Newey-West Correction of Standard Errors - Google搜尋趨勢與認知金融：從臺灣股票市場學到的新知

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146 weeks of data.

3.2 Ticker Symbols

A company listed in TAIEX also has a ticker symbol. For example, “2330” is the ticker symbol of “台積電”. We first used ticker symbols to retrieve their SVI from Google Trends. Next, we used the similar procedures described in the previous section to obtain the weighted SVI of all companies. The time series also had 146 weeks of data.

4. Newey-West Correction of Standard Errors

Newey-West correction of standard errors method¹⁰ is a method to estimate the coefficients of a linear regression model applied to time series data. It is used to correct autocorrelation (also called serial correlation) and heteroskedasticity in the error terms in the regression model. We used the statistical software SAS to run the regression.

Below are the variables names and their meaning.

y：average returns of TAIEX 𝑥𝑥1: Google SVI

𝑥𝑥2: trading volume of TAIEX 𝑥𝑥3: Taiwan Stock Price Index

10 Please refer to the appendix to know the details.

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𝑥𝑥4: Taiwan Economic Situation Index 𝑥𝑥5: Taiwan Political Index

𝑥𝑥6: Taiwan Investment Environment Index 𝑥𝑥7: Global Economic Index

𝑥𝑥8: Possibility of the Value of Your Portfolio Increases within six months We first converted all time series data into log10, and then used the difference between adjacent weeks ( 𝑥𝑥𝑖𝑖𝑖𝑖− 𝑥𝑥𝑖𝑖𝑖𝑖−1) to run the regression. In this way, the interpretation of the regression is easier: 1 percentage change of an independent variable will change a certain percentage of the dependent variable, specified by the coefficient of the independent variable in the regression model. Moreover, we can reduce the scale difference of the variables; hence increase predicting accuracy.

The linear regression model is as follows:

y_𝑖𝑖 = 𝛽𝛽₀+ ∑⁸_𝑖𝑖=1𝛽𝛽_𝑖𝑖𝑥𝑥_{𝑖𝑖𝑖𝑖}+ e_𝑖𝑖, and where t = 1, 2, ... ,146

We used the regression results to estimate what variables are significant in effecting the average returns of TAIEX and how long the effect lasts. Because the residuals had heteroscedasticity and autocorrelation, the method used HAC (Heteroskedasticity and Autocorrelation Consistent) estimators to correct them. We

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used Parzen kernel, an HAC estimator, to run the regression. The relationship between Newey-West correction of standard errors method and Parzen kernel is shown in the appendix.

5. Summary

In the chapter, we have explained the data sources and the methods we used to conduct our research. We downloaded the data from TEJ, Google Trends, and J.P.

Morgan Asset Management to help us test different behaviour hypothesis. After that, we used the frequency conversion method to process J.P. Morgan Asset Management data and the weighted sum approach to process Google Trends SVI data. Finally, we applied Newey-West correction of standard errors method to run the regression on the processed data. We present our results with analysis in the following chapter.

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Research Results and Analysis

This chapter presents the results and provides our analysis. In Section 1, we report the regression results based on the SVI by ticker symbols, various investor interview sentiment indexes and trading volume to identify which of them have influence on the average returns of TAIEX. In Section 2, we show the regression results based on the SVIs searched by company names and by ticker symbols of companies of different ranks. Additionally, we evaluated if the SVI based on the top-50 companies’ ticker symbols helps predict the average returns of TAIEX. In Section 3, we analyzed the p-value of the SVI searched by companies with different ranks in TAIEX to obtain deeper insights about investors’ behaviour in the Taiwan stock market. In Section 4, we ran regression, using the SVI with an increased trend to test the attention hypothesis of Da, Engelberg, and Gao (2011). In Section 5, we used data in different time lag to evaluate whether SVI can predict TAIEX average returns for a long period of time or not. In section 6, we summarise the chapter.

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1. Variables with a Significant Impact on Average Stock Returns

We first ran regression of all 7 variables on the average TAIEX returns. Following Da, Engelberg, and Gao (2009), we used the SVI searched by all companies’ ticker symbols to run the regression. The results are given in Table 1.

Table 1

Regression of all 7 variables on the average TAIEX returns Parameter Estimates

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Note. t = 146. 𝑙𝑙(𝑛𝑛) = 4. *p < 0.05. **p < 0.01. ***p < 0.001.

y ∶ average returns of TAIEX 𝑥𝑥₁: Google SVI

𝑥𝑥2: trading volume of TAIEX 𝑥𝑥3: Taiwan Stock Price Index 𝑥𝑥₄: Taiwan Economic Situation Index 𝑥𝑥5: Taiwan Political Index 𝑥𝑥6: Taiwan Investment Environment Index 𝑥𝑥7: Global Economic Index 𝑥𝑥₈: Possibility of the Value of Your Portfolio Increases within six months

Table 1 indicates that trading volume and investors’ interview sentiment of Taiwan Stock Prices are significantly related to the average TAIEX returns, while the other six variables are not (p > 0.05). Although Taiwan Economic Situation Index isn’t shown to have an impact on the average returns, this result is likely to be caused by other confounding interview sentimental variables. To test the hypothesis, we removed other interview sentimental variables 𝑥𝑥₅, 𝑥𝑥₆. 𝑥𝑥₇, and 𝑥𝑥₈ and then ran another regression. The results are shown in Table 2.

Table 2

Regression of two interview sentiment indexes, the SVI and trading volume on average TAIEX returns

Parameter Estimates

Parameter Estimate Approx. Std Err T-value Approx. Pr > |t|

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Intercept 0.000382 0.000767 0.50 0.6188

𝑥𝑥1 0.024569 0.0144 1.71 0.0895

𝑥𝑥2 0.031812 0.00949 3.35 0.001**

𝑥𝑥3 -0.00613 0.00231 -2.66 0.0088**

𝑥𝑥4 0.002872 0.00136 2.12 0.0361*

Note. t = 146. 𝑙𝑙(𝑛𝑛) = 4. *p < 0.05. **p < 0.01. ***p < 0.001.

y ∶ average returns of TAIEX 𝑥𝑥1: Google SVI

𝑥𝑥₂: trading volume of TAIEX 𝑥𝑥3: Taiwan Stock Price Index 𝑥𝑥4: Taiwan Economic Situation Index

Table 2 shows that investors’ interview sentiments of both Stock Price Index (p = 0.0088) and Taiwan Economic Situation Index (p = 0.0361) affect the average returns of TAIEX. Additionally, trading volume (p = 0.001) is significantly related to the TAIEX returns. This supports the research of Lee and Swaminathan (2000) that trading volume is an indication of a stock past performance and can be used to predict the stock future performance. It also agrees with that reported in Chuang, Ouyang, and Lo (2010), that trading volume is positively related to the average returns of TAIEX.

Among the three variables that impact TAIEX, trading volume and the investors’

interview sentiment of Taiwan Economic Situation are positively correlated to the average TAIEX returns: 1 % increases in trading volume and Taiwan Economic

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Situation will increase 0.031812% and 0.002872% in the average returns of TAIEX. We gauged that investors’ opinions about the economic of Taiwan in the future come from their observations of the changes in daily living, which reflect the reality. It therefore has positive correlation with the TAIEX returns.

By contrast, investors’ interview sentiment of Taiwan Stock Price is negatively correlated to the average TAIEX returns: 1% increase in Taiwan Stock Price Index will decrease 0.00613 in the average returns. This can be explained by the overconfidence and over-optimism hypothesis of De Bondt and Thaler (1995) in that while investors’

confidence about Taiwan Stock Price is positive, the actual TAIEX stocks returns are not so good as they believe.

2. Ticker Symbols vs. Company Names: SVIs for Investors Attention

Table 1 shows that the SVI based on the ticker symbols of all companies is not correlated to the average TAIEX returns. Since we used SVI to represent investors’

attention and companies with bigger market capital normally receive more attention, the SVI of companies with higher ranks in TAIEX might better reflect investors’ attention.

To verify this hypothesis, we used a top-down approach by separating the SVI of all companies’ ticker symbols into various ranks (top-800, top-700, top-600, top-500, top-400, top-300, top-200, top-100). After that, we ran regressions using each of the

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SVI series. The results show that only the SVI by ticker symbols of the top-100 companies have an impact on the average TAIEX returns while all others have not.

Table 3 presents the results of SVI based on ticker symbols of the top-100 companies.

Table 3

Regression of two interview sentiment indexes, trading volume and the SVI based on ticker symbols of the top-100 companies on average TAIEX returns

Parameter Estimates

Parameter Estimate Approx. Std Err T-value Approx. Pr > |t|

Intercept 0.000336 0.000756 0.44 0.6576

𝑥𝑥₁ 0.016388 0.00736 2.23 0.0276*

𝑥𝑥₂ 0.030368 0.00915 3.32 0.0012**

𝑥𝑥₃ -0.00563 0.00228 -2.47 0.0147*

𝑥𝑥₄ 0.002768 0.00135 2.05 0.0422*

Note. t = 146. 𝑙𝑙(𝑛𝑛) = 4. *p < 0.05. **p < 0.01. ***p < 0.001.

y ∶ average returns of TAIEX 𝑥𝑥₁: Google SVI

𝑥𝑥2: trading volume of TAIEX 𝑥𝑥3: Taiwan Stock Price Index 𝑥𝑥₄: Taiwan Economic Situation Index

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The result triggered our curiosity about whether the same pattern also exists in the SVI by company names for different ranks. To answer that question, we also separated the SVI of all company names into various ranks (top-800, top-700, top-600, top-500, top-400, top-300, top-200, top-100). We then ran regressions using each of the SVI series.

To our surprise, we found that all SVIs are significantly and positively related to the TAIEX average returns. Table 4 shows the regression result of the SVI searched by the top-100 company names. Regression of other SVI series has similar results. This result supports the attention hypothesis of Barber and Odean (2007) that individual investors would buy stocks that attract more attention where attention is measured by the Google search volume in our study. We will provide more in depth analysis of the p-value of SVIs under these regressions in the next Section.

Table 4

Regression of two interview sentiment indexes, trading volume and the SVI based on company names of the top-100 companies on average TAIEX returns

Parameter Estimates

Parameter Estimate Approx. Std Err T-value Approx. Pr > |t|

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Intercept 0.000275 0.000760 0.36 0.7183

𝑥𝑥1 0.038288 0.0132 2.89 0.0044**

𝑥𝑥2 0.02717 0.00811 3.35 0.0010**

𝑥𝑥3 -0.00606 0.00230 -2.63 0.0096**

𝑥𝑥4 0.003069 0.00138 2.22 0.0282*

Note. t = 146. 𝑙𝑙(𝑛𝑛) = 4. *p < 0.05. **p < 0.01. ***p < 0.001.

y ∶ average returns of TAIEX 𝑥𝑥1: Google SVI

𝑥𝑥₂: trading volume of TAIEX 𝑥𝑥3: Taiwan Stock Price Index 𝑥𝑥4: Taiwan Economic Situation Index

In Fan, Liao, and Chen (2014), the authors reported that the SVI based on the top-50 company names is significantly related to the average returns of TAIEX. To compare our results with theirs, we made two more SVIs based on the top-50 companies.

One used ticker symbols and the other used company names. We then ran two regressions using each of the series. The results are given in Tables 5 & 6.

Table 5

Regression of two interview sentiment indexes, trading volume and the SVI of ticker symbols for the top-50 companies on average TAIEX returns

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Parameter Estimates

Parameter Estimate Approx. Std Err T-value Approx. Pr > |t|

Intercept 0.000311 0.000756 0.41 0.6810

𝑥𝑥₁ 0.016982 0.00693 2.45 0.0155*

𝑥𝑥₂ 0.029725 0.00923 3.22 0.0016**

𝑥𝑥₃ -0.00566 0.00225 -2.52 0.0130*

𝑥𝑥₄ 0.002779 0.00133 2.08 0.0391*

Note. t = 146. 𝑙𝑙(𝑛𝑛) = 4. *p < 0.05. **p < 0.01. ***p < 0.001.

y ∶ average returns of TAIEX 𝑥𝑥₁: Google SVI

𝑥𝑥2: trading volume of TAIEX 𝑥𝑥3: Taiwan Stock Price Index 𝑥𝑥₄: Taiwan Economic Situation Index

Table 6

Regression of two interview-sentiment indexes, trading volume and the SVI based on top-50 company names on average TAIEX returns

Parameter Estimates

Parameter Estimate Approx. Std Err T-value Approx. Pr > |t|

Intercept 0.000232 0.000764 0.30 0.7618

𝑥𝑥1 0.033182 0.0109 3.05 0.0028**

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𝑥𝑥₂ 0.028716 0.00868 3.31 0.0012**

𝑥𝑥₃ -0.00597 0.00231 -2.59 0.0107*

𝑥𝑥₄ 0.003052 0.00139 2.20 0.0292*

Note. t = 146. 𝑙𝑙(𝑛𝑛) = 4. *p < 0.05. **p < 0.01. ***p < 0.001.

y ∶ average returns of TAIEX 𝑥𝑥1: Google SVI

𝑥𝑥₂: trading volume of TAIEX 𝑥𝑥3: Taiwan Stock Price Index 𝑥𝑥4: Taiwan Economic Situation Index

As the above two tables show, both SVIs searched by the top-50 company names and by the top-50 ticker symbols are significantly related to the average TAIEX returns, which agrees with that reported in Fan, Liao, and Chen (2014).

3. Analysis of Investors’ Behaviours

In the previous section, we have presented the regression results using the SVIs of company names and ticker symbols of various ranks. To better understand the relationship between these SVIs and investors’ attention, we plotted the p-value of SVIs for company names and ticker symbols under various ranks on Figure 1. The lower the p-value is, the more significant the SVI is in impacting the TAIEX average returns.

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Figure 1

p-value of the SVI searched by companies with different ranks in TAIEX

Figure 1 shows that all SVIs by ticker symbols have p-value indicating they are not significant in impacting TAIEX average returns, except the one from the top-100 companies. It suggests that investors in the Taiwan stock market normally don't use ticker symbols to conduct Google search for stock information. This makes sense, as the ticker symbols of Taiwanese stocks are 4-digit numerical values, which might be ambiguous and can be confused as product item number, specific year, phone extension and others by the Google search engine. The only exception is the top-100 ranked

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companies, which are traded more often; hence their ticker symbols are easily associated with the company name by the Google search engine. Moreover, investors tend to pay attention to the companies that have more capital, and likely to remember their ticker symbols. These explain why search volume using ticker symbols for the top-100 company is significantly related to TAIEX average returns.

By contrast, SVIs by company names of all ranks have p-values that indicate they are significantly related to the TAIEX average returns. This indicates that investors mostly use company names, not ticker symbols, to search for stock information to invest in the Taiwan stock market. This discovery endorses Google’s Chief Economist Hal Varian’s claim that Google search data can provide insights into people’s interests, intentions and future actions (see Varian 2011).

4. Verification of Investors Buying Attention

According to Barber and Odean (2007), investors pay attention to stock information when planning to purchase stocks. However, when planning to sell stocks, investors only pay attention to the stocks they own. Using Google search volume as the proxy for investors’ attention, this means that an increased search volume is a sign of buying intention, which leads to price pressure and a possible price increase. By contrast, selling intention has no impact on the search volume. Hence, a decreased trend

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in search volume of a certain stock is not directly connected to the decreased stock returns.

To test their hypothesis, we selected SVI indexes that have an increased trend, i.e.

It > It-1, from the SVI with all company names, which consists of 67 weeks of data. The other 79 weeks of data become the SVI with a decreased trend. The reason why we used the data from the SVI with all company names is because we believe the SVI with all company names represents investors’ attention in the Taiwan stock market the best.

Here, we expect the SVI with an increased trend will have an even more significant impact on the average TAIEX returns than the original SVI while the SVI with a decreased trend will have no impact on the TAIEX returns.

We first present the regression results from the SVI with all company names as the base line in Table 7. Then, we show the results from two regression results, one on the SVI with an increased trend and the other on the SVI with a decreased trend in Tables 8 and 9. We included trading volume and two interview sentimental variables when running the two regressions.

Table 7

Regression of two interview sentiment indexes, trading volume and SVI based on all

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company names on average TAIEX returns

Parameter Estimates

Parameter Estimate Approx. Std Err T-value Approx. Pr > |t|

Intercept 0.000355 0.000748 0.47 0.6360

𝑥𝑥₁ 0.042557 0.0159 2.68 0.0084**

𝑥𝑥₂ 0.027507 0.00821 3.35 0.0010**

𝑥𝑥₃ -0.00576 0.00226 -2.55 0.0120*

𝑥𝑥₄ 0.002885 0.00135 2.14 0.0345*

Note. t = 146. 𝑙𝑙(𝑛𝑛) = 4. *p < 0.05. **p < 0.01. ***p < 0.001.

y ∶ average returns of TAIEX 𝑥𝑥₁: Google SVI

𝑥𝑥2: trading volume of TAIEX 𝑥𝑥3: Taiwan Stock Price Index 𝑥𝑥₄: Taiwan Economic Situation Index

Table 8

Regression of an increased trend SVI with all company names, trading volume and interview sentimental variables on average TAIEX returns

Parameter Estimates

Parameter Estimate Approx. Std Err T-value Approx. Pr > |𝑡𝑡|

Intercept -0.00046 0.00142 -0.32 0.7469

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𝑥𝑥₁ 0.077757 0.0277 2.80 0.0068**

𝑥𝑥₂ 0.020013 0.0104 1.93 0.0584

𝑥𝑥₃ -0.00877 0.00490 -1.79 0.0783

𝑥𝑥₄ 0.005084 0.00331 1.54 0.1298

Note. t = 67. 𝑙𝑙(𝑛𝑛) = 1. *p < 0.05. **p < 0.01. ***p < 0.001.

y ∶ average returns of TAIEX 𝑥𝑥1: Google SVI

𝑥𝑥₂: trading volume of TAIEX 𝑥𝑥3: Taiwan Stock Price Index 𝑥𝑥4: Taiwan Economic Situation Index

Table 9

Regression of a decreased trend in SVI with all company names, trading volume and interview sentimental variables on average TAIEX returns

Parameter Estimates

Parameter Estimate Approx. Std Err T-value Approx. Pr > |𝑡𝑡|

Intercept -0.0275 0.0380 -0.72 0.4718

𝑥𝑥₁ -0.07284 0.2297 -0.32 0.7521

𝑥𝑥₂ 0.649021 0.8200 0.79 0.4312

𝑥𝑥₃ -0.04488 0.0460 -0.98 0.3325

𝑥𝑥₄ 0.028232 0.0309 0.91 0.3633

Note. t = 79. 𝑙𝑙(𝑛𝑛) = 1. *p < 0.05. **p < 0.01. ***p < 0.001.

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36 y ∶ average returns of TAIEX 𝑥𝑥1: Google SVI

𝑥𝑥₂: trading volume of TAIEX 𝑥𝑥₃: Taiwan Stock Price Index 𝑥𝑥4: Taiwan Economic Situation Index

In Table 8, we see that the SVI series with an increased trend is more significant in impacting the average TAIEX returns (smaller p-value) than that of the original SVI (see Table 7). Moreover, the SVI series with a decreased trend has no impact on the average returns of TAIEX (see Table 9). This supports the attention hypothesis of Barber and Odean (2007) that increased attention is connected to the increased stock prices while the decreased attention is not connected to the decreased stock prices.

5. Short-Term Average Returns Prediction.

In Da et al. (2009), the authors reported that SVI has the predictive power for Russell 3000 over two-week time. To compare our results on TAIEX with theirs, We used different lag period (in weeks) to run regression for 5 weeks. For example,

if lag = 1, y_𝑖𝑖 = 𝛽𝛽₀+ ∑⁸_𝑖𝑖=1𝛽𝛽_𝑖𝑖𝑥𝑥_{𝑖𝑖𝑖𝑖}+ e_𝑖𝑖, and where t = 1, 2, ... ,146,

if lag = 2, y_𝑖𝑖 = 𝛽𝛽₀+ ∑^𝑛𝑛=8_𝑖𝑖=1 𝛽𝛽_𝑖𝑖𝑥𝑥_{𝑖𝑖𝑖𝑖−1}+ e_𝑖𝑖−1, and where t = 2, 3, ... ,146,

and so on. The results are given in Table 10.

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Table 10

Regression of two sentiment indexes, trading volume and SVIs with all company names with different time lags on TAIEX average returns

Parameter Lag period

Intercept 𝑥𝑥1 𝑥𝑥2 𝑥𝑥3 𝑥𝑥4

1 0.000355 0.042557 0.027507 -0.00576 0.002885

p-value 0.636 0.0084** 0.001*** 0.012* 0.0345*

2 0.000466 -0.02834 -0.0355 -0.00618 0.00318

p-value 0.5793 0.1742 0.0032** 0.0204* 0.0425*

3 0.000838 0.053154 0.026307 -0.00239 0.001552

p-value 0.2246 0.003** 0.0069* 0.3188 0.3161

4 0.000698 -0.02902 -0.02396 -0.00351 0.002232

p-value 0.3465 0.0229* 0.0254* 0.1369 0.1331

5 0.000784 0.038865 0.01987 -0.00203 0.001666

p-value 0.2875 0.0115* 0.0327* 0.4556 0.3596

Note. 𝑙𝑙(𝑛𝑛) = 4. *p < 0.05. **p < 0.01. ***p < 0.001.

y ∶ average returns of TAIEX 𝑥𝑥₁: Google SVI

𝑥𝑥2: trading volume of TAIEX 𝑥𝑥3: Taiwan Stock Price Index

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38 𝑥𝑥4: Taiwan Economic Situation Index

Table 10 shows that only trading volume can predict the average returns of TAIEX for 5 weeks while investors’ sentiments on Taiwan Stock Index and Taiwan Economic Situation can be used to predict the returns for two weeks. Although Google SVI has predictive power for TAIEX returns on week 1, 3, 4 and 5, its p-value for the second week is not significant. This result is different from that of Da et al. (2009) on Russell 3000, which indicated that the SVI has continuously predicative power over two weeks.

6. Summary

Our empirical study found that trading volume, Google SVIs, and investors’

interview sentiments of Taiwan Stock Price Index and Taiwan Economic Situation Index are significant in predicting the TAIEX average returns. These results support behavior finance hypothesis that investors’ psychological states can affect financial stock markets. In particular, their attention, and overconfidence are significantly related to the TAIEX average returns.

We also discover investors in the Taiwan Stock Market normally use company names, not ticker symbols, to conduct Google search for information related to investment decisions. This finding endorses Google’s Chief Economist Hal Varian’s

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claim that Google search data can provide insights into people’s interests, intentions and

future actions (see Varian 2011).

In the next chapter, we will conclude the thesis and provide suggestions for future research.

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Conclusions and Outlooks

1. Review of Research Findings

Our empirical study of how investors’ attention and interview sentiments influence Taiwan stock market has produced many interesting results. First of all, we discover the investors in Taiwan stock market mostly use company names, not ticker symbols, to conduct Google search for information related to investment decisions. This finding endorses Google’s Chief Economist Hal Varian’s claim that Google search data can

provide insights into people’s interests, intentions and future actions (see Varian 2011).

Next, we found that only two of the six inventors’ interview sentiments provided by the J.P. Morgan confidence indexes are significant in influencing Taiwan stock market. The first one is investors’ sentiment about Taiwan Stock Price, which is shown to be negatively correlated to the average TAIEX returns. This result supports the

在文檔中 Google搜尋趨勢與認知金融：從臺灣股票市場學到的新知 - 政大學術集成 (頁 27-0)