 Correlation statistics under different regimes. Reg. 1 DPAC BUBBLE DPAC 1 0.6657 BUBBLE 0.6657 1 Reg. 2 DPAC BUBBLE DPAC 1 0.1915 BUBBLE 0.1915 1 Reg. 3 DPAC BUBBLE DPAC 1 0.271 BUBBLE 0.271 1 C. Zheng Journal of Innovation & Knowledge 7 (2022) 100207 15 means that when dealing with the relationship between stock market bubbles and financial security, if the state of financial security is acceptable, the stock market bubble should be properly controlled, and the bubble is the unstable factor of the market at this time. However, when the financial system is in a state of financial insecurity (serious), introducing measures to stimulate the capital market moderately and raising the level of the stock market bubble index moderately may help alleviate financial insecurity. (1) Impulse response and goodness of fit analysis Fig. 11 shows the impulse response of the stock market bubble index to the financial security index (DPAC) under three regimes. First, from the response direction, when the stock market bubble index (BUBBLE) brings a positive impact of one unit, the financial security index responds positively and reaches its peak in the lag of about one period. Then, the index falls rapidly, turns into a negative response, and reaches its lowest point in lag phase 2. Subsequently, the impact strength of each period slowly dips below the abscissa axis, and the fluctuation gradually decreases and reaches a stable state after lag phase 8. Generally speaking, except for the positive response of the first financial security index, the other periods are mainly a negative response, that is, the stock market bubble increases, the degree of financial security rises in the short term, and there is an overall decline. Second, from the perspective of response strength, with a decrease in the degree of risk, the impact effect reflected by the impulse response diagram is stronger. Under Reg. 1, the impact of one unit of the stock market bubble index (BUBBLE) on the financial security index reached a peak value of 0.005 in lag phase 1, and then fell to the lowest point of 0.004. However, in the state of Reg. 2, the peak value of the impact force is about 0.017 when in lag phase 1, and the lowest value is close to 0.018 when in lag phase 3. Under the condition of Reg. 3, the peak value of impact force reaches 0.052, and the lowest value reaches about 0. 052; the impact force is the largest and the impact effect is the most obvious. Thus, to improve financial security by regulating the degree of the stock market bubble, we should try our best to plan, and carry out directional regulation in the stages of Reg. 3 and Reg. 2, while in the state of Reg. 1, the policy effect is much worse under the same regulation intensity. Fig. 12 presents the relationship between the actual values, fitted values, and one-step predicted values of the financial security index (DPAC) and stock market bubble index (BUBBLE) variables. The actual values, fitted values, and predicted values of the stock market bubble index are consistent with each other, and the effect is good; there is a slight error between the actual and predicted values of the financial security index, which may be due to the many influencing factors of the financial security index. However, as the basic movement directions of these variables are consistent, the fitting effect should be acceptable. Fig. 13 shows the results of a comparison among variable prediction error, smoothing error, and standard residual. The distribution frequency of prediction error and standard residual is similar. Thus, the innovative MSIH (3)-VAR (3) model has a good fitting effect for each variable, and the results analyzed by the innovative MSIH (3)- VAR (3) model are robust. (1) Robustness test To verify the robustness of the conclusion of the innovative MSIH (3)-VAR (3) model which contains three regimes and three lag periods, we introduce the multiple linear regression method to study the relationship between the stock market bubble and financial security. As the main research objective of this study is to investigate the impact of the stock market bubble index (BUBBLE) on the financial security index (DPAC), the regression equation is established with the financial security index (DPAC) and the stock market bubble index (BUBBLE) as explanatory variables. As the financial security index and the stock market bubble index are obtained by principal component analysis, the index already contains many factors; thus, no additional control variables are set in the regression equation. Additionally, referring to the results of related studies, if the influence of the bubble sequence with lag phase 3 on the DPAC sequence is not significant, this regression directly takes the bubble sequence with lag phase 1 and lag phase 2 as explanatory variables, and examines the sign, size, and significance level of regression coefficients to verify the robustness of the innovative MS-VAR test. The sample interval is from January 2004 to June 2018, which is the same as that in the previous data. The regression equation is: DPACt¼aþbt1BUBBLEt1þbt2BUBBLEt2þetð10Þ Where ais the cut-off moment of regression, bt1;bt2are the regression coefficients, and etis the residual. The results are shown in Table 17. The regression result can be written as: DPACt¼0:03695 þ0:08213BUBBLEt10:05360BUBBLEt2ð11Þ Analysis of the regression results shows that the results of aare only significant at the 20% level, and its meaning is not obvious. Fig. 11. Impulse response diagram under different zone conditions. C. Zheng Journal of Innovation & Knowledge 7 (2022) 100207 16 However, the t value of bt1reaches 2.75, which is significant at the 1% level, and the regression coefficient is 0.0821329. Compared to the parameter estimation results of the innovative MSIH (3)-VAR (3) model in Table 12, the coefficient of BUBBLE-1 is 0.042371, which is the same sign and significant. It shows that the previous conclusion is relatively stable, that is, a larger stock market bubble with lag phase 1 will help improve the financial security situation. Similarly, the coefficient of bt2in Table 17 is-0.0535974, which is significant Fig. 12. Actual value, fitted value, and one-step predicted value of the variable. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Fig. 13. Prediction error, smoothing error, and standard residual of the variable. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Table 17 Multivariate regression results. DPAC coef std.err t-value P>|t| Bubble(t-1) 0.0821329 0.0298472 2.75*** 0.007 Bubble(t-2) 0.0535974 0.0298655 1.79* 0.075 _cons 0.0369546 0.0258777 1.43 0.155 Note: *, **, *** are significant at 10%, 5% and 1%, respectively. C. Zheng Journal of Innovation & Knowledge 7 (2022) 100207 17 at the 10% level. The result has the same sign as the coefficient of 0.0469 of BUBBLE-2 in Table 12, and its size is close to that of BUBBLE-2, which expresses the same economic meaning. This shows that the analysis results of the innovative MS-VAR model are relatively robust, and the model can divide data into regimes, and analyze the results more precisely. Hence, the application of this method is appropriate. Conclusion and implications Conclusion In this study, we establish a model covering investor behavior, SPBs, and financial security problems, and verify the interrelationship between the variables. Through simulation and empirical analyses, we obtain the affirmative conclusion that the above logical framework is established. Specifically, the basic conclusions of this study are as follows: (1) In this study, a comprehensive analysis method is used to superimpose some basic value and investor behavior characteristics, such as irrational investors without financial knowledge, and stock price fluctuation indicators. Subsequently, we extract the principal components, filter out the noise by the Kalman filtering method, and then construct the final SPB index. The SPB index in this study can not only synchronize with the sharp rise and fall of the stock market but also reveal the extent of support of the real economy in the rising stock market, which further confirms that the selected principal component index can better measure the size of the stock market bubble. (2) The corresponding indicators are selected according to economic security, banking, and insurance security, capital market security, and money market security. Subsequently, China'sfinancial security index is constructed based on the principal component method. The results show that during the sample period, China's financial security index has experienced roughly five fluctuations in the same direction. The performance of the financial security index in each stage is driven by the main economic indicators and has a profound economic background. (3) In this study, the stock bubble index discussed in Section 4 represents the bubble level, and the financial security index discussed in Section 5 represents the level of China'sfinancial security. The innovative MS-VAR model with a three-zone system and 3 lag stages is established (innovative MSIH (3) -VAR (3)), and the dynamic relationship between them is examined. The results show that the relevant parameters of the model are significant and have obvious economic significance. First, a Granger causality test is carried out on the stable firstorder differential financial security index (DPAC) and stock market bubble index (BUBBLE). The test results show that at the 5% significance level, we accept the original hypothesis that the financial security index is not the cause of the stock market bubble index. There is a unilateral Granger causality relationship between the stock market bubble index and the financial security index, that is, a change in the stock market bubble index can be used to explain changes in the financial security index. Second, according to the division results of the innovative MSIH (3) −VAR (3) model, Reg. 1−3 represent financial insecurity (serious), financial insecurity (mild), and financial security, respectively. An increase of 1 unit in the stock market bubble index with lag period 1 will lead to an increase in the financial security index of 0.042371 units, while an increase in 1 unit stock of the market bubble index with lag period 2 will reduce the financial security index by 0.0469 units. This shows that the stock market bubble index is the leading indicator of financial security. Third, from the analysis of the results of the three-regime innovative MSIH (3) - VAR (3) model, the probability of China'sfinancial security status staying in Reg. 2 and Reg. 3 is large, and the duration of Reg. 1 is only about half of that of the other regimes. This shows that China'sfinancial security situation is relatively stable and is in a relatively safe financial state most of the time, and the possibility of systemic financial risk is small. Fourth, from the perspective of correlation, the stock market bubble index is positively related to the financial security index under Reg. 1, and the correlation is negative under the other two regimes. The conclusion has significant implications for policymakers because Reg. 1 is a state of few stock market bubbles and financial insecurity (severe). It shows that when the financial situation is seriously unsafe, and stock market bubbles are few, policymakers can take measures to increase positive interest in the securities market and stimulate activity, that is, expand the stock market bubble to improve the security situation of the financial market. Fifth, the impulse response results show that given the positive impact of a unit stock on the market bubble index, the financial security index reaches a positive response peak in lag period 1, turning to a negative response and reaching the lowest point in lag period 2. Thereafter, the fluctuation slows down and reaches a stable state after lag period 8. This also shows that the initial impact of the stock market bubble on the financial security situation is a positive driving force, which will then turn negative and lead to a reduction in the degree of financial security. The above empirical conclusions can help us further understand the intrinsic relationship between China's stock market bubble level and financial security level, to facilitate regulators to introduce more targeted regulatory measures to respond to market concerns and to monitor market pain. Implications First, investors should strengthen the study of financial knowledge. Investors should study investment books, attend financial education lectures, and opt for higher education and other ways to learn relevant financial knowledge, improve their analysis and judgment ability, and try to form a stable investment method system based on their own characteristics. Second, investors should learn to control their emotions. Investors should be clear about the importance of controlling emotions so that they can make the most favorable judgment when their emotions fluctuate. In the face of a complex and changeable stock market environment, investors should have the ability to think independently, exercise rational investment thinking, and avoid wrong practices such as ''chasing up and killing down'', ''psychological account'', and ''herding effect''. Thirdly, investors should strengthen the ability of information collection and judgment. Due to information asymmetry and other characteristics of the stock market, the investment judgment formed by investors, based on diverse information, is often very different. Therefore, when investors pay attention to real-time dynamic information about the market, they should not only avoid blind listening and obedience, but should also not be over-confident, and should grasp the appropriate scale. This study used the basic value method, GSADF method, and other methods to empirically test the bubble level of China's securities market, and compare the results of different methods. It is found that Tobin's Q method and K bubble coefficient method are too simplistic, and may leave out important information, thus presenting the wrong bubble index. The GSADF method finds out whether there is a bubble from the stock price itself, and does not relate to the basic value. C. Zheng Journal of Innovation & Knowledge 7 (2022) 100207 18 Moreover, its recursive algorithm may also lead to insensitivity to the partial fluctuations in the share price. After repeated comparisons and attempts, we choose to use a series of indicators including basic value, investor behavior indicators, and stock price fluctuation indicators to construct the SPB index. The result is consistent with the actual market trend, and the measurement of the bubble level is better than with other methods. In the study of stock market bubbles affecting financial security, the general view is that stock market bubbles are not conducive to financial security. However, no study in the literature has discussed the micro-mechanism and time lag effect of the stock market bubble affecting financial security. The positive effects of stock bubbles with lag phase 1 on financial security and the negative effect of the stock market bubble with lag phase 2 on financial security are found in this study, which provides new perspectives and evidence for the research in this field. However, this study has some limitations. The coverage of this index is not extensive enough to ensure the causality of the bubble index and safety index, as the design methods of stock market bubbles and financial safety monitoring indicators are not sophisticated enough. Based on the above research methods and conclusions, the following are possible further research directions: First, we should enrich and improve the index design based on integrated basic values and emotions, and further analyze the critical level of bubble rupture, to provide early warnings for market participants and provide timely and accurate suggestions for regulatory authorities to deal with market risks; second, we can study the internal structure and interaction mechanism of stock index bubbles, such as industry and scale, and analyze the bubble situation of each sub-industry, and their interaction with each other and the overall bubble situation; finally, the research on stock market bubbles can be expanded to the study of asset bubbles including real estate bubbles, the existence and interaction mechanism of stock market and housing bubbles, and the impact of asset price bubbles on financial security.) Abbreviations and acronyms AIC Akaike information criterion BUBBLE Stock market bubble index CPI Consumer price index DPAC First-order differential financial security index FPE Final prediction error GDP Gross domestic product HQ Hannan-Quinn criterion KMO Kaiser-Meyer-Olkin LL Logarithmic likelihood LR Likelihood ratio M Number of shares traded M2 Broad money supply N Total stock market capitalization on SSE PAC Financial security index P/E Price to earnings ratio R Stock turnover amount Reg. Regime S Comprehensive evaluation score for each year SC Schwarz criterion SMC Squared multiple correlations of variables with all other variables SPB Stock price bubble SPBF SPB index by applying the Kalman filter algorithm SSE Shanghai Stock Exchange TTR Total market capitalization-weighted monthly market turnover ratio References Bernanke, B., & Ben, S. (1983). Nonmonetary effects of the financial crisis in the propagation of the great depression. American Economic Review,73(6), 257–276. 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