IPEK UNIVERSITY
DEPARTMENT OF ECONOMICS
WORKING PAPER SERIES
GOOGLE TRENDS AND
FORECASTING PERFORMANCE
OF EXCHANGE RATE MODELS
Levent Bulut
No: 15-05
August 2015
GOOGLE TRENDS AND FORECASTING PERFORMANCE OF EXCHANGE RATE
MODELS
Levent Bulut1
Abstract
In this paper, internet search data provided from Google Trends is utilized to nowcast the known
variates of alternative exchange rate determination models. The sample covers 12 OECD countries’
exchange rates for the period from Jan 2004 to June 2014. The results indicate that inclusion of
Google Trends-based nowcasting values of macro fundamentals to the current set of government
released-macro-economic variables improve the out-of-sample forecast of Purchasing Power Parity
model in seven currency pairs and of Monetary model in four currency pairs. In this paper we claim
that, for proper testing of the structural models, since there is a lag in the release of official data on
macro fundamentals, the literature should focus more on using ex ante variables on current macro
fundamentals and nowcasting of these variables with utilization of Google Search Inquiries can be
one alternative for this purpose. (JEL F31, F37, C52)
1
Assistant Professor of Economics, Ipek University, Department of Economics. Turan Gunes Blvd.
458. Cadde, Oran, Cankaya, Ankara, TURKEY, 06550, E-mail: lbulut@ipek.edu.tr, Phone: +90312-470-4686, Fax:
+90-312-470-0007, URL: www.leventbulut.wordpress.com
1
I.
INTRODUCTION
In an influential paper, (Meese & Rogoff, 1983) tested how well the existing empirical
exchange rate models of that time fit out of sample, and they found that, by using data from 1970s,
a random walk model performs as well as any estimated structural or various time series models.
These surprising findings, known as “Exchange rate disconnect puzzle” or “Meese- Rogoff
Puzzle”, would imply that if out-of-sample forecast is a valid approach for model comparison,
then, the standard economic models of exchange rate determination would be inadequate. (Meese
& Rogoff, 1983) findings have been widely re-examined in the literature by using different
currency pairs, different time periods, real-time versus revised official macro data, and different
linear structural models to assess the evidence in favor of economic fundamentals or structural
models. Also, the model specifications were tested by adopting some non-linear and nonparametric extensions to get better results against the random walk null. In this paper, internet
search data via Google Trends is utilized to nowcast the known variates of two structural exchange
rate determinations models; Purchasing Power Parity (PPP) model and Monetary model. Then, by
using the point-forecast criterion, the out-of-sample forecasting performance of these two
structural models were tested against the null of random walk with drift and without a drift.
By using internet search data, we aim to get a timely description of the state of the economy
way before the official data is released to the market participants. Government data releases in all
countries follow a lag and the market has access to these mostly monthly data in the midst of the
following month or later. On the other hand, the Google Trends data can provide weekly
information via search query indices on several macro fundamentals. But, it is worth clarifiying
that the aim of this paper is not to find a substitute for the official government data. In fact, the
official government data is the best available measure of macro fundamentals but since data
releases follow a lag, the data is not available per se at the time of decision making. Hence, by
utilizing the weekly internet search data, we can get a proxy to gauge the market expectations of
then current macro fundamentals. It is suggested in this paper that since exchange rates are mainly
driven by expectations, using Google Trends data would be beneficial in terms of capturing the
information set of decision makers as closely as possible. Then, a proper testing of forecasting
performance of structural exchange rate models can be conducted.
2
It is worth noting that whether we use the real time or revised official data, the lag in the
availability of the official data will always be a problem, the only difference would be that the
revised official data would be available to the market participants even with more lags. Hence, we
suggest to use Google Trends to nowcast exchange rate fundamentals to get a timely picture of the
macro fundamentals so that we can have a fair judgment on the performance of the structural
exchange rate models.
II.
LITERATURE REVIEW
Since the seminal work by (Meese & Rogoff, 1983), studies that re-examine different
currency pairs, different time periods, real time versus revised official macro data, and different
linear structural models have failed to overcome (Meese & Rogoff, 1983) findings. Yet, some
studies such as (Mark, 1995), (Engel et al., 2007), (Gourinchas & Rey, 2007) and (Molodtsova &
Papell, 2009) have found evidence in favor of structural models at short-horizon. But, as shown in
(Rogoff & Stavrakeva, 2008), these findings are not robust to alternative time windows and tests.
On the other hand, studies that seek alternative, mostly non-linear, specifications to overcome
(Meese & Rogoff, 1983) findings have some mixed findings2. While studies such as (Diebold &
Nason, 1990) and (Meese & Rose, 1991) failed to out-perform random walk null with non-linear
or non-parametric specifications, (Wang & Wu, 2012) adopt density forecast criterion for model
comparison and find some promising results in favor of structural models. Yet, the hunt for model
specification or forecast criterion to beat the random walk null will likely continue for quite some
time.
The contribution of this paper is to utilize the internet search data in the literature for
exchange rate disconnect puzzle. In this era of internet, information and telecommunication
technologies, every visited page on the internet and each search query in a search engine are
recorded in tremendous magnitudes. The use of these vast and raw data in the exchange rate
literature is, on the other hand, at its very early stages. There are some recent studies that
incorporate use of Big Data in economic analyses. (Einav & Levin, 2014) use social media
networks data in capturing market inflation expectations. (Lamont, 1997) looked at the frequency
2
(Maasoumi & Bulut, 2012) provide evidence of specification problems for the linear structural models.
3
of appearances of the word “shortage” in print newspapers and found that it contains information
that can be used as a predictor of U.S. inflation. As for Google search data, (Choi & Varian, 2012)
predicted initial claims for unemployment benefits in United States by using Google Trends data.
(Askitas & Zimmermann, 2009) find a strong correlation between index of Google search activity
and unemployment rates using German data. (D’Amuri, 2009) test and find strong evidence on the
empirical relevance of Google search index data on job search query in forecasting unemployment
in Italy. (Suhoy, 2009) utilize the Google query indices for Israel and find evidence that Google
Trends detects inferences about the state of the economy way before the official data releases.
(Koop & Onorante, 2013) check the predictive power of Google Trends probabilities on capturing
major turns and structural changes on the trending behavior of various conventional
macroeconomic variables such as employment, inflation, and production data. Use of Google
Trends data on exchange rate studies, on the other hand, is very limited. (Kristoufek, 2013), the
only paper we are aware-off, look at the relationship between a digital currency, Bitcoin, Google
Trends search queries, and Wikipedia and they found significant connection between search
queries and the value of the Bitcoin. To our knowledge, this paper will be the first one to
incorporate the Google search query index in evaluating forecasting performance of alternative
structural exchange rate models.
III.
DATA AND EMPIRICAL METHODOLOGY
Google Trends Data
The presumption in this paper is that search engines can provide an accurate and timely
information about the state of the economy. As shown in (Elgin, 2004), there is a significant
increase in the percentage of internet users referred by search engines (from 67% in 2001 to 88%
in 2004). Since google.com is the World’s most popular search engine with a market share of 59%
(for Mobile and Tables devices this ratio is 90.8%) as of March 20153, Google Trends data is used
in this paper.
3
Retrieved on March 25, 2015 at https://www.netmarketshare.com/search-engine-marketshare.aspx?qprid=4&qpcustomd=0
4
Google Trends provides a time series index of the volume of internet search queries on
search phrases entered on the Google search engine based on geographic locations and time. The
search query index for a given search phrase is not a nominal query volume in absolute terms,
instead it is an index number from 0 to 100 measured by query share. The normalized search query
index at a given point in time is calculated as the total search volume for each query in a given
geographical location divided by the total number of all search queries in the same location at that
time period. Hence, the index is a relative measurement. If the index number for a specific search
phrase goes down through time, it doesn’t necessarily mean that we have fewer searches for that
phrase. Instead, it is read as there are fewer searches now, as a percent of all searches, than there
were previously.
Let say that we want to nowcast the inflation in the US. Then, we collect Google Trends
data for keywords that are related with inflation in US. As indicated in (Guzman, 2011), search
query data can be considered as a measure of revealed expectations as because, people key in
certain words on the search engines for information they want to learn or for things they have some
concerns. The key point is to find out the certain keywords in native languages that will best
capture the macro fundamentals in the economy. Coming back to our example, to capture inflation
expectations in US, we collect Google Trends data for the search phrase “inflation” for United
States4. When the index number is increasing, we will interpret this as the nation is on average
feeling increasingly anxious about rising average price level in the economy. So, by using the
level of index number, we can capture an indicator that will show the general public’s revealed
expectation about the change in the average price level. One obstacle with search entry data is that,
for any macro fundamental, it is hard to come up with just one single search term that will best
predict the conventional fundamental in the economy. For almost all cases, we will have to analyze
multiple keyword searches, then come up with a common factor that will mimic the conventional
fundamental in the economy. In search for the common or relevant factors, we used maximumlikelihood factor analysis on Google Trends data for variable reduction purposes.
4
In this paper, depending on the availability of country level data for each week, 6-13 search entries were collected
for each macro-fundamental in each country.
5
Structural Models
In this paper, we selected PPP and monetary theories in exchange rate determination
models. The number of the structural models is limited to only two. Uncovered interest parity
model is excluded from the list because there is no information lag on the interest rate data for
countries, hence we do not anticipate any information gain by including the Google search data
for the interest rate in exchange rate forecasting. The Taylor rule based models are also excluded
from the list due to difficulty in finding relevant search entries for these models. The PPP model
is included in the analyses because it is relatively easier to come up with search entries that are
related to inflation in both countries. Likewise we include the Monetary model in the analyses,
since it is relatively easier to find search entries that will proxy key macro fundamentals of the
model such as real income and money demand components.
For each structural model, we run the following regression equation model:
𝑦𝑡 = 𝛼 + 𝛽𝑥𝑡 + 𝜀𝑡
(1)
where 𝑦𝑡 represents the change in the natural logarithm of the nominal spot exchange rate, 𝑥𝑡
stands for the vector of economic fundamentals for each structural model, and 𝜀𝑡 refers to
unexpected shocks to the return on exchange rate series. Exchange rate is defined in terms of US
dollar per one unit of foreign currency hence an increase in 𝑦𝑡 indicates depreciation rate of US
dollar (home country) against the foreign currency. For the PPP model 𝑥𝑡 is equal to real exchange
rate (𝑞𝑡 ). For the Monetary model, we use the simplified version of the monetary theory by
assuming same money demand parameters in each country.
Google Trends-Augmented Structural Models
We include the observations collected from search queries to check for the out-of-sample
forecasting performance gains for both the PPP and Monetary Models. TABLE 1 shows the
selective list of keywords that were collected. Even though the list is in English, in collection of
the data, we gathered data for entries searched for in native language of that country. For countries
with more than one commonly used languages, (i.e., Denmark, Hong Kong, Singapore), we
collected data for entries that are searched in both languages.
6
TABLE 1 shows the list of search entries (in native languages) we use to capture the
movements in macro fundamentals that are related to each structural model. If the public is
concerned over the inflation rate, we expect them to enter keywords such as “Inflation”, “Rate of
Inflation”, “Price Index”, “Consumer Price Index”, and “CPI” in the Google search engine.
Likewise, we use the Google Search entries “Cash”, “Checking Account”, “Debit Card”, “Need
Cash”, “ATM”, “Need Credit”, and “Bank” to capture the money demand in the economy. Search
entries for “Need Job”, “Resume”, “Recruitment Agency”, “Interview”, “Job Vacancy”, “Buy a
Stock”, “Donate”, “Save”, “Restaurant”, “Luxury”, “Invest”, “Vacation” and “Spend Money”
were used the capture the real income and buying power in the economy.
How successful is Google Trends to capture the price movements in the economy? To
better assess the relevancy of the index of Google search query with the actual price movements,
we show the correlation between the price level in the economy and the natural log of the index of
Google search query. TABLE 2 shows that, in absolute terms, the average correlation between the
Google search index and the country’s price level is around 0.5. The range of correlation is in
between -.96 to .97. Canada, Japan, Hong Kong and U.K. have relatively lower average correlation
than the other nations in the sample. It is worth noting that the correlations are between the
currently available index of search entries and the official consumer price index data for the same
period which will be available to the public after a month. In Figure 1, Figure 2, and Figure 3, we
also plot the price level data and the index of Google search query (the query that has the highest
correlation with the price level) on the same graph to check the relation between these two
variables across time. The figures indicate that the most recent indices of search queries track the
price level in the nation at higher precision than earliest periods. It might be due to the fact that
internet penetration rate rises in the sample countries through time. Even though higher searches
for a given term through increasing internet penetration does not necessarily imply a higher query
index, one can claim that the increase in the percentage of population with internet access can help
better pick up nowcasting values of certain macro variables.
Model Specifications
In this paper, for the regression equation in (1), we look at three different specifications of
𝑥𝑡 for the vector of exchange rate fundamentals. In the first specification, we look at the core
7
structural model with only the macroeconomic fundamentals of that model. In the second
specification, we only use the related Google Trends data as the regressor in the exchange rate
equation. Hence, for the PPP model, we only include the Google Trends factor scores that are
related to the PPP fundamentals as the predictors for the exchange rate return series. Likewise, for
the Monetary model, we only include the Google Trends factor scores that are related to the
Monetary model fundamentals. In the third specification, we include the Google Trends factor
scores into the each structural model as additional regressors and call it as Google Trendsaugmented structural model.
TABLE 3 summarizes the three specifications that are adopted for each structural model.
All variables are transformed by taking the natural logarithm multiplied by 100 to have
interpretable coefficients. Home country is US and the spot exchange rate (𝑠𝑡 ) is defined as the
dollar value of one unit of foreign currency, hence an increase in 𝑠𝑡 refers to dollar depreciation.
The real exchange rate (𝑞𝑡 ) is measured as 𝑞𝑡 = 𝑠𝑡 + 𝑝𝑡∗ − 𝑝𝑡 . Price levels in US (𝑝𝑡 ) and in the
foreign country (𝑝𝑡∗ ) are calculated by the monthly CPI indices. M1 is used as a proxy for the
money supply level in US (𝑚𝑡 ) and in the foreign country (𝑚𝑡∗ ). In the absence of data on M1, we
used M2 as an alternative measurement. We used industrial production index (base year is 2010)
𝑃𝑃𝑃
𝑃𝑃𝑃
as a proxy for the total income in US (𝑦𝑡 ) and in the foreign country (𝑦𝑡∗ ). 𝐺𝑇𝑈𝑆
and 𝐺𝑇𝐹𝑂𝑅
refer
to vectors of PPP related Google search factor scores for US and the foreign country, respectively.
𝑀𝑀
𝑀𝑀
Likewise, 𝐺𝑇𝑈𝑆
and 𝐺𝑇𝐹𝑂𝑅
indicate the Monetary model related Google search factor scores for
US and the foreign country, respectively. Since we have collected 15-20 Google search entries
for each country, when entering the Google Trends data into the analysis, we implement factor
analysis on Google Trends series and only include the factor scores extracted from these analyses.
Model Comparison
As for model comparison in exchange rate determination models, the conventional point
forecast criterion is applied. In this criterion, the model comparison is done by out-of-sample
approach that compares the mean squared prediction error (MSPE) implied by the structural model
with the one implied by the benchmark random walk model. By dividing the sample into training
and forecasting sub-samples, the out-of-sample forecasts are calculated with rolling regression
method. Out of 125 monthly observations, the size of the training sample is set to 60 to produce
65 out-of-sample forecasts. Specifically, the data from January 2004 to January 2009 is used to
get the first out-of-sample forecast of exchange rate returns for February 2009. In other words,
8
𝛼̂ 𝑎𝑛𝑑 𝛽̂ , the standard OLS estimate of (1) are derived from the first 60 observations. Then, the
realized values of economic fundamentals are employed to produce the out-of-sample forecast for
the following month. Then, the data in the training sample is rolled by one month: the first
observation is dropped from the sample and February 2009 observations are added to produce the
second out-of-sample forecast for the next month. This procedure is repeated until all the available
data in the forecasting sub-sample is exhausted.
As for model comparison, MSPE measured from out-of-sample forecasts of the structural
model is compared with the one produced by the benchmark model and for statistical significance,
we used the test for equal predictability of a structural model and a martingale difference model
proposed by (Clark & West, 2006, 2007) (CW test, henceforth). In this approach of point forecast
accuracy testing, a loss differential function (𝑑𝑡 ) is defined as the difference between the squared
prediction error from the structural model i (𝑆𝑃𝐸𝑖 ) and the one from benchmark model (𝑆𝑃𝐸𝑏 ).
Then, the equal predictive accuracy is tested by checking whether the population mean of 𝑑𝑡 is
zero or not. Under the null, we have the following:
𝐻0 = 𝐸[𝑑𝑡 ] = 𝐸[𝑆𝑃𝐸𝑏 − 𝑆𝑃𝐸𝑖 ] = 0.
(2)
The CW test controls for the fact that under the null, MSPE of the structural model and the
benchmark model’s MSPE are not same as they are nested models. Hence, as suggested in (Clark
& West, 2006), we use the following adjusted loss differential function (𝑑̃ ):
2
𝑑̃ = 𝑆𝑃𝐸𝑏 − 𝑆𝑃𝐸𝑖 − 𝑎𝑑𝑗 = 𝑆𝑃𝐸𝑏 − 𝑆𝑃𝐸𝑖 − (𝑦̂ 𝑏 − 𝑦̂ 𝑖 ) .
(3)
Since the competing models are nested, when the null of random walk movements in
exchange rates is true, the structural model will produce a noise. Hence, under the null, the MSPE
of the structural model will be higher by construction. Therefore, the CW test statistics adjusts for
this biasness. (Clark & West, 2006) show that the adjusted test statistics, 𝑑̃ , is distributed normally
with mean-zero. In testing the point forecast accuracy, the CW test statistics takes the following
form:
𝐶𝑊 =
𝑑̃
𝑎𝑣𝑎𝑟
̂ (𝑑̃)1/2
.
(4)
9
A statistically significant positive CW test statistics is read as better performing structural model i
over the benchmark model b.
IV.
EMPIRICAL FINDINGS
TABLE 4 shows the CW test statistics and corresponding p-values for the out-of-sample
forecasts comparison of PPP model against the driftless random walk null. The first column uses
real exchange rate as the only macroeconomic fundamental to predict the changes in logged
exchange rate series. In 6 out of 11 currency pairs, the PPP model can beat the null of driftless
random walk model at statistically significant levels. As shown in the second column, if we use
only the PPP-related Google search factor scores as the predictor for exchange rate returns, we
find that Google Trends data can perform better, out-of-sample, for Japan, Singapore, and Sweden.
On the other hand, when we use Google Trends factor scores along with the PPP fundamental in
the augmented model, we find statistically significant better out-of-sample forecasts for all
countries but Hong-Kong and United Kingdom. It is worth mentioning that the predictive power
of PPP model (the value of the CW test statistics and the corresponding p-values) has improved
significantly after the inclusion of Google Trends factor scores into the model. Besides, with the
inclusion of Google Trends factor scores, we can now provide evidence in favor of the PPP model
against the driftless random walk for Israel, Sweden, and Switzerland.
The role of index of Google search query is even more obvious when we use the random
walk with a drift as the benchmark model. As shown in TABLE 5, PPP fundamental can beat the
random walk with a drift null in 2 out of 11 countries. Google Trends, on the other hand, provides
more evidence against the null, shown in the 2nd column. With the inclusion of the Google Trends
factor scores to the PPP fundamentals, shown in the third column, the number of countries with
better performing out-of-sample forecasts increases to 9. Only for Hong Kong and UK, the Google
Trends-augmented PPP model fails to outperform the null.
As for Monetary model, the nowcasts of the fundamentals derived from Google search
query indices provide significant forecast performance gain over the official data on Monetary
model fundamentals. As shown in the first column of TABLE 6, when the null is a driftless random
10
walk, Monetary model can beat the null, out-of-sample, only for Japan. But, after the inclusion of
Monetary model related Google Trends factor scores into the model, shown in the third column,
beside Japan, we get evidence in favor of the Google Trends-augmented Monetary model for
Australia, Canada and Singapore. This is a significant gain.
Finally, when we use the random walk with a drift model as our benchmark, shown in
TABLE 7, we get evidence of better performing Google Trends-augmented monetary model over
the null in 5 out of 11 countries while this number was just one when we use only the Monetary
model fundamentals.
To sum up, the results indicate that inclusion of Google Trends-based nowcasting values
of macro fundamentals to the current set of official-data based macro fundamentals improve the
out-of-sample forecast of the PPP and Monetary models over the null of random walk with drift
and without a drift. These significant performance gains deserve careful attention on the use of
official data in the literature on exchange rate disconnect puzzle. In this paper we claim that, for
proper testing of the structural models, since there is a lag in the release of official data on macro
fundamentals, the literature should focus more on using ex ante variables on current macro
fundamentals and nowcasting of these variables with utilization of Google search inquiries can be
one alternative for this purpose.
In this paper, we only use the factor scores derived from Google Search query indices. It
would be interesting to search for specific search entries that are contemporaneously correlated
with macro fundamentals. Google Correlate function can be utilized for this purpose. Google
Correlate provides the hundred most correlated search terms with any user-provided data. Then,
with some variable selection mechanism such as stepwise regression or LASSO, one can get search
entries that are mostly correlated for any macro-fundamentals, then use it in exchange rate
forecasting. We will leave this exercise to future studies.
11
V.
CONCLUSION
This paper can be the first one to incorporate the Google Trends data to assess the
forecasting performance of alternative exchange rate models against the random walk null. The
findings necessitate further investigation as Google Trends-augmented structural models perform
better in out-of-sample forecasting against the random walk null. This study focuses only two
structural exchange rate models but further studies are needed to check the findings for other
currency pairs and more sophisticated structural exchange rate models.
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VI.
REFERENCES
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14
TABLE 1
Google Search Queries
PPP model
Monetary model
Inflation, Rate of Inflation, Price Index,
Cash, Checking Account, Debit Card, Need
Consumer Price Index, CPI, Cost of
Cash, ATM, Need Credit, Bank, Need Job,
Living, Rising Prices, Falling Prices,
Resume, Recruitment Agency, Interview, Job
Deflation, Retail Price Index, Current
Vacancy,
Inflation, Expensive, Cheapest, Cost,
Restaurant, Luxury, Invest, Vacation, Spend
Competitiveness, Exchange Rate.
Money.
Buy
a
Stock,
Donate,
Save,
Notes: The table shows the common Google search entries that are employed to nowcast the macro fundamentals
of each structural model. The full list of each search query in native languages of each country is provided at the
appendix.
15
TABLE 2
Correlation Coefficients
Price Level vs. Google Search Query
Abs. Mean
Min
Max
Australia
0.58
-0.53
0.92
Canada
0.43
-0.74
0.79
Denmark
0.56
-0.03
0.86
Euro Area
0.55
-0.96
0.97
Hong Kong
0.47
-0.50
0.85
Israel
0.78
0.64
0.89
Japan
0.13
-0.12
0.58
Singapore
0.51
-0.21
0.87
Sweden
0.70
0.38
0.88
Switzerland
0.62
-0.81
0.85
UK
0.47
-0.90
0.67
United States
0.64
-0.91
0.65
Note: The table shows the absolute value of the mean, the minimum and the
maximum correlations between the price level and index of Google Search
queries (measured in natural log) used for PPP model in each country. The list of
all search queries is provided at the appendix.
16
TABLE 3
Model Specifications
Models
Set of Regressors
(1)
𝑃𝑃𝑃
(2)
𝐺𝑇 𝑃𝑃𝑃
(3)
𝑃𝑃𝑃 + 𝐺𝑇 𝑃𝑃𝑃
(4)
𝑀𝑀
(5)
𝐺𝑇 𝑀𝑀
(6)
𝑀𝑀 + 𝐺𝑇 𝑀𝑀
𝑥𝑡 = 𝑞𝑡
𝑃𝑃𝑃
𝑃𝑃𝑃
𝑥𝑡 = {𝐺𝑇𝑈𝑆
, 𝐺𝑇𝐹𝑂𝑅
}
𝑃𝑃𝑃
𝑃𝑃𝑃
𝑥𝑡 = {𝑞𝑡 , 𝐺𝑇𝑈𝑆
, 𝐺𝑇𝐹𝑂𝑅
}
𝑥𝑡 = {(𝑚𝑡 − 𝑚𝑡∗ ), (𝑦𝑡 − 𝑦𝑡∗ ), 𝑠𝑡 }
𝑀𝑀
𝑀𝑀
𝑥𝑡 = {𝐺𝑇𝑈𝑆
, 𝐺𝑇𝐹𝑂𝑅
}
𝑀𝑀
𝑀𝑀
𝑥𝑡 = {(𝑚𝑡 − 𝑚𝑡∗ ), (𝑦𝑡 − 𝑦𝑡∗ ), 𝑠𝑡 , 𝐺𝑇𝑈𝑆
, 𝐺𝑇𝐹𝑂𝑅
}
Notes: The table shows the list of regressors for each model specification. The definition for each variable is
provided in the text. All macro fundamentals are measures in natural logarithm multiplied by 100. Factor analysis
is used to get the factor scores of natural logarithm of the Google Trends data. Model specifications (3) and (6)
refer to Google Trends-augmented PPP and MM models, respectively.
17
TABLE 4
PPP Model against the null of driftless Random Walk
Australia
Canada
PPP
1.590
GTFA PPP+GTFA
1.043 1.845
(0.058)
(0.150) (0.035)
1.341
(0.092)
Denmark
1.578
(0.060)
Euro Area
Hong Kong
Israel
1.618
UK
0.783 1.733
-0.992 -0.265
(0.672)
(0.838) (0.604)
0.890
1.408
1.405
0.442
(0.330)
Switzerland
(0.539) (0.048)
-0.447
(0.082)
Sweden
-0.098 1.691
(0.218) (0.044)
(0.082)
Singapore
(0.104) (0.006)
(0.055)
(0.188)
Japan
1.269 2.613
1.160
0.073 1.376
(0.471) (0.087)
1.731 2.768
(0.044) (0.004)
2.107 2.360
(0.019) (0.011)
1.353 2.005
(0.090) (0.025)
0.293 1.947
(0.125)
(0.385) (0.028)
-0.344
0.784 0.742
(0.634)
(0.218) (0.231)
Notes: The table shows the CW test statistics (p-values are in the second rows) for the
OLS out-of-sample forecasts of exchange rate returns under the null of driftless random
walk. PPP stands for Purchasing Power Parity Model. GFTA stands for Google Trends
factor scores. We use rolling window regression with a window of 60 observations. 1 st,
2nd, and 3rd columns stand for the model specifications (1), (2), and (3) of TABLE 3,
respectively.
18
TABLE 5
PPP Model against the null of Random Walk with drift
Australia
Canada
PPP
0.830
GTFA PPP+GTFA
0.547 1.567
(0.205)
(0.293) (0.061)
0.498
(0.310)
Denmark
1.462
(0.074)
Euro Area
Hong Kong
Israel
1.557
Singapore
Sweden
UK
0.585 1.764
(0.280) (0.041)
0.641 1.641
(0.262) (0.053)
-0.241
-1.017 -0.261
(0.595)
(0.844) (0.6030
0.842
1.235
0.517 1.334
(0.303) (0.093)
2.111 2.800
(0.111)
(0.019) (0.003)
-0.601
1.054 1.388
(0.725)
(0.148) (0.085)
0.335
(0.369)
Switzerland
(0.275) (0.014)
(0.062)
(0.201)
Japan
0.600 2.253
0.792
1.354 2.033
(0.090) (0.023)
0.049 2.273
(0.216)
(0.480) (0.013)
-0.795
1.457 1.154
(0.785)
(0.075) (0.126)
Notes: The table shows the CW test statistics (p-values are in the second rows) for
the OLS out-of-sample forecasts of exchange rate returns under the null of random
walk with a drift. PPP stands for Purchasing Power Parity Model. GFTA stands for
Google Trends factor scores. We use rolling window regressions with a window of
60 observations. 1st, 2nd, and 3rd columns stand for the model specifications (1), (2),
and (3) of TABLE 3, respectively.
19
TABLE 6
Monetary Model (MM) against the null of driftless Random Walk
MM
GTFA
MM+GTFA
0.512
2.037
1.861
Australia
(0.305)
(0.023)
(0.034)
Canada
Denmark
Euro Area
Hong Kong
Israel
Japan
Singapore
Sweden
Switzerland
UK
0.224
1.467
1.798
(0.412)
(0.074)
(0.038)
-0.013
0.499
0.241
(0.505)
(0.310)
(0.405)
-0.810
-0.653
-0.688
(0.789)
(0.742)
(0.753)
-0.614
-0.129
0.425
(0.729)
(0.551)
(0.336)
-0.164
-0.512
1.204
(0.565)
(0.695)
(0.116)
2.289
0.777
2.595
(0.013)
(0.220)
(0.006)
1.122
2.548
2.664
(0.133)
(0.007)
(0.005)
-0.149
0.247
0.634
(0.559)
(0.403)
(0.264)
0.755
-0.062
0.032
(0.226)
(0.525)
(0.487)
-0.377
-0.599
-0.861
(0.646)
(0.725)
(0.804)
Notes: The table shows the CW test statistics (p-values are in the second rows) for the
OLS out-of-sample forecasts of exchange rate returns under the null of driftless random.
MM stands for Monetary model. GFTA stands for Google Trends factor scores. We use
rolling window regressions with a window of 60 observations. 1 st, 2nd, and 3rd columns
stand for the model specifications (4), (5), and (6) of TABLE 3, respectively.
20
TABLE 7
Monetary Model (MM) against the null of Random Walk with a drift
Australia
Canada
Denmark
Euro Area
Hong Kong
Israel
Japan
Singapore
Sweden
MM
GTFA
MM+GTFA
-0.227
1.763 1.333
(0.589)
(0.041) (0.094)
-0.519
1.130 1.375
(0.697)
(0.131) (0.087)
0.081
(0.468)
(0.350) (0.457)
-1.106
-1.302 -1.419
(0.864)
(0.901) (0.920)
0.052
(0.590) (0.332)
-0.704
0.016 1.477
(0.758)
(0.494) (0.072)
1.932
0.858 2.389
(0.029)
(0.197) (0.010)
-0.980
1.526 1.672
(0.835)
(0.066) (0.050)
0.094
1.269
(0.105)
UK
-0.229 0.437
(0.479)
(0.463)
Switzerland
0.386 0.108
0.958
(0.171)
0.638 0.430
(0.263) (0.334)
-0.462 0.035
(0.677) (0.486)
-1.279 -1.463
(0.897) (0.926)
Notes: The table shows the CW test statistics (p-values are in the second rows)
for the OLS out-of-sample forecasts of exchange rate returns under the null of
random walk with a drift. MM stands for Monetary model. GFTA stands for
Google Trends factor scores. We use rolling window regressions with a
window of 60 observations. 1st, 2nd, and 3rd columns stand for the model
specifications (4), (5), and (6) of TABLE 3, respectively.
21
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