Can investors use technical analysis to generate positive risk-adjusted returns by observing historical transaction data? The study investigates whether technical indicators (TIs) are beneficial to the returns and risk management of China’s stock market investors. It is conducted from the perspective of a distribution forecast rather than a traditional point forecast. The study investigates the TIs’ predictability on the distribution of returns. It also examines the TIs’ impact on risk management. A high-dimensional-same-frequency information distribution forecasting model, the LASSO-EGARCH model, is built. The LASSO regression’s results show that the TIs have limited ‘explanatory power’ for the return prediction. However, the adaptive moving average and turnover rate show significant and robust effects. The statistical evaluation and economic evaluation show that the TIs information’s integration cannot improve the direction forecast’s accuracy, nor does it have excess profitability. However, it enables the return distribution to have a better calibration. The above conclusion reveals that the usefulness of the analysis for China’s stock market lies in its risk management when the stock price plunges, rather than in excess profits. This may provide a reference for investors who prefer the TIs’ analysis.

Contents

## 1. Introduction

Forecasting stock prices is a classic problem. However, non-linear and non-stationary characteristics make the stock market a complex system. Forecasting has thus become a difficult task. The efficient market hypothesis (EMH) proposed by Fama (1995) states that in an efficient information market, it is not possible to predict the stock prices and that stocks behave in a random walk manner. However, the scientific community has proposed various methods for forecasting the stock market (Cavalcante et al., 2016). These methods can be divided into fundamental and technical analyses. The fundamental analysis uses potential factors, such as macroeconomic variables that affect a company or industry, as forecasting factors. The technical analysis relies on the historical price and trading volume information to forecast stock market trends, such as technical indicators (TIs). Wang and Li (2020) empirically found breakdowns in the link between China’s stock market and the macroeconomy. They noted that the real economy could not predict the stock markets’ booms or busts. Therefore, this study focuses on technical analysis. Technical analysts believe that most of the stock’s information is reflected in the recent prices and volumes. They also believe that the movement trends are hidden in them. Many participants in the financial market use technical analysis (Park & Irwin, 2009). Technical traders have a larger fraction than the fundamentalists and arbitrageurs in the equilibrium of the financial markets (Gong et al., 2021). The technical analysis has been the most common method used in the literature (Atsalakis & Valavanis, 2009; Cavalcante et al., 2016). Furthermore, as Nazário et al. (2017) and Bustos and Pomares-Quimbaya (2020) introduced in their articles, TIs have been the most popular forecasting information. They have been used as signals to indicate when to buy and sell stocks.

## 2. Literature review

Many aspects of the literature have been researched regarding the TIs’ significance and usefulness. Many studies have found that technical analysis methods have predictive power or can generate profits. For example, Zhu and Pan (2003) concluded that the money flow index (MFI) has a high predictive accuracy for China’s stock prices. Park and Irwin (2007) found that 56 of 95 selected modern technical analysis studies produced supporting evidence for its profitability. Ko et al. (2014) showed that applying a moving average time strategy to a portfolio classified by a book-to-market ratio in the Taiwan stock market can generate higher returns than a buy-and-hold strategy. Lin (2018) proposed a new TI that exhibits statistically and economically significant in-sample and out-of-sample predictive power. It outperforms the well-known TIs and macroeconomic variables. Mohanty et al. (2020) believe that TIs under a deep learning framework can improve financial market forecasts’ quality. However, there is no consensus on whether the TI analysis is effective in the literature. Dong (2011) concludes that basic TIs have a weaker impact on the Chinese small and medium-sized companies’ stock prices. This is far inferior to financial information. Fang et al. (2014) studied the profitability of 93 market indicators and found no evidence that they could predict the stock market returns. Nazário et al. (2017) classified and coded the technical analysis documents of the past 55 years, focusing on the stock analysis. They found that the research results ‘supporting technical analysis’ and ‘not supporting technical analysis’ account for almost equal proportions. A more detailed overview of the technical analysis can be found in Bustos and Pomares-Quimbaya (2020), Fang et al. (2014), Gandhmal and Kumar (2019), and Nazário et al. (2017). This is where the role and influence of the stock markets’ TIs are systematically reviewed.

The related documents mainly focus on point forecasts. Therefore, they only study the impact on the stock market’s mean returns. However, the return is always accompanied by risk. TIs may also have an impact on risk. However, there is little research on this aspect. In contrast, this study researches the distribution forecasting’s perspective. As compared with a point forecast, a distribution forecast provides a more complete information description. The return is examined from the two aspects of the mean and median of the distribution. The risk is characterised by the conditional heteroscedasticity to realise the dual study of the TIs’ impact on the return and risk. With the help of the distribution forecast’s overall evaluation, the combinations of models are considered. The statistical and economic significance of TIs is further explored.

This study uses the GARCH family framework. The conditional mean of the returns is described by three models: constant, ARMA process, and LASSO regression with high-dimensional-same-frequency TI information. The GARCH process is used to characterise conditional volatility. The GARCH model proposed by Bollerslev (1986) has shown good empirical effects in the literature, as described by Milosevic et al. (2019). However, a large number of scholars believe that it is necessary to consider the leverage effect of the returns. Models with leverage include the TARCH model (GJR-GARCH model) and the EGARCH model. The EGARCH model proposed by Nelson (1991) is widely used. Wang and Wang (2008) believed that the skewed Student’s t-distribution provides the best choice for the characterisation and prediction of the actual volatility of China’s stock market. The volatility described by the conditional variance adopts the EGARCH model with skewed Student’s t-distribution residuals. The return distribution forecast is hereby realised under the GARCH framework. The direction predictability and excess profitability based on the mean and median forecasts can be tested. The risk characteristics can also be investigated based on the Value at Risk (VaR). Furthermore, based on the distribution forecast’s overall statistical evaluation, the TI information’s significance and usefulness can be revealed through the model combination and comparison.

## 3. Models and methods

### 3.1. Model selection and construction

The TIs considered in this study were high-dimensional and had the same frequency of information. Three models were established and analysed by comparison: (1) EGARCH, which only models conditional variance; (2) ARMA-EGARCH, which models conditional mean and EGARCH model’s conditional variance; and (3) the conditional mean and EGARCH model’s conditional variance. The residuals are all set to obey the skewed Student’s t-distribution.

#### 3.1.1. EGARCH model

The EGARCH model is selected for three reasons: (1) It relieves the non-negative constraints of the parameters to be estimated. This is more flexible. (2) It allows the return innovation to throw asymmetric shocks on the volatility. This is a leverage effect, which is consistent with the investors’ experience. It is manifested as a strong increase in the volatility caused by negative windfall returns. The impact is greater than the positive windfall returns. (3) Many empirical studies show that for China’s stock market, the EGARCH model has better performance. The EGARCH model with a skewed Student’s t-distribution error was selected as the base model. It is represented as: (1) {Yt=μ+εt,lnht=ω+βlnht−1+α|εt−1ht−1|+γεt−1ht−1,εt|It−1iid∼2(λ+λ−1)ht[fv(εtλht)I(εt≥0)+fv(λεtht)I(εt<0)].(1)

In Model (1), Yt is the return at moment t, εt is the residual, and ht is the heteroscedasticity of Yt. μ is the constant conditional mean of Yt, and γ is the leverage coefficient. It−1 represents the information set at moment t-1, and fv(·) is the density function of the students’ t-distribution with a freedom degree of ν.

#### 3.1.2. ARMA-EGARCH model

In Model (1), the conditional mean is set as a constant. However, the conditional mean of returns may be time-variant. To describe the return series’ autocorrelation characteristics, the ARMA model of the conditional mean is considered based on Model (1). This is recorded as the ARMA-EGARCH model, expressed as: (2) {Yt=ϕ0+ϕ1Yt−1+⋯+ϕpYt−p+θ1εt−1+⋯+θqεt−q+εt,lnht=ω+βlnht−1+α|εt−1ht−1|+γεt−1ht−1,εt|It−1iid∼2(λ+λ−1)ht[fv(εtλht)I(εt≥0)+fv(λεtht)I(εt<0)].(2)

Model (2)’s first equation implies that the conditional mean of Yt obeys the ARMA(p, q) process. Suppose the unconditional expectation of Yt is μ then, ϕ0=(1−ϕ1−⋯−ϕp)μ here. With the expression of the lag operator B, Model (2)’s first equation can be written as:

ϕ(B)(Yt−μ)=θ(B)εt, where ϕ(B)=1−ϕ1B−⋯−ϕpBp and θ(B)=1+θ1B+⋯+θqBq. To stabilise the ARMA (p, q) process, the values of {ϕi} should satisfy that the roots of ϕ(B)=0 are outside the unit circle. To make the process reversible, the values of {θi} should satisfy that the roots of θ(B)=0 are outside the unit circle.

#### 3.1.3． LASSO-EGARCH model

The intention is to analyse the TIs’ impact on the returns by examining the dynamic evolution process of the return series itself. The rational choice would be to add the TIs as exogenous variables to the conditional mean equation to construct a new model based on Model (1) or Model (2). We have tried to add TIs to the ARMA-EGARCH (Model (2)). However, for many return samples, the model is not identifiable. The optimisation cannot converge. Therefore, we only add the TIs to Model (1) to build Model (3), which is shown as: (3) {Yt=δ0+δ1X1,t−1+⋯+δmXm,t−1+εt,lnht=ω+βlnht−1+α|εt−1ht−1|+γεt−1ht−1,εt|It−1iid∼2(λ+λ−1)ht[fv(εtλht)I(εt≥0)+fv(λεtht)I(εt<0)].(3)

In Model (3), X1,t−1, X2,t−1,…,Xm,t−1 are the values of the TIs at moment t-1. What we want to study is the TIs’ predictive effect on the returns. The value of TIs lags behind the returns by one period. The subscript of Yt is t, and the subscripts of the TI variables are t-1. When many TIs are used, this is a high-dimensional problem. The direct parameter estimation of Model (3) is likely to face the ‘dimension disaster’. Since TIs are mainly derived from the price and volume information, there may be multicollinearity problems. Before realising the entire model’s parameter estimation, the TIs’ multicollinearity diagnosis and dimensionality reduction were performed. Hong et al. (2016) indicated that in the past two decades, dimensionality reduction methods have made considerable progress. Among them, the LASSO regression has many good properties. It can perform parameter estimation while selecting variables, solve the incalculable problem of the traditional model selection methods when the number of variables is large and reduces the model selection’s uncertainty. Therefore, Model (3)’s dimensionality reduction will be realised by the LASSO regression, called the LASSO-EGARCH model. This is a high-dimensional same-frequency information model.

According to the three models’ construction, the comparison between Model (1) and Model (2) can test whether the conditional mean of the return has dynamic evolution characteristics. A comparison between Model (1) and Model (3) shows the TIs gain information. With the help of the quantitative results of the statistical evaluation when comparing Models (2) and (3), we can examine the relative importance of the TI information embedded within the fluctuation of the return itself. This serves to verify whether the historical information is reflected in the price at a given time.

### 3.2. Models’ parameter estimation and forecasting

Model (1) uses the maximum likelihood method closely related to the Kullback-Leibler distance loss for the parameter estimation. Model (2) involves the problem of ARMA (p, q) order determination. The maximum possible values of p and q are set to pmax and qmax (in the following calculation: pmax = 5, qmax = 2). The order is determined by the Akaike information criterion (AIC). It is realised by the auto.arima () function of the R software package: forecast. Model (3) involves high-dimensional TIs. If the maximum likelihood estimation is directly used, it will encounter the ‘dimension disaster’. Before realising the entire model’s parameter estimation, a multicollinearity diagnosis and LASSO regression on TIs to achieve ‘dimensionality reduction’ are performed. Model (3)’s estimation process is discussed below.

#### 3.2.1. Multicollinearity diagnosis

In multiple linear regression, multicollinearity may occur when there is a strong correlation between the explanatory variables. At this time, a small change in the model or data may cause large changes in the coefficient estimates. This makes the results unstable and difficult to explain.

The variance inflation factor (VIF) is an important measure of multicollinearity, defined as (4) VIFj=11−Rj2, (4) where Rj2 represents the R-square when the jth variable regresses on all the other variables.

The condition number is another indicator for measuring the total multicollinearity. It is often expressed by κ, and is defined as (5) κ=λmaxλmin.(5)

This is where λ is the eigenvalue of the matrix XTX and X represents an explanatory variables’ data matrix. When the matrix X is orthogonal, the condition number is κ=1.

Generally, if the VIF is too large (greater than five or 10), there is multicollinearity. Empirically, when κ>15, there is multicollinearity. When κ>30, the multicollinearity is serious.

#### 3.2.2. LASSO regression

The methods to address the multicollinearity include eliminating unimportant explanatory variables and increasing the sample size. Eliminating the influence of the multicollinearity on the regression models has been a priority for statisticians over the past decades. Statisticians are also committed to improving the classical least squares method and proposing methods to improve the estimator’s stability at the cost of biased estimates. The common methods include principal component regression, partial least squares regression, ridge regression, and LASSO regression.

The concepts of principal component regression and partial least squares regression are to linearly combine the original independent variables through the variables’ correlation. Many independent variables are transformed to a smaller number of ‘comprehensive variables’ to achieve the purpose of ‘dimensionality reduction’. However, such methods do not essentially achieve dimensionality reduction and cannot intuitively analyse the original variables’ relative importance. The ridge regression increases the coefficient sum of squares’ penalty term based on the square loss. Therefore, the coefficient must make the residual sum of squares small but not inflate the coefficient. In principle, the LASSO regression is similar to the ridge regression. However, the LASSO regression’s penalty term is not the coefficients’ sum of squares. It is the sum of the coefficients’ absolute values. Due to the absolute value’s characteristics, the LASSO regression does not reduce the coefficient values, such as ridge regression. It filters out some coefficients to realise the variable selection while estimating the parameters. LASSO was iproposed by Tibshirani (1996). It is a compressed estimation, retains the advantages of subset shrinkage, and is an effective estimation for processing data with multicollinearity.

Suppose there are random samples (xi,yi), i=1, 2, ⋯, n, where xi=(xi1, xi2, ⋯, xip)T is a p-dimensional independent variable and yi is the response variable for the ith observation. Assuming that yi is independent of the observations, the corresponding LASSO estimate can be expressed as: (6) (α, ̂β̂)=argmin{∑i=1n(yi−αi−∑j=1pβjxij)2},s.t. ∑j=1p|βj|≤t.(6)

In Model (6), t is a harmonic parameter and t≥0. By controlling t, the sum of the absolute values of the regression coefficients becomes smaller. As t gradually decreases, some regression coefficients shrink and move toward or equal 0. When the corresponding regression coefficient was 0, the independent variable was removed from the model.

Model (6) can be solved by using the least angle regression (LAR) algorithm by Effron et al. (2004). The Mallows (1973) criterion Cp was used for the model selection.

Model (3)’s conditional mean equation is solved by the LASSO regression. The coefficient δi corresponding to the TI variable Xi, t−1 can be obtained.

#### 3.2.3. Forecasting of the return distribution

For a given return sample {Yt}, assuming that the parameters of the one-step-ahead prediction remain unchanged, the conditional mean prediction of Yt+1 is μ̂t+1. In Model (1), μ̂t+1=μ, in Model (2), μ̂t+1=ϕ0+ϕ1Yt+⋯+ϕpYt−p+1+θ1ε̂t+⋯+θqε̂t−q+1, and in Model (3), μ̂t+1=δ0+δ1X1,t+δ2X2,t+⋯+δmXm,t. Let the conditional variance prediction of Yt+1 be ĥt+1, thereafter ĥt+1= exp (ω+βlnĥt+α|ε̂tĥt|)+γε̂tĥt.

Therefore, the distribution function of Yt+1 is predicted as (7) F̂t+1|t(y)=P(Yt+1≤y)=P(μ̂t+1+ĥt+1zt+1≤y)=zP(zt+1≤y−μ̂t+1ĥt+1)=Fzt+1(y−μ̂t+1ĥt+1),(7) where zt+1=εt+1ht+1 is the standardised residual. This obeys a skewed Student’s t-distribution with a mean of 0 and a variance of 1. Fzt+1(·) is the cumulative distribution function of zt+1. Thus, the density function of Yt+1 is (8) ft+1|t(y)=1ĥt+1fzt+1(y−μ̂t+1ĥt+1),(8) wherein fzt+1(·) is the density function of zt+1.

## 5. Robustness test

### 5.1. Multicollinearity diagnosis of TI and LASSO regression’s results

The robustness test was performed from January 4, 2012 to July 31, 2018. January 4, 2016 to July 31, 2018 is the out-of-sample prediction interval. A multicollinearity diagnosis is performed on 39 TIs, and the condition number κ=460677.7 is calculated. TIs have serious multicollinearity overall. Simultaneously, VIFs were calculated (see ). Except for ADX, PSY, MFI, and VHF, all VIFs exceed five. Among them, VOL and HSL reach 106, and K, D and J’s VIF values reach 109. The TIs’ multicollinearity characteristics are consistent with the empirical period’s conclusions.

Are technical indicators helpful to investors in china’s stock market? A study based on some distribution forecast models and their combinations

Yanyun

Yao

Shangzhen

Cai

Huimin

Wanghttps://doi.org/10.1080/1331677X.2021.1974921

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The significance Im1’s calculated results and importance indices Im2 appear in . There are 26 values of Im1: more than 90% where the SAR’s and BR’s values were one. There are 10 values of Im2 at more than 50%. The corresponding TIs are JCS, JCM, MA1, MA2, JCL, PVI, AMA, DDD, OBV, and HSL. Considering Im1 and Im2 we believe that the nine TIs of JCS, JCM, MA1, MA2, JCL, PVI, AMA, DDD, and HSL are important indicators that affect the returns during the robustness test period. Among them, the AMA’s and HSL’s results are consistent with those of the empirical period. This means that when analysing TIs, regardless of market conditions, AMA and HSL must be noted. According to the securities investment technical analysis theory, AMA is a classic TI. The long-term moving average is relatively reliable but it often lags. This ‘adjustable’ feature of AMA makes it an important impact indicator of the returns, regardless of the market conditions. The AMA’s predictability for financial returns has attracted attention. HSL refers to the frequency of the stocks changing hands in a certain period. It is one of the indicators reflecting the stocks’ liquidity and one of the most important TIs reflecting the market transactions’ activity. From a behavioural finance perspective, it also reflects investor sentiment to a certain extent. This should be one of the reasons why it has become an important indicator of the returns. The various TIs’ focus is different, and the effective TIs are unrealistic. There is a significant difference in the results of the significance and importance indexes between the robustness test period and the empirical period. This is not only related to the market conditions but also the macro-political and economic environment. Therefore, the TIs’ ‘explanatory power’ is different in different periods.

Are technical indicators helpful to investors in china’s stock market? A study based on some distribution forecast models and their combinations

Yanyun

Yao

Shangzhen

Cai

Huimin

Wanghttps://doi.org/10.1080/1331677X.2021.1974921

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What is the explanatory power of TIs during the robustness test period? The R-square of the LASSO regression has a maximum of 9.63% and a minimum of 1.42%. This is a slight increase from the empirical period. As shown in the lower part of Figure 2 for each LASSO regression, the TIs’ impact on the returns during this period is the same as that of the empirical period, with only weak explanatory power.

### 5.2. Fitting effect in-sample and statistical evaluation out-of-sample

The sample of the robustness test period’s fitting effect is also characterised by the average log-likelihood function, as shown in the right half of Figure 3. Cumulatively, as in the empirical period, LASSO-EGARCH (green line) has the best fitting effect, followed by ARMA-EGARCH (red line), and thereafter EGARCH (black line). However, after 2017, the LASSO-EGARCH’s average log-likelihood function at many moments is much lower than that of EGARCH and ARMA-EGARCH. This means that the TIs at such time points are no longer ‘information’ but ‘noise’. Their introduction reduces the fitting effect. TIs represent historical information. They have explanatory power and can be used as ‘information’, meaning that the market is ‘ineffective’. Conversely, the TI predictions’ failure may indicate an increase in China’s stock market’s effectiveness.

Thereafter, the robustness test period’s out-of-sample statistical evaluation is conducted. This includes the PIT evaluation, score evaluation, marginal calibration, sharpness evaluation, and VaR evaluation. The HL test was adopted for the PIT evaluation. The results appear in the lower part of . During this period, the forecasting effect on returns was generally better than that of the empirical period. The statistics of M(i, j) cannot reject the null hypothesis at the 5% significance level. The first four moments obtained good prediction results. For the W statistic, the ARMA-EGARCH model is the best and does not reject the null hypothesis. This means that the corresponding PITs can be regarded as independent and identically distributed in a uniform distribution U(0, 1). This is followed by the EGARCH model, and finally, the LASSO-EGARCH model. However, EGARCH and LASSO-EGARCH rejected the null hypothesis.

The score evaluation and sharpness analysis results appear in the lower parts of and . LASSO-EGARCH is still the best Bayesian winner. However, its rankings on the average logarithmic score and average CRPS are both the worst. Both the 50% and 90% prediction intervals of LASSO-EGARCH have the smallest average width. This indicates that it has the best sharpness. This conclusion is consistent with the empirical results. The marginal calibration effect is illustrated in Figure 6. Although the graph’s fluctuation characteristics are quite different from the marginal calibration graph (Figure 5) in the empirical period, there are still common points. There is thus no significant difference between EGARCH and ARMA-EGARCH. However, LASSO-EGARCH is quite different from them. It has great ‘non-synchronisation’ with the other two models and shows a better left-tail calibration. During this period, LASSO-EGARCH shows good right-tail calibration.

Are technical indicators helpful to investors in china’s stock market? A study based on some distribution forecast models and their combinations

Yanyun

Yao

Shangzhen

Cai

Huimin

Wanghttps://doi.org/10.1080/1331677X.2021.1974921

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As for the VaR back-test, we can form a conclusion as per the bottom half of . The robustness test period’s conclusion is consistent with that of the empirical period. For the 1% and 5% tail risk, all three models provided a good description at a 5% significance level. However, for the 1% tail risk, at the 10% significance level, the EGARCH and ARMA-EGARCH models reject the null hypothesis, while the LASSO-EGARCH model cannot reject the null hypothesis. Further exploration revealed that the LASSO-EGARCH model has improved its risk underestimation compared with the EGARCH and ARMA-EGARCH models.

## 6. Model combination and economic evaluation

As Kim and Upneja (2021) stated, an individual model may not be able to capture the data’s different features because of the time series’ complex nature. However, using a combination of methods may reduce the variance of the estimated error and improve the recognition performance. Furthermore, being inspired by the marginal calibration’s results, we examine the distribution prediction’s linear combination obtained from the three models. We then conduct an economic evaluation. Referring to Yao et al. (2020), three combinations were considered as equal weight combination (EW), logarithmic score combination (SW), and CRPS combination (CW). Two-point forecasts are derived from the forecasted distribution of the returns. These are the mean and median values. Thereafter, the mean and median’s direction accuracies were calculated. These were denoted as DA1 and DA2. Furthermore, a simulated trading strategy was designed based on the returns’ direction forecast. The transaction is divided into two situations: short and non-short selling. The state of holding at a maximum of one unit of the asset at hand is always maintained. In the short-selling situation, if the forecast direction is positive, then buy; otherwise, sell. In the non-short-selling situation, if the forecast direction is positive, buy if there is no asset at hand. Continue to hold the position if there is a unit of the asset at hand. Otherwise, when the forecast direction is non-negative, continue to be short if there is no asset at hand, and sell if there is a unit of the asset at hand. Similarly to Yao et al. (2020), the ratio of the strategic mean transaction return to the ideal mean transaction return is calculated. This is the strategy-ideal ratio. It is recorded as Rate(1) in the short-selling and Rate(2) in non-short-selling situations. Finally, Pesaran and Timmermann (1992) PT test was used to perform the directional accuracy test on DA1 andDA2. Anatolyev and Gerko (2005) EP test was employed to perform the excess profit test on Rate(1).

The direction accuracies and strategy-ideal ratios of the three individual models and the three combined models during the empirical period and the robustness test period are listed in . The two best values in each column are shown in bold. The PT and EP tests’ results that are significant at the 5% and 1% levels are marked with ** and ***, respectively. During the empirical period, LASSO-EGARCH does not have the best performance regarding the direction accuracy nor the strategy-ideal ratio. The combined models SW and CW are relatively better, and those Rate(2) of EW under the mean forecast have the best performance. However, both the PT and EP tests did not show their significance during the empirical period. Therefore, although the combined models show relatively good economic evaluation effects, the degree is unclear. During the robustness test period, the mean forecast of LASSO-EGARCH has a higher positive strategy-ideal ratio than EGARCH and ARMA-EGARCH. The strategy-ideal ratio of the median forecast of LASSO-EGARCH is negative. However, it is better than the other two individual models. The combined models’ SW and CW show an ‘absolute’ leading effect. They have significant directional accuracy and excess profitability through the PT and EP tests.

Yanyun

Yao

Shangzhen

Cai

Huimin

Wanghttps://doi.org/10.1080/1331677X.2021.1974921

Display Table

## 7. Conclusions

Three individual models are established, namely EGARCH, ARMA-EGARCH, and LASSO-EGARCH. Their residuals are set to obey the skewed Student’s t-distribution. The LASSO-EGARCH model contains high-dimensional-same-frequency TI information. The results show that there is serious multicollinearity in TIs and that the LASSO regression is suitable. The LASSO regression’s results show that the TIs for the return forecasts’ ‘explanatory power’ is limited. The TIs’ significance and importance have changed in different periods. However, the AMA and HSL have shown a higher significance and greater importance than other TIs. The AMA’s importance may be related to its own ‘adjustable’ characteristics. HSL may also be related to its ability to reflect the market trading activity and investor sentiment.

The distribution forecast’s PIT evaluation shows that during the empirical period, the three models are inadequate to predict the return distribution. However, LASSO-EGARCH is better than the other two models. During the robustness test period, LASSO-EGARCH is the worst. This may indicate that TIs have a certain predictive effect on the returns in the ‘bull’ market. However, in the state of ‘consolidation’ and ‘bear’, they have no predictive effect. LASSO-EGARCH is the best Bayesian winner and has the best sharpness. However, it performs the worst regarding the average logarithmic score and average CRPS. Regarding the marginal calibration, EGARCH and ARMA-EGARCH have almost the same effect. LASSO-EGARCH behaves differently: It has better left-tail calibration and is clearly ‘asynchronous’ with the two other models. VaR back-tests show that LASSO-EGARCH has a better 1% left-tail risk assessment. This means that the TI information is beneficial to the management when the stock market crashes. Furthermore, three combinations of the individual models: the EW, SW, and CRPS combination (CW) were examined. The economic evaluation was conducted on the individual and combined models. Overall, only SW and CW have a better direction accuracy and excess profitability. However, they are not significant during the empirical period but are significant during the robustness test period.

Comprehensively, it can be concluded that the TI information will not enable investors to obtain more economic profit, but in the ‘consolidation’ and ‘bear’ market conditions, it will be beneficial to risk management. After adding the TI information into the model, investigating the model combination based on the logarithmic score and CRPS can improve the economic benefits based on the return distribution. However, its significance is related to the market state. Therefore, in the state of the ‘consolidation’ and ‘bear’ markets, investors should notice the TI information to help risk management. When an individual TI information embedding model cannot provide the predictability of returns and excess profitability, it cannot be discouraged. The combination of several individual models can be considered based on the distribution forecast evaluation to increase profitability.

This study may have some limitations, such as no integration of the ARMA and TI information for the mean value modelling of returns. Furthermore, there was no addition of the TI information to the conditional volatility modelling. The model is limited to the GARCH framework, and rationality is subject to further discussion. The samples have been subjectively selected according to the natural year, and its rationality is also to be discussed, although Zaremba and Nikorowski (2019) noted that transaction costs impact the abnormal performance of the stock market. We fail to consider transaction costs in the simulated trading strategy. Overcoming the above limitations will also be our future research direction.