Estimating suicide occurrence statistics using Google Trends
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Abstract
Data on the number of people who have committed suicide tends to be reported with a substantial time lag of around two years. We examine whether online activity measured by Google searches can help us improve estimates of the number of suicide occurrences in England before official figures are released. Specifically, we analyse how data on the number of Google searches for the terms ‘depression’ and ‘suicide’ relate to the number of suicides between 2004 and 2013. We find that estimates drawing on Google data are significantly better than estimates using previous suicide data alone. We show that a greater number of searches for the term ‘depression’ is related to fewer suicides, whereas a greater number of searches for the term ‘suicide’ is related to more suicides. Data on suicide related search behaviour can be used to improve current estimates of the number of suicide occurrences.
Keywords
nowcasting search data Google Trends official statistics1 Introduction
The identification of causes of suicide attempts and suicide occurrences is a topic which has attracted the interest of a number of scientists in psychology and psychiatry [1, 2, 3, 4, 5, 6, 7, 8, 9] as well as in other social sciences such as demography, sociology and economics [10, 11, 12, 13, 14, 15, 16]. One of the challenges of analysing and modelling suicides from a macroscopic perspective is a long time lag in their reporting in official statistics. Identifying additional sources and data which would help estimate the number of suicide occurences before official data are available is thus of high importance and interest. In recent years, studies of the online activity of Internet users have proven fruitful in various fields ranging from medicine [17, 18], ecology [19, 20] and epidemiology [21, 22, 23, 24, 25] to linguistics [26], politics [27], sociology [28] and economics, finance and behavioural science [29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49]. For example, previous studies have provided evidence that online data may help us reduce delay and cost in measuring human behaviour [22, 40, 42, 43, 47], allow us to measure aspects of society and our environment that were previously difficult to measure [34, 41, 44, 45], and in some cases, even predict future actions [30, 35, 38, 39, 48, 49].
Here, we investigate whether data on searches relating to depression and suicide can help us address the problem of delayed data on suicides, and generate estimates of the number of suicide occurrences before official figures are released. A number of previous studies have attempted to investigate whether online search data might provide an avenue for creating quicker estimates of the number of suicide occurrences [50, 51, 52, 53, 54, 55]. However, these analyses were subject to a number of important restrictions. For example, McCarthy [50] examined the possible link between suicide occurrences and online activity in the USA. A strong negative correlation of -0.9 was reported between the yearly number of suicide occurrences and the yearly search activity for the term ‘suicide’. This finding was, however, based on a very limited data sample only (specifically, annual data between 2004 and 2007). Page et al. [51] studied monthly online search activity of suicide-related search terms in Australia between 2004 and 2011. They found no evidence for a significant link to suicide rates. However, their analysis was very restricted due to the availability of suicide data in Australia. Page et al. therefore limited themselves to analysing seasonal patterns in search activity and its relationship to changes in unemployment, which is frequently reported to be connected to suicides rates. No connection to suicide rates or suicide statistics was thus examined. Sueki [52] analysed a monthly suicide time series for Japan between 2004 and 2009 by calculating cross-correlation coefficients. Using the terms ‘suicide’, ‘depression’ and ‘suicide method’ translated into Japanese, Sueki found that increasing numbers of suicide occurrences coincide with increased online search activity for the ‘depression’ term only. At the same time, increasing search activity for the ‘depression’ term also appeared to be linked to a decrease in the actual suicide rates three months both earlier and later. The author thus suggests that the Internet could help prevent suicides by providing meaningful information to individuals who are depressed. The relevance of the results is, however, again weakened by a limited dataset (a monthly time series from 2004 to 2009). Yang et al. [53] investigated monthly suicide time series for Taipei in Taiwan, covering the time period from 2004 to 2009. The authors analysed 37 suicide-related search terms and reported that searches for a number of terms could be connected to the number of suicide occurrences for specific age groups, as well as specific types of suicide. However, we note that the authors did not control for possible non-stationarity of either suicide or online search data. Hagihara et al. [54] studied suicide rates in Japan between 2004 and 2010 for individuals with an age between 20 and 40. Utilizing the Box-Jenkins transfer function, the authors found several positive links between online search activity and suicidal behaviour. However, considering the number of observations (77), the number of analysed terms (20), the number of lags included in the transfer functions (12) and seasonal adjustments, it is difficult to exclude the possibility that the low number of statistically significant connections at specific lags may result from statistical error. In addition, Gun III and Lester [55] carried out a cross-sectional correlation analysis of state-level data from the USA in 2009. A positive correlation was found for all three search terms which they use - ‘commit suicide’, ‘how to suicide’ and ‘suicide prevention’. However, in this final study, the authors restrict themselves to a cross-sectional analysis and do not investigate the possibility of using search data to improve estimates across time.
Even though generalisations are difficult to make based on the reviewed studies, due to difficulties with data access and the potential methodological limitations described above, the search terms ‘suicide’ and ‘depression’ seem to be leading candidates for a model of suicidal behaviour which incorporates online search data. We therefore make use of these terms in our analysis. At the same time, we avoid the methodological pitfalls identified in the previous studies. Specifically, we study monthly time series of suicide occurrences in England between 2004 and 2013, which provides enough data for reliable estimation and statistical analysis. Further, we control for specific dynamic properties of the suicide and search query data - seasonality, non-stationarity and possible lagged dependence. The dataset analysed here also makes it possible to investigate the potential for using online searches to estimate suicide incidence numbers in practice, before the official data arrives. We refer to this as a ‘nowcasting’ analysis, in which we are ‘predicting the present’ [40].
2 Methods
2.1 Data
We study monthly suicide occurrence statistics in England between 2004 and 2013 provided by Office for National Statistics (ONS, www.ons.gov.uk).^{1} These data are made available with a pronounced lag of approximately 24 months. Suicide numbers are given for both males and females and different age brackets. Due to the coarseness of the data, we conduct our analysis on the overall occurrences, but do not investigate differences between gender and age groups.
Previous studies have suggested that searches for the terms ‘suicide’ and ‘depression’ may relate to real world suicide rates. We obtain data on the number of Google searches made for these terms from the website Google Trends (trends.google.com). Data are retrieved from Google at monthly granularity and relate to searches made in England only. The number of queries for a given term is rescaled to a value between 0 and 100. This holds for all search data retrieved from Google Trends, potentially weakening the value of Google data in modelling, as the actual number of searches is not provided. However, compared to other alternatives such as Twitter or Wikipedia data, Google search data provide much longer time series with easy geographical localisation. Both these characteristics are crucial for our analysis.
2.2 Models
2.3 Model testing and performance
We apply a standard set of tests during the estimating procedure. First, we test whether the model would benefit from adding polynomial (usually squared and cubic) transformations of the dependent variables, using the Ramsey’s RESET test [57]. If we reject the null hypothesis of the test, the model should be re-specified with further variables. Second, we run tests to ensure that the variance of the error terms is not unevenly distributed, or heteroskedastic, as this makes statistical tests less efficient. We use the ARCH effect test [58] to test for heteroskedasticity. To deal with static heteroskedasticity, we employ heteroskedasticity and autocorrelation consistent standard errors [59]. Third, to seek further evidence that the model is well specified, we test for normality of residuals using the Jarque-Bera test [60]. This test is less essential as rejecting normality of residuals usually does not have any serious consequences for the estimated model. However, not rejecting normality is usually taken as a sign of a very well specified and functional model. Fourth, we investigate whether the parameters of our model change across time using the CUSUM test [61]. If the null hypothesis is not rejected, the estimated model is considered stable in time. We test for significance of separate regressors using a t-test, and joint significance using an F-test. In both cases, to avoid problems which could be caused by autocorrelation and heteroskedasticity, we use robust standard errors.
2.4 Nowcasting performance
The relationship we are investigating here is of most interest due to potential practical exploitation, where Google search data could be used to estimate the number of suicide occurrences in the past month, before the official counts arrive. Such estimates are often referred to as ‘nowcasts’ [40], as the goal is not to forecast future values of a time series, but to estimate the value of the time series for the current period, drawing on past values of the time series and other relevant indicators. Estimates of these kinds are often constructed using standard forecasting methods.
We note that while finding a model that can describe the time series well is of value, good explanatory power does not necessarily imply that the model can be used to make estimates in practice. This is particularly true for models of non-stationary and seasonal time series, which can deliver very good fits but only poor forecasting performance. For this reason, we carry out a separate analysis to determine the nowcasting performance that can be achieved by including Google search data.
3 Results
3.1 Basic analysis
Descriptive statistics of data on suicide occurrences
Mean | SD | Min | Max | Skewness | Ex. kurtosis | Jarque-Bera | p-value | |
---|---|---|---|---|---|---|---|---|
Suicides | 370.20 | 20.65 | 302 | 468 | 0.3797 | 0.3328 | 3.4377 | >0.1 |
Autocorrelation and unit-root tests
Q(12) | p-value | ADF | p-value | KPSS | p-value | |
---|---|---|---|---|---|---|
Suicides | 41.9279 | <0.01 | −5.4869 | <0.01 | 0.4956 | 0.0451 |
-Depression | 496.0180 | <0.01 | −2.3241 | >0.1 | 0.7141 | 0.0131 |
-Suicide | 410.2039 | <0.01 | −1.2876 | >0.1 | 1.2190 | <0.01 |
To investigate whether data from Google can help us to estimate the number of suicide occurrences in England before official figures are released, we follow the findings of the previous studies and analyse data on Google searches for terms ‘depression’ and ‘suicide’. Figure 1 depicts the search query time series. We find that both follow a very similar pattern in time (with a Pearson’s correlation of 0.6580, \(p < 0.01\)). Both series are strongly autocorrelated (Q-test: see Table 2), and are identified as non-stationary and unit root processes (KPSS and ADF tests: see Table 2). From a methodological point of view, the presence of unit roots does not rule out a standard regression procedure, as long as both explanatory variables - in our case the Google searches - are unit root processes, which holds in our case [65].
Coefficients for correlations between data onGooglesearches for ‘depression’ and ‘suicide’ and official data on suicide occurrences
Depression (Google) | p-value | Suicide (Google) | p-value | |
---|---|---|---|---|
Suicides | 0.2124 | 0.0198 | 0.1626 | 0.0760 |
Depression (Google) | 0.6580 | <0.01 |
3.2 Models
As a base model, we create a model which controls for reported seasonal patterns in suicide occurrences and takes into account the most recent suicide statistics at our disposal. We approximate the two year lag in the release of suicide statistics for England by assuming that at each point in time, the most recent data we have is for 24 months ago. Specifically, we use a simple autoregressive model with the seasonal dummy variables specified in Eq. (1). As we are working with data at monthly frequency, monthly seasonal dummies are utilised. For the autoregressive term, we use a time lag of 24 months, to reflect the delay in data release. The ‘Google model’ controls for the same factors as the base model but also incorporates data on Google searches for the terms ‘depression’ and ‘suicide’ (Eq. (2)). Data on both terms are included at various lags, from 0 to 12 months, to account for both instantaneous as well as lagged effects. This allows us to investigate whether data on Google searches at different lags may help us estimate suicide rates. Such a detailed analysis has not been performed for the suicide data in the literature yet.
Model quality
\(\boldsymbol{R^{2}}\) | \(\boldsymbol {\bar{R}^{2}}\) | MAPE | RESET | p-value | |
---|---|---|---|---|---|
Base model | 0.2263 | 0.1144 | 5.6401 | 0.1712 | >0.1 |
Control model | 0.2810 | 0.2326 | 5.8724 | 0.4308 | >0.1 |
Google model | 0.4620 | 0.3362 | 4.9390 | 0.2473 | >0.1 |
Google vs Base | +0.2357 | +0.2218 | −0.7011 | - | - |
In contrast, the complete Google model (Eq. (3)), where data on online searches enrich the base model, provides a more notable improvement, leading to an \(R^{2}\) of 0.46. This provides initial evidence that data on searches for these terms may help us estimate suicide rates before official data are released. Model improvement is demonstrated not only by an increase in \(R^{2}\) (0.46 compared to 0.23) but also by increases in adjusted \(R^{2}\) (\(\bar{R}^{2}\)) which accounts for the number of independent variables in the regression (0.34 compared to 0.11). Furthermore, the mean absolute percentage error (MAPE) of the model decreases from 5.64% to 4.94%.
Additional tests
J-B test | p-value | ARCH effect | p-value | CUSUM | p-value | |
---|---|---|---|---|---|---|
Base model | 1.7621 | >0.1 | 17.6826 | >0.1 | 4.1902 | <0.01 |
Control model | 0.9725 | >0.1 | 11.3692 | >0.1 | 0.7985 | >0.1 |
Google model | 0.2470 | >0.1 | 9.9840 | >0.1 | 0.2472 | >0.1 |
Model improvement through inclusion ofGoogledata
Depression | p-value | Suicide | p-value | Joint | p-value |
---|---|---|---|---|---|
4.7620 | <0.01 | 7.9329 | <0.01 | 5.6225 | <0.01 |
3.3 Nowcasting analysis
Our analysis is limited by the number of data points which overlap between the official records of the number of suicide occurrences and search data from Google. Data on suicides are available only at monthly granularity, with the most recent records stemming from 2013, whereas online search data are available from 2004 only. As a result, our analysis is limited to ten years of monthly data points, or 120 data points. Up to this point, the results we have reported are all drawn from ‘in-sample’ analyses, where models are fitted to the full data set. However, the question remains as to whether a relationship between online data and official statistics on suicides could be used in practice to estimate the number of suicide occurrences in the past month, before the official data are released with several months delay.
Nowcasting performance
Base model | Googlemodel | |
---|---|---|
Mean absolute error | 29.559 | 15.059 |
Root mean squared error | 41.564 | 34.59 |
Mean absolute percentage error | 7.728 | 7.125 |
4 Discussion
Counts of the number of suicide occurrences in England are released with a delay of two years. Here, we investigate whether estimates of the number of suicide occurrences can be generated using data from Google searches. We find that using Google data, estimates of the number of suicides between 2004 and 2013 can be improved in comparison to estimates from previous suicide data alone.
Our findings are in line with the hypothesis that data on Google searches for ‘depression’ and ‘suicides’ may help improve estimates of the number of suicide occurrences in England before official figures are released. The results we report highlight the potential value of online communication data for creating new proxy measures of psychiatric illness across large populations.
Footnotes
- 1.
Monthly suicide occurrences are available at https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/deaths/adhocs/005582numberofsuicidesbymonthofoccurrenceregionsofenglandandwales1981to2013. Occurrence counts are provided for regions of England, which we sum to get statistics for all of England. The complete dataset is attached as Additional file 1 - Dataset.
- 2.
In our analysis, we have evaluated polynomials up to \(p=4\). Selection of \(p=2\) provides the most stable results.
- 3.
Interested readers are referred to the Statistical Bulletins of ONS at http://www.ons.gov.uk for comparison of the reported delay and the actual data availability.
Notes
Acknowledgements
The authors acknowledge funding from the Research Councils UK via Grant EP/K039830/1 and the Czech Science Foundation via Grant 16-00027S.
Supplementary material
References
- 1.Barraclough B, Pallis D (1975) Depression followed by suicide: a comparison of depressed suicides with living depressives. Psychol Med 5:55-61 CrossRefGoogle Scholar
- 2.Pallis D, Barraclough B, Levely A, Jenkins J, Sainsbury P (1982) Estimating suicide risk among attempted suicides: I. The development of new clinical scales. Br J Psychiatry 141:37-44 CrossRefGoogle Scholar
- 3.Burk F, Kurz A, Moller H-J (1985) Suicide risk scales: do they help to predict suicidal behaviour? Eur Arch Psychiatr Neurol Sci 235:153-157 CrossRefGoogle Scholar
- 4.Kosky R, Silburn S, Zurbrick S (1990) Are children and adolescents who have suicidal thoughts different from those who attempt suicide? J Nerv Ment Dis 178:1-67 CrossRefGoogle Scholar
- 5.Loftin C, McDowall D, Wiersema B, Cottey T (1991) Effects of restrictive licensing of handguns on homicide and suicide in the District of Columbia. N Engl J Med 325:1615-1620 CrossRefGoogle Scholar
- 6.Hughes D (1996) Suicide and violence assessment in psychiatry. Gen Hosp Psych 18:416-421 CrossRefGoogle Scholar
- 7.Pirkis J, Burgess P, Meadows G, Dunt D (2001) Suicidal ideation and suicide attempts as predictors of mental health service use. Med J Aust 175:542-545 Google Scholar
- 8.Rusch N, Zlati A, Black G, Thornicroft G (2014) Does the stigma of mental illness contribute to suicidality? Br J Psychiatry 205:257-259 CrossRefGoogle Scholar
- 9.Kolves K, De Leo D (2014) Suicide rates in children aged 10-14 years worldwide: changes in the past two decades. Br J Psychiatry 205:283-285 CrossRefGoogle Scholar
- 10.Schapiro M, Ahlburg D (1982) Suicide: the ultimate cost of unemployment. J Post Keynes Econ 5:276-280 CrossRefGoogle Scholar
- 11.Ahlburg D, Schapiro M (1984) Socioeconomic ramifications of changing cohort size: an analysis of U.S. postwar suicide rates by age and sex. Demography 21:97-108 CrossRefGoogle Scholar
- 12.Wasserman I (1984) Imitation and suicide: a reexamination of the Werther effect. Am Sociol Rev 49:427-436 CrossRefGoogle Scholar
- 13.Platt S (1984) Unemployment and suicidal behaviour: a review of the literature. Soc Sci Med 19:93-115 CrossRefGoogle Scholar
- 14.Stack S, Haas A (1984) The effect of unemployment duration on national suicide rates: a time series analysis, 1948-1982. Sociol Focus 17:17-29 CrossRefGoogle Scholar
- 15.Stack S (1987) The effect of female participation in the labor force on suicide: a time series analysis, 1948-1980. Sociol Forum 2:257-277 CrossRefGoogle Scholar
- 16.Morrell S, Taylor R, Quine S, Kerr C (1993) Suicide and unemployment in Australia 1907-1990. Soc Sci Med 36:749-756 CrossRefGoogle Scholar
- 17.Linkov F, Bovbjerg DH, Freese KE, Ramanathan R, Eid GM, Gourash W (2014) Bariatric surgery interest around the world: what Google Trends can teach us. Surg Obes Relat Dis 10:533-539 CrossRefGoogle Scholar
- 18.Telem DA, Pryor AD (2014) Google Trends: is it a real tool to predict the future of bariatric surgery or merely a marketing landmine? Surg Obes Relat Dis 10:538-539 CrossRefGoogle Scholar
- 19.McCallum ML, Bury GW (2013) Google search patterns suggest declining interest in the environment. Biodivers Conserv 22:1355-1367 CrossRefGoogle Scholar
- 20.Verissimo D, MacMillan DC, Smith RJ, Crees J, Davies ZG (2014) Has climate change taken prominence over biodiversity conservation? Bioscience 64:625-629 CrossRefGoogle Scholar
- 21.Polgreen PM, Chen Y, Pennock DM, Nelson FD, Weinstein RA (2008) Using Internet searches for influenza surveillance. Clin Infect Dis 47:1443-1448. http://cid.oxfordjournals.org/content/47/11/1443.full.pdf+html CrossRefGoogle Scholar
- 22.Ginsberg J Mohebbi MH, Patel RS, Brammer L, Smolinski MS, Brilliant L (2009) Detecting influenza epidemics using search engine query data. Nature 457:1012-1014 CrossRefGoogle Scholar
- 23.Carneiro H, Mylonakis E (2009) Google Trends: a web-based tool for real-time surveillance of disease outbreaks. Clin Infect Dis 49:1557-1564 CrossRefGoogle Scholar
- 24.Seifter A, Schwarzwalder A, Geis K, Aucott J (2010) The utility of ‘Google Trends’ for epidemiological research: Lyme disease as an example. Geosp Health 4:135-137 CrossRefGoogle Scholar
- 25.Dugas A, Hsieh Y-H, Levin SR, Pines JM, Mareiniss DP, Mohareb A, Gaydos CA, Perl TM, Rothman RE (2012) Google Flu Trends: correlation with emergency department influenza rates and crowding metrics. Clin Infect Dis 54:463-469 CrossRefGoogle Scholar
- 26.Mocanu D, Baronchelli A, Perra N, Gonçalves B, Zhang Q, Vespignani A (2013) The Twitter of Babel: mapping world languages through microblogging platforms. PLoS ONE 8:e61981 CrossRefGoogle Scholar
- 27.Metaxas PT, Mustafaraj E (2012) Social media and the elections. Science 338:472-473 CrossRefGoogle Scholar
- 28.Grabowicz PA, Ramasco JJ, Goncalves B, Eguiluz VM (2014) Entangling mobility and interactions in social media. PLoS ONE 9:e92196 CrossRefGoogle Scholar
- 29.Preis T, Reith D, Stanley HE (2010) Complex dynamics of our economic life on different scales: insights from search engine query data. Philos Trans R Soc A 368:5707-5719 CrossRefMATHGoogle Scholar
- 30.Goel S, Hofman J, Lehaie S, Pennock DM, Watts DJ (2010) Predicting consumer behavior with Web search. Proc Natl Acad Sci USA 7:17486-17490 CrossRefGoogle Scholar
- 31.Vosen S, Schmidt T (2011) Forecasting private consumption: survey-based indicators vs. Google trends. J Forecast 30:565-578 MathSciNetCrossRefMATHGoogle Scholar
- 32.Drake MS, Roulstone DT, Thornock JR (2012) Investor information demand: evidence from Google searches around earnings announcements. J Account Res 50:1001-1040 CrossRefGoogle Scholar
- 33.Bordino I, Battiston S, Caldarelli G, Cristelli M, Ukkonen A, Weber I (2012) Web search queries can predict stock market volumes. PLoS ONE 7:e40014 CrossRefGoogle Scholar
- 34.Preis T, Moat HS, Stanley HE, Bishop SR (2012) Quantifying the advantage of looking forward. Sci Rep 2:350 Google Scholar
- 35.Preis T, Moat HS, Stanley HE (2013) Quantifying trading behavior in financial markets using Google Trends. Sci Rep 3:1684 Google Scholar
- 36.Kristoufek L (2013) Can Google Trends search queries contribute to risk diversification? Sci Rep 3:2713 Google Scholar
- 37.Kristoufek L (2013) Bitcoin meets Google Trends and Wikipedia: quantifying the relationship between phenomena of the Internet era. Sci Rep 3:3415 Google Scholar
- 38.Moat HS, Curme C, Avakian A, Kenett DY, Stanley HE, Preis T (2013) Quantifying Wikipedia usage patterns before stock market moves. Sci Rep 3:1801 CrossRefGoogle Scholar
- 39.Curme C, Preis T, Stanley HE, Moat HS (2014) Quantifying the semantics of search behavior before stock market moves. Proc Natl Acad Sci USA 111:11600-11605 CrossRefGoogle Scholar
- 40.Choi H, Varian H (2012) Predicting the present with Google Trends. Econ Rec 88:2-8 CrossRefGoogle Scholar
- 41.Botta F, Moat HS, Preis T (2015) Quantifying crowd size with mobile phone and Twitter data. R Soc Open Sci 2:150162 MathSciNetCrossRefGoogle Scholar
- 42.Barchiesi D, Moat HS, Alis C, Bishop S, Preis T (2015) Quantifying international travel flows using Flickr. PLoS ONE 10:e0128470 CrossRefGoogle Scholar
- 43.Barchiesi D, Preis T, Bishop S, Moat HS (2015) Modelling human mobility patterns using photographic data shared online. R Soc Open Sci 2:150046 MathSciNetCrossRefGoogle Scholar
- 44.Seresinhe CI, Preis T, Moat HS (2015) Quantifying the impact of scenic environments on health. Sci Rep 5:16899 CrossRefGoogle Scholar
- 45.Seresinhe CI, Preis T, Moat HS (2016) Quantifying the link between art and property prices in urban neighbourhoods. R Soc Open Sci 3:160146 MathSciNetCrossRefGoogle Scholar
- 46.Preis T, Moat HS, Bishop SR, Treleaven P, Stanley HE (2013) Quantifying the digital traces of Hurricane Sandy on Flickr. Sci Rep 3:3141 Google Scholar
- 47.Preis T, Moat HS (2014) Adaptive nowcasting of influenza outbreaks using Google searches. R Soc Open Sci 1:140095 CrossRefGoogle Scholar
- 48.Moat HS, Preis T, Olivola CY, Liu C, Chater N (2014) Using big data to predict collective behavior in the real world. Behav Brain Sci 37:92-93 CrossRefGoogle Scholar
- 49.Garcia D, Tessone CJ, Mavrodiev P, Perony N (2014) The digital traces of bubbles: feedback cycles between socio-economic signals in the Bitcoin economy. J R Soc Interface 11:20140623 CrossRefGoogle Scholar
- 50.McCarthy MJ (2010) Internet monitoring of suicide risk in the population. J Affect Disord 122:277-279 CrossRefGoogle Scholar
- 51.Page A, Chang S-S, Gunnell D (2011) Surveillance of Australian suicidal behaviour using the Internet? Aust NZ J Psychiatry 45:1020-1022 CrossRefGoogle Scholar
- 52.Sueki H (2011) Does the volume of Internet searches using suicide-related search terms influence the suicide death rate: data from 2004 to 2009 in Japan. Psychiatry Clin Neurosci 65:392-394 CrossRefGoogle Scholar
- 53.Yang AC, Tsa S-J, Huang NE, Peng C-K (2011) Association of Internet search trends with suicide death in Taipei City, Taiwan, 2004-2009. J Affect Disord 132:179-184 CrossRefGoogle Scholar
- 54.Hagihara A, Miyazaki S, Abe T (2012) Internet suicide searches and the incidence of suicide in young people in Japan. Eur Arch Psychiatry Clin Neurosci 262:39-46 CrossRefGoogle Scholar
- 55.Gun JF III, Lester D (2013) Using Google searches on the Internet to monitor suicidal behavior. J Affect Disord 148:411-412 CrossRefGoogle Scholar
- 56.Almon S (1965) The distributed lag model between capital appropriations and expenditures. Econometrica 33:178-196 CrossRefGoogle Scholar
- 57.Ramsey J (1969) Tests for specification errors in classical linear least squares regression analysis. J R Stat Soc B 31:350-371 MathSciNetMATHGoogle Scholar
- 58.Engle R (1982) Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50:987-1007 MathSciNetCrossRefMATHGoogle Scholar
- 59.Arellano M (1987) Computing robust standard errors for withing-group estimators. Oxf Bull Econ Stat 49:431-434 CrossRefGoogle Scholar
- 60.Jarque C, Bera A (1980) Efficient tests for normality, homoskedasticity and serial independence of regression residuals. Econ Lett 6:255-259 MathSciNetCrossRefGoogle Scholar
- 61.Barnard G (1959) Control charts and stochastic processes. J R Stat Soc B 21:239-271 MATHGoogle Scholar
- 62.Dickey D, Fuller W (1979) Distribution of the estimators for autoregressive time series with a unit root. J Am Stat Assoc 74:427-431 MathSciNetMATHGoogle Scholar
- 63.Kwiatkowski D, Phillips P, Schmidt P, Shin Y (1992) Testing the null of stationarity against alternative of a unit root: how sure are we that the economic time series have a unit root? J Econom 54:159-178 CrossRefMATHGoogle Scholar
- 64.Engle R, Granger C (1987) Co-integration and error correction: representation, estimation and testing. Econometrica 55:251-276 MathSciNetCrossRefMATHGoogle Scholar
- 65.West K (1988) Asymptotic normality, when regressors have a unit root. Econometrica 56:1397-1417 MathSciNetCrossRefMATHGoogle Scholar
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