Exploring the impact of macroeconomic changes on financial market stability using big data analytics

In order to portray macroeconomic uncertainty more clearly, the selection of economic indicators in this paper is mainly based on the following three considerations: first, the selection of indicators should reflect the economic operating conditions as much as possible. Second, the selection of indicators can truly portray economic uncertainty at the macro level. Thirdly, the indicators are required to be monthly data with a high degree of completeness and suitable for model estimation. Considering the above three premises, the results of the selected indicators are shown in Table 1. In this paper, monthly data for 10 macroeconomic indicators is selected, and the sample selection range is from January 2005 to June 2023.

In the statistics of economic data, there will be a situation that does not count the data of January, this paper uses the average value of the proximate month to replace the data of the missing value month. Since GDP is only a quarterly statistic, this paper adopts the interpolation method to process the data and obtain monthly data on GDP. Fixed asset investment and total retail sales of consumer goods are calculated from cumulative values to obtain the current value. The fluctuation chart of the data clearly shows that some of the data are affected by seasonality and need to be seasonally adjusted, such as fiscal revenue, fiscal expenditure, fixed asset investment completion, total retail sales of consumer goods, imports, exports, GDP, M2, and M0. Therefore, this paper adopts the X-12 method for the time series to exclude the influence of seasonal factors. In addition, because the data used in this paper include both direct and index data, the seasonally adjusted and non-seasonally adjusted data are centred in order to avoid the effect of data magnitude on the results of the measurement.

In the literature on measuring macroeconomic uncertainty, related studies usually use the GARCH (1,1) model. Therefore, this paper also uses the GARCH (1,1) model to measure macroeconomic movements. The model is briefly described below.

The GARCH model is an extension of the ARCH model [21]. The expression of ARCH(p)$$ARCH\left( p \right)$$ model is:

Mean value equation: (1)yt=βxt+εt$${y_t} = \beta {x_t} + {\varepsilon _t}$$

Variance equations: (2)σt2=a0+a1εt−12+a2εt−22+⋯⋯+aqεt−p2$$\sigma _t^2 = {a_0} + {a_1}\varepsilon _{t - 1}^2 + {a_2}\varepsilon _{t - 2}^2 + \cdots \cdots + {a_q}\varepsilon _{t - p}^2$$

where σt2$$\sigma _t^2$$ is the conditional variance.

The GARCH model, on the other hand, adds the autoregressive part of σt2$$\sigma _t^2$$ the RACH model. That is, the GARCH(p,q)$$GARCH\left( {p,q} \right)$$ model is set up in the form: (3)yt=βXt+εt$${y_t} = \beta {X_t} + {\varepsilon _t}$$ (4)σt2=a0+a1εt−12+⋯⋯+aqεt−q2+γ1σt−12+⋯⋯+γpσt−p2$$\sigma _t^2 = {a_0} + {a_1}\varepsilon _{t - 1}^2 + \cdots \cdots + {a_q}\varepsilon _{t - q}^2 + {\gamma _1}\sigma _{t - 1}^2 + \cdots \cdots + {\gamma _p}\sigma _{t - p}^2$$

And GARCH(1,1)$$GARCH\left( {1,1} \right)$$ model can be expressed as:

Mean value equation: (5)yt=βxt+εt$${y_t} = \beta {x_t} + {\varepsilon _t}$$

Variance equations: (6)σt2=a0+a1εt−12+γ1σt−12$$\sigma _t^2 = {a_0} + {a_1}\varepsilon _{t - 1}^2 + {\gamma _1}\sigma _{t - 1}^2$$

If the coefficients of εt−12$$\varepsilon _{t - 1}^2$$ and σt−12$$\sigma _{t - 1}^2$$ in the conditional variance equation are significant, the value of the conditional variance can be used to express macroeconomic uncertainty: (7)σt2=0.0048−0.0611Et−12+0.9252σt−12Z=(1.2227)$$\begin{array}{l} \sigma _t^2 = 0.0048 - 0.0611E_{t - 1}^2 + 0.9252\sigma _{t - 1}^2 \\ Z = \left( {1.2227} \right) \\ \end{array}$$

1)

Smoothness test

Before constructing the GARCH model, the first need to ensure that the data is smooth. Therefore, here, we need to do the smoothness test of macroeconomic indicators. This paper takes the commonly used ADF test, and the results are shown in Table 2. As can be seen from the table, under the 5% significance level, the hypothesis that the macroeconomic indicators are not smooth can be rejected. That is, it is concluded that the indicators are smooth.

This paper takes the data of China’s indicators from 2005 to 2023 as the sample data, which covers China’s financial data during the subprime crisis in 2008 and the great capital market turbulence in 2015, so the research results are more informative. The sample data is based on the China Economic Yearbook and China Financial Statistics Yearbook.

Because the different scales of each indicator in the financial market stability index system will lead to bias in the accuracy of the result of principal component selection, this paper needs to standardise the relative data as shown in Equation (8) before carrying out the principal component analysis: (8)Yij=Xij−X¯ivar(Xi),1≤i≤25,1≤j≤19$${Y_{ij}} = \frac{{{X_{ij}} - {{\bar X}_i}}}{{\operatorname{var} ({X_i})}},1 \le i \le 25,1 \le j \le 19$$

In the above equation, X_ij is the raw data of the indicator value in year j for the ind indicator, Y_ij is the data after X_ij standardisation, X¯i$${\bar X_i}$$ is the sample mean of variable X_i, and var(Xi)$$\operatorname{var} ({X_i})$$ represents the sample variance of variable X_i.

In this paper, we use SPSS software to carry out principal component analysis [23] on the indicator system constructed above so as to calculate the size of financial market stability.

The principal component eigenvalues and contribution rates are shown in Table 6. The eigenvalues of the first five principal components in the table are all greater than 1, and the cumulative variance contribution rate is as high as 90.350%, indicating that the first five principal components contain almost all the indicator information. It is evident that the eigenvalues of the 1st to 5th principal components have a significant variance, while the eigenvalues following the 6th principal component gradually become smaller. So, this paper chooses the first 5 principal components to replace the original 25 indicators.

From the principal component analysis it is possible to obtain the coefficients of the factor expressions, i.e., factor loadings, for each original variable, and the results are shown in Figure 1. From the figure, it can be seen that the absolute value of the loading coefficient of exchange rate volatility, fiscal deficit/GDP, bank deposit/loan ratio, external debt/GDP, external debt/foreign exchange income, debt service ratio, external debt liability ratio, external debt ratio is larger in Principal Component 1, which indicates that the Principal Component 1 is able to comprehensively represent these eight indicators. The absolute value of the loading coefficients of real estate development investment/investment in fixed assets, real estate sales/completed area, monetisation degree, bank loans/GDP, insurance depth, foreign exchange reserves/GDP, and premiums/GDP is larger in Principal Component 2, which indicates that Principal Component 2 is able to comprehensively represent these 7 indicators. The larger absolute values of the loading coefficients of GDP growth rate, securities price-earnings ratio, stock market capitalisation/GDP, current account balance/GDP, and business sentiment index in principal component 3 indicate that principal component 3 is able to comprehensively represent these five indicators. The larger absolute values of the loading coefficients of the M2 growth rate, unemployment rate, fixed asset investment growth rate, and import/export/GDP in Principal Component 4 indicate that Principal Component 4 is able to represent these four indicators comprehensively. The loading coefficient of the inflation rate in principal component 5 is larger in absolute value, so principal component 5 represents the indicator of the inflation rate.

Figure 1.

Factor load

After extracting the principal components, the principal components are then new indicators that replace the original indicators, and Figure 2 shows the five principal component scores for each year from 2005 to 2023, calculated based on the factor score coefficients. The analysis shows that the principal component scores of each factor show an overall increasing trend over time. Among them, the score of principal component 2 can reach 6.837 in 2023.

Figure 2.

Principal component score

The Financial Market Stability Indicator’s composite score is calculated using the calculated principal component score, and the results are shown in Figure 3, as shown in the diagram. In 2005~2023, the score of the comprehensive evaluation of financial market stability showed an overall upward trend, and in 2008, due to the emergence of the global subprime mortgage crisis, the score reached the lowest value of -2.214. In 2023, the financial market stability assessment score rose to 5.847. It shows that with the continuous change of macroeconomic conditions, the stability of financial markets has also changed accordingly.

Figure 3.

Comprehensive evaluation score

After calculating the comprehensive evaluation score Y value, the financial market stability index is calculated by mapping the Y value to the interval [0, 100] according to the general expression of the index. The transformation formula is: (9)Index=Y−MinYMaxY−MinY$$Index = \frac{{Y - MinY}}{{MaxY - MinY}}$$

MaxY indicates the maximum value of the composite evaluation score, and MinY indicates the minimum value.

Figure 4 shows the trend of the financial market stability index from 2005-2023. As can be seen from the figure, the stability index has fluctuated many times, but the overall trend is also upward, in which the financial market stability index in 2008 was the lowest at 1.324. Subsequently, the stability index has gradually increased and reached 50.45 in 2023, an increase of nearly 50 times compared with the previous year.

Figure 4.

Financial market stability index change trend

If the analysis of the vector autoregressive model is to be carried out, the first thing to be carried out is to test the smoothness of the indicator data by testing whether the data is smooth or not through the unit root test, and the results are shown in Table 7, where Table Δ indicates the form of first-order differencing. Table 7 shows that X, Y, CV₁, CV₂ at a 5% significant level due to the presence of a unit root, the indicator data are not smooth, after the first-order differencing of the data, ΔX, ΔY, ΔCV1, ΔCV2 at 5% significance level, the series are all smooth. This leads to the conclusion that Y, X, CV₁, and CV₂ are first order single integer series, and there may be a long term stable effect between the variables.

The key to the empirical analysis of the vector autoregressive model lies in the determination of the number of lags, and * indicates the lags selected according to the corresponding guidelines, as shown in Table 8. As can be seen from the table, the empirical analysis in this paper selects lag 2 as the optimal lag order.

Through the unit root test as well as the determination of the lag order, the data of the indicators after the first-order differencing are all smooth at the 5% level of significance, and the variables show a stable and influential relationship in the long run. However, it is not possible to determine that the selected macroeconomic changes are the Granger causes of financial market stability, so this section carries out the Granger causality test on the selected indicators, and the results are shown in Table 9. From the results of the test, it can be seen that the original hypothesis is rejected at 5% and 10% significant levels if the lag is 2. Therefore, it can be assumed that at this point, macroeconomic changes are the Granger cause of the financial market stability index variable, i.e., macroeconomic changes cause financial market instability.

If the values of all the characteristic roots of the model are less than 1, then the model is stable. Otherwise, the model is unstable. The judgement results are shown in Table 10. The data in the table shows that all the characteristic roots of the model are less than 1. Therefore, it can be concluded that the model in this paper is stable.

By estimating the vector autoregressive model, the results were calculated as shown in Table 11. The parameter estimation result of R² is 99.74 per cent, which indicates that the equation is well fitted. By sign analysis of the coefficients of X(−1) and X(−2), it is found that macroeconomic changes will contribute to the stability of the financial market in the first period, but will affect the stability of the financial market in the second period. By judging the values of the coefficients, it is found that the negative impact on financial market stability will outweigh the positive impact, i.e., ultimately, macroeconomic changes will have a negative impact on the financial market stability index.

Figure 5 shows a X vs. Y shock, with the lag of the shock in horizontal coordinates (in years) and the impulse response function value in vertical coordinates, representing the response of Y to a X shock. The solid red line in the figure shows the values of the response in the normal case without shocks, the dark red dotted line shows the impulse response values in the case of a one-period shock, and the yellow underlined line shows the impulse response values in the case of a two-period shock. In the first period, macroeconomic fluctuations have an upward impact on the stability of the financial market, suggesting that macroeconomic fluctuations contribute to the stability of the financial market in that period. However, the second period produces a more drastic downward impact, indicating that macroeconomic changes in the second period result in less stability in the financial market. When macroeconomic fluctuations occur, they ultimately have an impact on the stability of financial markets through various transmission channels.

Figure 5.

Pulse response result

The importance of different influences on financial market stability is analysed by analysing the degree of contribution of each variable to the shocks of endogenous variables, and the results are shown in Figure 6, where the left side is the period, the right side is variable, and the connecting lines in the middle indicate the degree of contribution of each variable in different periods, and the thickness of the lines indicates the size of the degree of contribution. Changes in macroeconomics, changes in stock market capitalization/GDP, and changes in real estate development investment/whole society fixed asset investment all contribute to financial market stability to a relatively large extent. It can be seen that the impact of the financial market stability index on itself has been a gradual process of decreasing, finally dropping to 12.79%. In comparison, the influence of macroeconomic fluctuation changes on financial market stability is a gradual process of increasing. From the degree of explanation in the last period, it can be seen that the degree of explanation of the impact of macroeconomic changes on the stability of the financial market is the highest, about 36.68 per cent. All the variables in the later periods of the degree of contribution to the stability of the financial market slowed down, so that the contribution of macroeconomic changes to the stability of the financial market is very obvious. However, in the later period of time, it will converge to a stable state.

Figure 6.

Variance decomposition