Source-linked AI summary
A Dynamic Linear Model to Forecast Hotel Registrations in Puerto Rico Using Google Trends Data
Roberto Rivera
TL;DR
Google Trends search query volume changes from week to week, complicating its use in forecasting hotel nonresident registrations in Puerto Rico. The paper models multiple outputs as observations of an unobservable search process; it reports more precise association inference and more realistic prediction intervals than using one output, but better forecast performance only for horizons over six months.
Problem
Google Trends search query volume changes weekly, while its sampling process is not fully specified, creating a challenge for using it to forecast Puerto Rico hotel nonresident registrations.
Source: §2 · pp. 1–2, §3.1 · p. 3Method
A Dynamic Linear Model treats multiple Google Trends outputs as observations of an unobservable search-query process and relates lagged SQV to hotel nonresident registrations.
Source: §2 · p. 2, §4.1.1 · p. 6Results
The model provides more precise inference on the lagged association and more realistic prediction intervals than a model using one SQV output, while forecast performance is better only beyond six months.
Source: §6 · p. 12Takeaways & Limitations
The model supports inference on the lagged association between true SQV and hotel nonresident registrations, with evidence of a statistically significant linear association.
Source: §6 · p. 12The search settings and region constrain the SQV data: this study used U.S. searches, where most surveyed visitors originated.
Source: §3.2 · p. 3
Abstract
from arXiv · showhide
Recently, studies have used search query volume (SQV) data to forecast a given process of interest. However, Google Trends SQV data comes from a periodic sample of queries. As a result, Google Trends data is different every week. We propose a Dynamic Linear Model that treats SQV data as a representation of an unobservable process. We apply our model to forecast the number of hotel nonresident registrations in Puerto Rico using SQV data downloaded in 11 different occasions. The model provides better inference on the association between the number of hotel nonresident registrations and SQV than using Google Trends data retrieved only on one occasion. Furthermore, our model results in more realistic prediction intervals of forecasts. However, compared to simpler models we only find evidence of better performance for our model when making forecasts on a horizon of over 6 months.
2 Introduction
The study addresses forecasting Puerto Rico hotel nonresident registrations as a proxy for tourism demand, while examining whether Google Trends search data can inform that task. It models weekly Google Trends outputs as observations of an unobservable process and compares the resulting forecasts with alternatives.
2 Introduction
- Google Trends has been used to model temporal processes, but its search query volume series changes from week to week.The algorithm’s process for generating its results is not exactly known.Source: §2 · p. 1
- Forecasting nonresident hotel registrations provides a statistical approach to planning for Puerto Rico’s tourism sector.The registrations serve as a proxy for tourism demand.Source: §2 · p. 2
- The proposed Dynamic Linear Model treats each weekly Google Trends output as data representing an unobservable process and compares its registration forecasts with alternatives.The analysis also examines the lagged association between registrations and search query volume.Source: §2 · p. 2
3 Data
The study combines hotel-registration data with Google Trends search query volume (SQV) to examine forecasting in Puerto Rico. It treats the changing weekly Google Trends outputs as sampled observations and uses U.S.-based search settings and 11 downloads.
3 Data
- Hotel nonresident registrations cover January 2004 to September 2012, while Google Trends’ normalized query volumes were converted from seven-day to monthly data for modeling.Registrations are an imperfect but intuitively useful proxy for the number of tourists.Source: §3 · p. 2
3.1 Challenges in using Google SQV data
- For fixed settings, Google Trends outputs can change at all time points from week to week, consistent with SQV being an observed version of a true search-query process.The sampling procedure and sample size are unspecified, and Google’s search functionality and ranking algorithm may also change.Source: §3.1 · pp. 2–3
3.2 Choice of Google Trends Settings to obtain SQV data
- The study selected the United States as its region and used nine queries; SQV was downloaded on 11 consecutive Thursdays from October 2 to December 11, 2014.The U.S. choice reflects the reported origin of most surveyed visitors, while travel-related queries from other countries often yielded little or no volume.Source: §3.2 · pp. 3–4, Table 1 · p. 4
4 Forecasting Models
The paper frames hotel registrations and search traffic as temporal processes that can be decomposed into trend or association, seasonality, and irregular dependence. Its Dynamic Linear Model uses multiple Google Trends outputs to represent latent search volume, estimate its lagged association with registrations, and forecast against standard alternatives.
4 Forecasting Models
- NHNR is decomposed into a trend or search-traffic association, seasonality, and irregular time dependence, modeled additively with stochastic approaches.Exploratory analysis did not support non-parametric alternatives such as neural networks or regression splines.Source: §4 · p. 4
4.1 Dynamic Linear Model
- The DLM represents observed time series through a measurement equation and evolves its unobserved state vector through transition equations.The state vector cannot be observed directly, and the model can accommodate features such as nonstationarity and multiple data sources.Source: §4.1 · p. 5
4.1.1 Dynamic Linear Model for NHNR
- The NHNR dynamic linear model uses β to represent the linear association between registrations at time t and true SQV at time t−1; β ≠ 0 implies SQV is a leading indicator, though it is not directly observed.It assumes a fixed seasonal component with a period of 12.Source: §4.1.1 · p. 6
4.1.2 Estimation of parameters and Kalman recursions
- Parameters were estimated with the EM algorithm, confidence intervals used asymptotic Normality and an estimated Hessian, and Kalman recursions produced predictions.EM alternates an expectation step for latent variables with maximization of the expected log likelihood.Source: §4.1.2 · pp. 6–7
4.2 Benchmark forecasting models
- SARIMA, Holt-Winter, and seasonal-naïve models were fitted on January 2004–September 2012 data and compared using a held-out October 2012–September 2013 period.The seasonal-naïve forecast repeats the NHNR value from the same month in the prior year.Source: §4.2 · p. 7
5 Results
Using 11 Google Trends outputs supported stronger inference on the lagged NHNR–SQV association and more realistic prediction intervals. DLM1 performed best against alternatives only for forecasts beyond six months.
5 Results
- NHNR was strongly seasonal, peaking in March and during December–April, with September the lowest month.Registrations peaked at 1,575,131 in 2012; seasonality did not appear to vary widely year to year.Source: §5 · p. 7, Figure 1 · p. 8
- The three Google Trends retrievals were similar but differed visibly: December had stronger later peaks, while October outputs had lower seasonal troughs.Source: §5 · p. 7, Figure 2 · p. 9
5.1 DLM results to determine association between X1,t and X2,t−1
- Prewhitened NHNR and SQV showed a significant but moderate one-month lag association, with a lag-1 cross-correlation of 0.32.The figure’s right panel reports cross-correlation using SQV averaged over 11 algorithmic outputs.Source: §5 · p. 8, Figure 2 · p. 9, §5.1 · p. 10
- DLM1’s β estimate was virtually the same as DLM2’s, but its 95% confidence interval excluded zero while DLM2’s included it.Using 11 Google Trends outputs supported better inference on the association than using one output.Source: §5.1 · p. 9, Table 2 · p. 10
- DLM2’s prediction intervals were too optimistic: at 12 months they were about 22% shorter than DLM1’s.The difference in interval length increased with forecast horizon.Source: §5.1 · p. 9, Figure 3 · p. 10
5.2 Forecast accuracy
- For horizons over 6 months, DLM1 performed best; for short-term forecasts, HW was generally best.No model performed best across both short- and long-term horizons.Source: Table 3 · p. 11, §5.2 · p. 11
6 Conclusions
The study accounts for uncertainty in Google Trends SQV to infer its lagged association with Puerto Rico hotel registrations and compare forecasts against alternatives. DLM1 provides more precise association inference and more realistic prediction intervals, but its advantage over simpler models appears only at longer horizons.
6 Conclusions
- DLM1 gives more precise inference on the lagged association and more realistic prediction intervals than a single-download model, but outperforms simpler alternatives only at longer horizons.Source: §6 · p. 12
- Holt-Winter has the smallest forecast errors at horizons of six months or less, while the authors advise against Holt-Winter and SARIMA for long-term forecasts.They identify Holt-Winter as more useful to tourism managers for the shorter horizon; DLM1 beats the seasonal-naive model universally over the longer horizon.Source: §6 · pp. 12–13
- Search-query selection was mostly heuristic, and preliminary analysis found weekly SQV noisier with higher SQV forecast errors than its monthly counterpart.The authors call for more objective query-selection methods and further research on latent-process models with mixed-frequency data.Source: §6 · p. 13
- Google provides limited detail about how its SQV data are obtained, while the data-generation mechanism can affect the appropriate modeling approach.The authors argue that greater transparency could improve the prospects for using SQV data.Source: §6 · pp. 13–14
- Forecast-accuracy significance tests need substantial out-of-sample data—at least 40 observations—to be useful, and covariance estimates depend on assumptions about observation and system errors.The authors leave Bayesian treatment of uncertainty in covariance-parameter estimation for future work.Source: §6 · p. 14