To avoid spurious regression results [ 21 , 22 ], we must determine whether our time series are stationary (I(0)) or have co-integrated relationships. After we extract the 9 first components, we conduct a KPSS test [ 23 ] and an ADF test [ 24 , 25 ] to check the variables’ stationarity. As shown in Table 3 only C 1 is not stationary. We therefore define DC 1,t = C 1,t −C 1,t−1 (difference once), and find that it is stationary. Subsequently all the 10 variables (CCI, DC 1 , C i ∈ {2, 3, ⋯, 9} ) are stationary.

We project our topic variables on the selected 9 components, (C 1 , C 2 , …, C 9 ), and define where X = (x 1 , x 2 , …, x 34 ) T refers to our 34 topic time series and c i refers to the entries of the 9 component vectors as listed in Table 2 .

Judging from the scree plot, we arbitrarily retain the first 9 PCA components since they represent the majority of information on the original topic covariances (about 85%), thus ensuring we retain all relevant information for accurate modeling. Not all 9 components need to be included in our transitional model since each carries increasingly less information. In fact, whether we choose 8, 9, or 10 components should be of little significance to our transitional model.

Therefore we perform a principal components analysis (PCA) [ 18 ] to ensure the orthogonality of our components and to avoid the issue of multicollinearity in future regression models. Furthermore, this procedure reduces dimensionality and may provide information on the underlying components of the covariances of our 34 Google trends time series. We list the 10 highest ranked components with their loadings in Table 1 and provide a scree plot in Fig 5 . A Kaiser-Meyer-Olkin Measure of Sampling Adequacy (KMO) test [ 19 ] and Squared Multiple Correlation (SMC) test [ 20 ] indicate that the PCA was indeed a suitable procedure with the large majority of values well above 0.8 (1.0 is optimal).

Each of the 34 Google trends time series (corresponding to the ECQ questionnaire topics) can be taken as independent variables, representing a certain facet of consumer confidence. However, we need to determine the degree of multicollinearity to investigate whether each variable independently represents consumer confidence, and to ensure the validity of later regression models used to fit a potential C3I based on these 34 independent variables to the CCI.

Then, our transitional model (i.e. Model 2 in Fig 4 ) can be written as follows: (2) where t 0 = 47.

As indicated in Table 6 , all three tests imply there is a structural change in the time series, which may have resulted from the NBSC standardization in November 2009. We therefore add dummy variable D to all the independent variables of our model, where the first time period comprises 47 months and the second time period comprises 42 months. (1)

A normalization of CCI data in reference to 1996 data [ 17 ] ended in November 2009 leading to an apparent discontinuity in the CCI data in 2009–2010 as shown in Fig 1 . To determine whether our CCI data is biased by structural changes or not, we conduct as Structural Change test [ 29 ]. The results are summarized in Table 6 ; the null-hypothesis that no structural change occurred must be rejected. In other words, the results indicate a structural change is likely to have occurred in November 2009 possibly because of the use of new survey or normalization methods [ 17 ].

We conduct a Granger Causality test [ 27 ] between our independent variables, C i ∈ {2, 3, ⋯, 9} and DC 1 vs. one dependent variable, namely CCI t , to look for Granger-causative relationships between CCI and independent variables. The results in Table 5 indicate that independent variable C 2 is Granger causative of the CCI. Results in behavioral science [ 28 ] indicate that people tend to discount older information in favor of newer information. We therefore choose variables that were lagged one and two units for testing. Refering to the results, we add C 2 at lag 1 and lag 2 in our independent variables.

After determining the principal components of our Google trend time series data, i.e. the components that best describe consumer confidence as indicated from Google query volume with respect to our 34 survey topics, we perform a Vector Auto-regression (VAR) [ 26 ] to determine the degree of auto-correlation in our CCI data. As shown in Table 4 , we find a considerable degree of auto-correlation, indicating the necessity to include CCI at lag 1 and C 3 at lag 2 as independent variables in future analysis. This finding is intuitive, since consumers may factor previous confidence into their assessment of future conditions along with other present information.

Results

We then proceed with a Stepwise Regression [30] as follows:

Set an appropriate significance level of 0.05. Fit Eq 2 by Ordinary Least Squares (OLS). If all the parameters pass the test, then stop, otherwise, proceed to step 4. Select the variable with the lowest significance level, and drop it. Fit the new equation, minus the variable, by OLS. Repeat step 3 and step 4, until all variables pass the test.

As shown in Table 7 the resulting model exhibits a good fit as indicated by a significant adjusted R2 (0.923). We conduct a White Test [31] to determine whether the regression has heteroscedasticity. As indicated by the results shown in Table 8, this is the case. Therefore, we re-run our stepwise model with robust standard errors [32]. The results are shown in Table 9. The results improve considerably: all parameters pass the test and we observe an improved adjusted R2. However, we must point out that although the use of robust standard errors improves the estimate, we can not guarantee that the regression has no heteroscedasticity.

Using the regression results we can model C3I as shown in Eq (3). (3)

This fitted equation preserves the major components of the PCA (C 2 −C 6 ) to avoid significant information loss. We can formulate our final fitted model using the original indices as shown in Eq (4). (4) where XT = (x 1 , x 2 , …, x 34 ); and the entries of A, B, and C are provided in Table 10.

This result indicates that the C3I is partially shaped by its own previous values. We speculate that people may extrapolate their present confidence to an assessment of future economic confidence, in addition to other relevant information.

The first part of Eq (4), i.e. t ≤ 47 corresponds to the period before December 2009. Matrix A, shown in Table 11, can be split into 2 categories of topics, namely those that contribute positively to C3I and those that contribute negatively according to their coefficients. Note that the topics themselves do not contribute to C3I. The attention they receive in the population, measured by Google trends volume, is used as an indicator of the population’s pre-occupation with the topic in relation to the C3I. The topics in Table 11 thus reveal the internal topical structure of this particular measurement of consumer confidence through a behavioral measure and which topics contribute negatively or positively to our estimation of C3I. As shown in Tables 11, 12, and 13 we see that a number of topics that contribute positively to our estimation of C3I change polarity after November 2009. This change may indicate that the population changed its assessment of these topics, leading to a different contribution to their consumer confidence, or potentially a change in how the CCI is measured. For example, when a large number of individuals search for “over capacity” this might occur because of the perception of over capacity as a negative issue, while some years later, people might search for the same topic from the position that over capacity is improving, hence making a positive contribution to their consumer confidence.

Matrices A, B, and C indeed reveal significant changes in the structure of the C3I over time. In Tables 11, 12 and 13, we show how certain topics contribute positively or negatively to C3I values. In particular we see that before December 2009 (Table 11) positive topics include “stocks”, “CPI”, and “trade balance”. Negative topics notably include “prices”, e.g. “housing”, “fuel”, “food”, “over capacity”, and concerns about “economic transition”. Examining Table 12 we find that these are not influencing C3I as strongly after November 2009. Rather, the top ranked positively contributing topics are now “over capacity”, “real estate”, and “housing prices”. We do note that the negatively contributing topics continue to include “exchange rates” and “foreign exchange”.

Comparing Tables 11 and 12 with 13 reveals that the “future” influence of topics in our C3I model might overall be less than its current influence. Positive topics such as “real estate sales”, “population aging” and negative topics such as “crude or food price”, “exchange rate” have much lower parameter values in Table 13. In addition, these results shows that social media influence on C3I in our model increases after November 2009 possibly indicating that the public is increasingly expressing their outlook through online activity.

As shown in Fig 6, our Google Trends data indicates a consistent downward trend in consumer confidence from 2007 to the present which is not mirrored by official CCI data. However, Google Trends data presumably provides only a partial indicator of the factors that shape consumer confidence. We can therefore not conclude that our Google Trends model indicates an actual downtrend in consumer confidence. This result does point to an interesting divergence between two different, but related measures of consumer confidence. We also note that after the observed discontinuity, CCI does exhibit a slight downward trend.

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larger image TIFF original image Download: Fig 6. The contribution of Google Trends Data to our C3I model plotted over time reveals a downward trend possibly indicating that the public are losing economic confidence as judged from search engine queries. https://doi.org/10.1371/journal.pone.0120039.g006

Finally, we compare C3I values generated by our model to the actual CCI values in Fig 7 which highlights the strong degree of correspondence between our model and actual CCI values as reported by the Chinese National Bureau of Statistics. In fact, after conducting our original analysis, we obtained new Google Trends data for the period July 2013 to May 2014, nearly a year, and re-applied the model developed from the original to this new Google Trends data. As shown in Fig 7 our model outcomes match the new C3I values quite well, in spite of the renormalization that Google applies to each new data request, indicating that the C3I model is robust to minor changes in the underlying Google Trends data.