## Tourism forecasts for The Bahamas using Google Trends (2004–2018)

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---

### Introduction
- Tourism contributes about 48 percent of GDP and 56 percent of employment in The Bahamas; projected to reach 60 percent of GDP and 70 percent of the workforce by 2030.
- Tourist arrivals to The Bahamas increased by 9.8 percent over the past decade, reaching over 6.5 million visitors (including cruise passengers) in 2018; about 80 percent of visitors come from the U.S.
- Objective: develop an econometric model of monthly tourist arrivals to The Bahamas from the U.S. (January 2004–December 2018) using Google Trends data and assess forecasting accuracy versus a benchmark ARIMA model.
- Key finding preview: Google Trends-augmented forecast models perform significantly better than traditional time-series models, improving predictability of tourist arrivals by about 30 percent relative to the benchmark ARIMA model.

### Related literature
- Two strands covered:
  - Determinants of international tourism flows.
  - Use of Google search data to improve economic and financial forecasts.
- Prior findings summarized:
  - Developed countries show higher income and real exchange rate elasticities for tourism; small island countries tend to be less sensitive (Zhang, Song, and Huang (2009); Culiuc (2014)).
  - Caribbean tourism sensitive to source-market income and price factors, but high-end destinations like The Bahamas less so (Wolfe and Romeu (2011); Laframboise and others (2014)).
  - Internet search data has been useful for forecasting unemployment, consumption, housing, vehicle purchases, movie admissions, investor appetite, crude oil prices, and tourism flows in multiple country studies (Choi and Varian; Vosen and Schmidt; Carrière-Swallow and Labbé; Bangwayo-Skeete and Skeete; Rivera; Yang and others).
- This study extends time-series tourism demand models with Google Trends to test predictive power for The Bahamas.

### Data overview
- Sample: monthly data January 2004–December 2018.
- Tourist arrivals data: Ministry of Tourism; stop-over tourists arriving via air from the U.S. amount to 1.63 million (or about 25 percent of total) in 2018.
- Macroeconomic covariates:
  - Personal income in the U.S.: Haver Analytics.
  - Real effective exchange rate (REER): IMF World Economic Outlook database.
- Google Trends:
  - Country-specific, high-frequency index normalized 0–100; Google accounts for over 90 percent of search activity.
  - Google Trends data collected daily over a 30-day period and averaged to minimize sampling measurement error.
  - Selected search term: “The Bahamas travel” (most relevant among tested keywords).
- Seasonality and stationarity:
  - All series seasonally adjusted using X-13ARIMA-SEATS.
  - ADF and PP tests indicate variables are stationary after logarithmic transformation.
- Descriptive statistics (180 observations):
  - Tourist arrivals from the U.S.: Mean 96,670; Std Dev 29,721; Min 25,541; Max 159,441.
  - Personal income in the U.S.: Mean 13,590; Std Dev 2,230; Min 9,737; Max 18,017.
  - REER: Mean 101.6; Std Dev 5.58; Min 89.5; Max 112.7.
  - Google Trends: Mean 51.5; Std Dev 13.1; Min 32.0; Max 100.0.

### Empirical methodology
- Benchmark univariate ARIMA specification (selected ARMA(1,1) by AIC):
  - log(A_t,c) = α + sum_{i=1}^{12} β_i log(A_{t−i,c}) + ε_t
- Extended model with exogenous macro variables:
  - Adds monthly personal income (U.S.) and REER (Bahamas) as log(X_{t−i,c}) lags.
- Internet search activity-augmented model:
  - Adds log(G_{t−i,c}) for Google Trends related to travel to The Bahamas.
- Lag selection:
  - Personal income and REER best contemporaneous.
  - Google Trends best at lag order of 2 months.
- Note: objective is prediction, not causal identification.

### Estimation results (selected coefficients and fit)
- Model specifications:
  - Model 1: ARIMA (benchmark)
  - Model 2: ARIMA with Income
  - Model 3: ARIMA with Income & REER
  - Model 4: ARIMA with Income, REER & Google
- Key coefficient estimates (Model 4 in brackets where provided):
  - Google Trends: 0.14*** [0.055]
  - Personal Income (U.S.): 0.24 [0.170]
  - REER (Bahamas): -0.20 [0.376]
  - AR(1): 0.95*** [0.050]
  - MA(1): -0.76*** [0.084]
- Model fit indicators:
  - Adjusted R^2: Model 1 = 0.31; Model 4 = 0.33.
  - AIC for Model 4 = -1.953; SIC for Model 4 = -1.828.
- Interpretation:
  - Personal income and REER have expected signs but are statistically insignificant at conventional levels in the full specification.
  - Google Trends coefficient positive and statistically significant, improving in-sample fit—online searches in the U.S. provide additional predictive information beyond historical arrivals and macro variables.
  - High persistence in arrivals indicated by AR(1) = 0.95***.

### Forecast evaluation (out-of-sample performance: 2018 holdout)
- Forecast accuracy metrics used: MAE, RMSE, Theil I Inequality Coefficient (U-Theil).
- Out-of-sample metrics (Models 1–4; estimation January 2004–December 2017, test on final 12 months covering 2018):
  - Model 1 (ARIMA): MAE 0.04787; RMSE 0.06385; Theil 0.00277
  - Model 2 (with Income): MAE 0.04148; RMSE 0.05556; Theil 0.00241
  - Model 3 (with Income & REER): MAE 0.04213; RMSE 0.05673; Theil 0.00246
  - Model 4 (with Income, REER & Google): MAE 0.03261; RMSE 0.04543; Theil 0.00197
- Percent improvement compared to benchmark Model 1:
  - Model 2: MAE 13.3; RMSE 13.0; Theil 13.0
  - Model 3: MAE 12.0; RMSE 11.2; Theil 11.2
  - Model 4: MAE 31.9; RMSE 28.8; Theil 28.9
- VAR model results (lag length p = 4 by AIC) — comparison summary:
  - Baseline VAR (Model 1): Adjusted R^2 0.30157; RMSE 0.10794; Theil 0.00470
  - VAR with Income & REER (Model 2): Adjusted R^2 0.30240; RMSE 0.10776; Theil 0.00470
  - VAR with Income, REER & Google (Model 3): Adjusted R^2 0.35008; RMSE 0.09712; Theil 0.00423
  - Percent improvement for Google-augmented VAR versus benchmark: Adjusted R^2 16.1; RMSE 10.0; Theil 10.0
- Summary of forecast evaluation:
  - The model augmented with Google Trends (Model 4) improves forecast accuracy by about 30 percent compared to the benchmark ARIMA (Model 1) and by more than 20 percent compared to the model extended only with macro variables (Model 3).
  - VAR results corroborate greater forecast superiority when Google Trends are included (boosting adjusted R^2 by more than 16 percent and lowering RMSE and Theil by 10 percent).

### Conclusion and policy implications
- Main conclusion: incorporating Google Trends online search data significantly improves forecasting of monthly tourist arrivals to The Bahamas from the U.S. for 2004–2018.
- Practical implications:
  - Internet search data can aid real-time surveillance and provide more reliable forecasts of tourism activity.
  - Policymakers and private firms in the tourism industry would benefit from internet search data-augmented forecast models for better planning and investment.
- Additional notes:
  - High degree of persistence in arrivals from the U.S. (statistically significant autoregressive lags).
  - Personal income and REER effects have expected signs but are not statistically significant in this sample—consistent with The Bahamas as a high-end destination.
  - Cumulative change in the REER amounted to 3.7 percent between 2004 and 2018.

### Appendix: Figures, unit-root tests, and correlations
- Figures plotted:
  - Seasonally adjusted and unadjusted Tourist Arrivals (series showing values up to 180000 with monthly markers from 004-01 through 018-07).
  - Seasonally adjusted and unadjusted Google Trends (index plotted from 0 to 120 with monthly markers from 004-01 through 018-07).
- Unit Root Tests (ADF and PP) — selected statistics (all variables in logs and seasonally adjusted):
  - Tourist arrivals: Levels Intercept -9.72**; Levels Intercept & Trend -11.97***; First differences Intercept -28.17***; First differences Intercept & Trend -28.11***; (additional reported values include Levels Intercept -10.27***, Levels Intercept & Trend -10.32***, First differences Intercept -52.68***, First differences Intercept & Trend -57.91***).
  - Personal income: Levels Intercept -2.05; Levels Intercept & Trend -5.47***; First differences Intercept -16.18***; First differences Intercept & Trend -16.43***; (additional values include Levels Intercept -0.91, Levels Intercept & Trend -2.63*, First differences Intercept -15.24***, First differences Intercept & Trend -15.22***).
  - REER: Levels Intercept -4.35**; Levels Intercept & Trend -4.38**; First differences Intercept -10.34***; First differences Intercept & Trend -10.34***; (additional values include Levels Intercept -2.05**, Levels Intercept & Trend -2.84**, First differences Intercept -9.26***, First differences Intercept & Trend -9.29***).
  - Google Trends: Levels Intercept -7.13***; Levels Intercept & Trend -9.35***; First differences Intercept -26.55***; First differences Intercept & Trend -26.68***; (additional values include Levels Intercept -5.42***, Levels Intercept & Trend -9.45***, First differences Intercept -49.29***, First differences Intercept & Trend -73.45***).
- Correlation between search terms and tourist arrivals (ADF lag table) — selected correlations:
  - Lag 0: The Bahamas 0.26; The Bahamas Travel 0.34; The Bahamas Beach 0.40; The Bahamas Hotels 0.28; The Bahamas Resorts 0.12; The Bahamas Flights 0.20.
  - Lag 1: The Bahamas 0.40; The Bahamas Travel 0.47; The Bahamas Beach 0.46; The Bahamas Hotels 0.45; The Bahamas Resorts 0.24; The Bahamas Flights 0.25.
  - Lag 2: The Bahamas 0.43; The Bahamas Travel 0.47; The Bahamas Beach 0.44; The Bahamas Hotels 0.44; The Bahamas Resorts 0.33; The Bahamas Flights 0.25.
  - Lags 3–5 show smaller correlations (e.g., Lag 3 The Bahamas Travel 0.24; Lag 4 The Bahamas Beach 0.05; Lag 5 The Bahamas Beach -0.04).
- Notes:
  - ADF and PP statistics indicate rejection of unit roots in first differences for the listed series.
  - Google Trends series show strong stationarity test statistics in both levels and first differences.
  - Correlation table shows the highest contemporaneous associations (Lag 0–2) between Google search terms "The Bahamas", "The Bahamas Travel", "The Bahamas Beach", and tourist arrivals.

*Source: IMF working paper content (I. INTRODUCTION – V. CONCLUSION, wpiea2020022-print-pdf).*

### References .............................................................................................................

### Tourism forecasts for The Bahamas using Google Trends (2004–2018)

### Introduction
- Tourism contributes about 48 percent of GDP and 56 percent of employment in The Bahamas; projected to reach 60 percent of GDP and 70 percent of the workforce by 2030.
- Tourist arrivals to The Bahamas increased by 9.8 percent over the past decade, reaching over 6.5 million visitors (including cruise passengers) in 2018; about 80 percent of visitors come from the U.S.
- Objective: develop an econometric model of monthly tourist arrivals to The Bahamas from the U.S. (January 2004–December 2018) using Google Trends data and assess forecasting accuracy versus a benchmark ARIMA model.
- Key finding preview: Google Trends-augmented forecast models perform significantly better than traditional time-series models, improving predictability of tourist arrivals by about 30 percent relative to the benchmark ARIMA model.

### Related literature
- Two strands: determinants of international tourism flows; use of Google search data to improve economic and financial forecasts.
- Prior findings summarized:
  - Developed countries show higher income and real exchange rate elasticities for tourism; small island countries tend to be less sensitive (Zhang, Song, and Huang (2009); Culiuc (2014)).
  - Caribbean tourism sensitive to source-market income and price factors, but high-end destinations like The Bahamas less so (Wolfe and Romeu (2011); Laframboise and others (2014)).
  - Internet search data has been useful for forecasting unemployment, consumption, housing, vehicle purchases, movie admissions, investor appetite, crude oil prices, and tourism flows in multiple country studies (Choi and Varian; Vosen and Schmidt; Carrière-Swallow and Labbé; Bangwayo-Skeete and Skeete; Rivera; Yang and others).
- This study extends time-series tourism demand models with Google Trends to test predictive power for The Bahamas.

### Data overview
- Sample: monthly data January 2004–December 2018.
- Tourist arrivals data: Ministry of Tourism; stop-over tourists arriving via air from the U.S. amount to 1.63 million (or about 25 percent of total) in 2018.
- Macroeconomic covariates:
  - Personal income in the U.S.: Haver Analytics.
  - Real effective exchange rate (REER): IMF World Economic Outlook database.
- Google Trends:
  - Country-specific, high-frequency index normalized 0–100; Google accounts for over 90 percent of search activity.
  - Google Trends data collected daily over a 30-day period and averaged to minimize sampling measurement error.
  - Selected search term: “The Bahamas travel” (most relevant among tested keywords).
- Seasonality and stationarity:
  - All series seasonally adjusted using X-13ARIMA-SEATS.
  - ADF and PP tests indicate variables are stationary after logarithmic transformation.
- Descriptive statistics (180 observations):
  - Tourist arrivals from the U.S.: Mean 96,670; Std Dev 29,721; Min 25,541; Max 159,441.
  - Personal income in the U.S.: Mean 13,590; Std Dev 2,230; Min 9,737; Max 18,017.
  - REER: Mean 101.6; Std Dev 5.58; Min 89.5; Max 112.7.
  - Google Trends: Mean 51.5; Std Dev 13.1; Min 32.0; Max 100.0.

### Empirical methodology
- Benchmark univariate ARIMA specification (selected ARMA(1,1) by AIC):
  - log(A_t,c) = α + sum_{i=1}^{12} β_i log(A_{t−i,c}) + ε_t
- Extended model with exogenous macro variables:
  - adds monthly personal income (U.S.) and REER (Bahamas) as log(X_{t−i,c}) lags.
- Internet search activity-augmented model:
  - adds log(G_{t−i,c}) for Google Trends related to travel to The Bahamas.
- Lag selection:
  - Personal income and REER best contemporaneous.
  - Google Trends best at lag order of 2 months.
- Note: objective is prediction, not causal identification.

### Estimation results (selected coefficients and fit)
- Model specifications shown (Models 1–4):
  - Model 1: ARIMA (benchmark)
  - Model 2: ARIMA with Income
  - Model 3: ARIMA with Income & REER
  - Model 4: ARIMA with Income, REER & Google
- Key coefficient estimates (Model 4 in brackets where provided):
  - Google Trends: 0.14*** [0.055]
  - Personal Income (U.S.): 0.24 [0.170] (positive but not statistically significant in Model 4)
  - REER (Bahamas): -0.20 [0.376] (negative but not statistically significant in Model 3/4)
  - AR(1): 0.95*** [0.050] (high persistence)
  - MA(1): -0.76*** [0.084]
- Model fit indicators:
  - Adjusted R^2: Model 1 = 0.31; Model 4 = 0.33.
  - AIC and SIC reported for models; AIC for Model 4 = -1.953; SIC = -1.828.
- Interpretation:
  - Personal income and REER have expected signs but are statistically insignificant at conventional levels.
  - Google Trends coefficient positive and statistically significant, improving in-sample fit—online searches in the U.S. provide additional predictive information beyond historical arrivals and macro variables.

### Forecast evaluation (out-of-sample performance: 2018 holdout)
- Forecast accuracy metrics used: MAE, RMSE, Theil I Inequality Coefficient (U-Theil).
- Definitions provided for MAE, RMSE, U-Theil as equations (5), (6), (7).
- Out-of-sample metrics (Models 1–4; based on January 2004–December 2017 estimation, test on final 12 months covering 2018):
  - Model 1 (ARIMA): MAE 0.04787; RMSE 0.06385; Theil 0.00277
  - Model 2 (with Income): MAE 0.04148; RMSE 0.05556; Theil 0.00241
  - Model 3 (with Income & REER): MAE 0.04213; RMSE 0.05673; Theil 0.00246
  - Model 4 (with Income, REER & Google): MAE 0.03261; RMSE 0.04543; Theil 0.00197
- Percent improvement compared to benchmark Model 1:
  - Model 2: MAE 13.3; RMSE 13.0; Theil 13.0
  - Model 3: MAE 12.0; RMSE 11.2; Theil 11.2
  - Model 4: MAE 31.9; RMSE 28.8; Theil 28.9
- VAR model results (lag length p = 4 by AIC) — comparison summary:
  - Baseline VAR (Model 1): Adjusted R^2 0.30157; RMSE 0.10794; Theil 0.00470
  - VAR with Income & REER (Model 2): Adjusted R^2 0.30240; RMSE 0.10776; Theil 0.00470
  - VAR with Income, REER & Google (Model 3): Adjusted R^2 0.35008; RMSE 0.09712; Theil 0.00423
  - Percent improvement for Google-augmented VAR versus benchmark: Adjusted R^2 16.1; RMSE 10.0; Theil 10.0
- Summary:
  - The model augmented with Google Trends (Model 4) improves forecast accuracy by about 30 percent compared to the benchmark ARIMA (Model 1) and by more than 20 percent compared to the model extended only with macro variables (Model 3).
  - VAR results corroborate greater forecast superiority when Google Trends are included (boosting adjusted R^2 by more than 16 percent and lowering RMSE and Theil by 10 percent).

### Conclusion and policy implications
- Main conclusion: incorporating Google Trends online search data significantly improves forecasting of monthly tourist arrivals to The Bahamas from the U.S. for 2004–2018.
- Practical implications:
  - Internet search data can aid real-time surveillance and provide more reliable forecasts of tourism activity.
  - Policymakers and private firms in the tourism industry would benefit from internet search data-augmented forecast models for better planning and investment.
- Additional notes:
  - High degree of persistence in arrivals from the U.S. (statistically significant autoregressive lags).
  - Personal income and REER effects have expected signs but are not statistically significant in this sample—consistent with The Bahamas as a high-end destination.
  - Cumulative change in the REER amounted to 3.7 percent between 2004 and 2018.

*Source: IMF working paper content (I. INTRODUCTION – V. CONCLUSION, wpiea2020022-print-pdf).*

### Appendix Figure 1. Seasonally-Adjusted and Unadjusted Data

### Appendix Figure 1. Seasonally-Adjusted and Unadjusted Data

### Figures
- Seasonally adjusted and unadjusted series plotted for:
  - Tourist Arrivals (series showing values up to 180000 with monthly markers from 004-01 through 018-07). Legend: "Seasonally adjusted" and "Unadjusted".
  - Google Trends (index plotted from 0 to 120 with monthly markers from 004-01 through 018-07). Legend: "Seasonally adjusted" and "Unadjusted".
- Source: Google Trends; Ministry of Tourism; author’s calculations.

### Unit Root Tests (ADF and PP)
- Variables: All variables are in logs and seasonally adjusted.
- Test frameworks shown: ADF and PP; results reported for "Levels" and "First differences" with specifications "Intercept" and "Intercept & Trend".
- ADF and PP test statistics reported (rows correspond to series; columns correspond to Levels and First differences under Intercept and Intercept & Trend):

  - Tourist arrivals
    - Levels Intercept: -9.72**
    - Levels Intercept & Trend: -11.97***
    - First differences Intercept: -28.17***
    - First differences Intercept & Trend: -28.11***
    - (Additional columns repeated) Levels Intercept: -10.27***
    - Levels Intercept & Trend: -10.32***
    - First differences Intercept: -52.68***
    - First differences Intercept & Trend: -57.91***

  - Personal income
    - Levels Intercept: -2.05
    - Levels Intercept & Trend: -5.47***
    - First differences Intercept: -16.18***
    - First differences Intercept & Trend: -16.43***
    - (Additional columns repeated) Levels Intercept: -0.91
    - Levels Intercept & Trend: -2.63*
    - First differences Intercept: -15.24***
    - First differences Intercept & Trend: -15.22***

  - REER
    - Levels Intercept: -4.35**
    - Levels Intercept & Trend: -4.38**
    - First differences Intercept: -10.34***
    - First differences Intercept & Trend: -10.34***
    - (Additional columns repeated) Levels Intercept: -2.05**
    - Levels Intercept & Trend: -2.84**
    - First differences Intercept: -9.26***
    - First differences Intercept & Trend: -9.29***

  - Google Trends
    - Levels Intercept: -7.13***
    - Levels Intercept & Trend: -9.35***
    - First differences Intercept: -26.55***
    - First differences Intercept & Trend: -26.68***
    - (Additional columns repeated) Levels Intercept: -5.42***
    - Levels Intercept & Trend: -9.45***
    - First differences Intercept: -49.29***
    - First differences Intercept & Trend: -73.45***

- Significance notation: *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.
- Note: "Levels" and "First differences" labelling appears for both ADF and PP panels. Source: Author's estimations.

### Correlation Between Search Terms and Tourist Arrivals (ADF Lag table)
- Series/columns: The Bahamas, The Bahamas Travel, The Bahamas Beach, The Bahamas Hotels, The Bahamas Resorts, The Bahamas Flights.
- Lag (months) rows and reported values:

  - Lag 0:
    - The Bahamas: 0.26
    - The Bahamas Travel: 0.34
    - The Bahamas Beach: 0.40
    - The Bahamas Hotels: 0.28
    - The Bahamas Resorts: 0.12
    - The Bahamas Flights: 0.20

  - Lag 1:
    - The Bahamas: 0.40
    - The Bahamas Travel: 0.47
    - The Bahamas Beach: 0.46
    - The Bahamas Hotels: 0.45
    - The Bahamas Resorts: 0.24
    - The Bahamas Flights: 0.25

  - Lag 2:
    - The Bahamas: 0.43
    - The Bahamas Travel: 0.47
    - The Bahamas Beach: 0.44
    - The Bahamas Hotels: 0.44
    - The Bahamas Resorts: 0.33
    - The Bahamas Flights: 0.25

  - Lag 3:
    - The Bahamas: 0.28
    - The Bahamas Travel: 0.24
    - The Bahamas Beach: 0.20
    - The Bahamas Hotels: 0.22
    - The Bahamas Resorts: 0.14
    - The Bahamas Flights: 0.13

  - Lag 4:
    - The Bahamas: 0.19
    - The Bahamas Travel: 0.13
    - The Bahamas Beach: 0.05
    - The Bahamas Hotels: 0.12
    - The Bahamas Resorts: 0.13
    - The Bahamas Flights: 0.09

  - Lag 5:
    - The Bahamas: 0.14
    - The Bahamas Travel: 0.10
    - The Bahamas Beach: -0.04
    - The Bahamas Hotels: 0.10
    - The Bahamas Resorts: 0.13
    - The Bahamas Flights: 0.08

- Source: Author's estimations.

### Notes and interpretation highlights
- All reported variables are in logs and seasonally adjusted for unit root testing.
- ADF and PP statistics indicate rejection of unit roots in first differences for the series listed (large negative values with ** and *** significance for first differences).
- Google Trends series show strong stationarity test statistics in both levels and first differences (many significant statistics at ** and *** levels).
- Correlation (ADF lag table) shows the highest contemporaneous associations (Lag 0–2) between Google search terms "The Bahamas", "The Bahamas Travel", "The Bahamas Beach", and tourist arrivals, with smaller correlations at longer lags (Lags 3–5).

*Source: Google Trends; Ministry of Tourism; author’s calculations. Appendix Figure 1 and accompanying tables from the source PDF.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020022-print-pdf.pdf_