Box-Jenkins Transfer Function Models Research Articles

Firearm-related internet searches as a correlate of future firearm suicides: Cross-correlation analyses of monthly Google search volumes and method-specific suicide rates in the United States

• This is a cross-correlation analysis of monthly Google search volumes and rates of suicide by the three most common methods in the USA. • Box-Jenkins transfer function models, the benjamini-hochberg method, and sensitivity analysis were applied. • The search volume of one firearm-related term ( gun suicide ) correlated with the rate of firearm suicides. • The search volume of one term ( “laid off” ) correlated with the rate of poisoning- and asphyxiation-specific suicide. • Cross-correlations elucidated in this study may provide guidance on development of novel suicide-prevention strategies. No previous study has investigated correlations between monthly Google search volumes (MGSVs) of suicide-related search terms and suicide-method specific monthly suicide rates (MSRs). This study examined if the trends in MGSVs of suicide-related terms preceded the variations in method-specific MSRs. MGSVs of 97 candidate suicide-related terms were obtained by averaging 10 timeseries data per term retrieved from Google Trends. Robust time-series analysis methods were applied to MGSVs and firearm-, poisoning-, and asphyxiation-specific MSRs in the United States between 2004 and 2017. Cross-correlation coefficients between MGSVs and methodspecific MSRs were calculated at lags of −3 to −1 (months). In the main analysis, the Benjamini-Hochberg procedure was applied to determine significant correlations while minimizing falsepositive findings. Afterwards, a sensitivity analysis identified the cross-correlations reproducible in two different time spans. Fifty-six search terms with no invalid MGSV data were analyzed. MGSVs of 14 terms correlated with firearm-, poisoning-, or asphyxiation-specific MSRs in one or more lags. In the sensitivity analysis, two terms consistently showed significant positive cross-correlations: gun suicide (with firearm-specific suicides; lag -3) and “laid off” (with poisoning- and asphyxiationspecific suicides; lag -2). Age- or gender-specific search volumes, lags outside the 1- to 3-month range, non-English searches, and confounding factors of MGSV and MSR were not explored. MGSVs of one firearm-related term ( gun suicide ) correlated with future firearmspecific MSRs. MGSVs of one method-neutral term (“ laid off” ) correlated with future poisoning- and asphyxiation-specific MSRs. These terms may be incorporated in novel nowcasting or predictive models for method-specific suicides.

Box-Jenkins Transfer Function Modelling for Reliable Determination of VO2 Kinetics in Patients with COPD

Oxygen uptake (VO2) kinetics provide information about the ability to respond to the increased physical load during a constant work rate test (CWRT). Box-Jenkins transfer function (BJ-TF) models can extract kinetic features from the phase II VO2 response during a CWRT, without being affected by unwanted noise contributions (e.g., phase I contribution or measurement noise). CWRT data of 18 COPD patients were used to compare model fits and kinetic feature values between BJ-TF models and three typically applied exponential modelling methods. Autocorrelation tests and normalised root-mean-squared error values (BJ-TF: 2.8 ± 1.3%; exponential methods A, B and C: 10.5 ± 5.8%, 11.3 ± 5.2% and 12.1 ± 7.0%; p < 0.05) showed that BJ-TF models, in contrast to exponential models, could account for the most important noise contributions. This led to more reliable kinetic feature values compared to methods A and B (e.g., mean response time (MRT), BJ-TF: 74 ± 20 s; methods A-B: 100 ± 56 s–88 ± 52 s; p < 0.05). Only exponential modelling method C provided kinetic feature values comparable to BJ-TF features values (e.g., MRT: 75 ± 20 s). Based on theoretical considerations, we recommend using BJ-TF models, rather than exponential models, for reliable determinations of VO2 kinetics.

Ambulance Dispatches From Unaffected Areas After the Great East Japan Earthquake: Impact on Emergency Care in the Unaffected Areas.

Although dispatching ambulance crews from unaffected areas to a disaster zone is inevitable when a major disaster occurs, the effect on emergency care in the unaffected areas has not been studied. We evaluated whether dispatching ambulance crews from unaffected prefectures to those damaged by the Great East Japan Earthquake was associated with reduced resuscitation outcomes in out-of-hospital cardiac arrest (OHCA) cases in the unaffected areas. We used the Box-Jenkins transfer function model to assess the relationship between ambulance crew dispatches and return of spontaneous circulation (ROSC) before hospital arrival or 1-month survival after the cardiac event. In a model whose output was the rate of ROSC before hospital arrival, dispatching 1000 ambulance crews was associated with a 0.474% decrease in the rate of ROSC after the dispatch in the prefectures (p=0.023). In a model whose output was the rate of 1-month survival, dispatching 1000 ambulance crews was associated with a 0.502% decrease in the rate of 1-month survival after the dispatch in the prefectures (p=0.011). The dispatch of ambulances from unaffected prefectures to earthquake-stricken areas was associated with a subsequent decrease in the ROSC and 1-month survival rates in OHCA cases in the unaffected prefectures.

Reproduction, condition and abundance of the Mediterranean bluefish (Pomatomus saltatrix) in the context of sea warming

AbstractThis study evaluates the link between sea warming and three important aspects of the population dynamics of bluefish, Pomatomus saltatrix, in the north‐western (NW) Mediterranean: condition (health measures), reproduction and abundance (as reflected in catch per unit effort, CPUE). We compared the bluefish populations from two areas with different thermal regimes: the Gulf of Roses and the Ebre Delta. First, in order to compare the condition and reproduction parameters of the two populations, specimens were collected from the commercial catch landed in two ports located in these areas. Several indicators of fish condition and reproduction such as hepatosomatic index, gonadosomatic index, maturation timing, length‐at‐first maturity, fecundity, egg quality and atresia (ovarian follicle resorption) were analysed and compared between study areas. Second, time series analyses of sea surface temperatures (SST) and monthly bluefish CPUEs in the two study areas were assessed using Box–Jenkins transfer function models. Our results indicate that bluefish benefit from sea warming in the NW Mediterranean, particularly in the northernmost zone, as evidenced by increasing fish condition in these waters. Sea warming may favour the changes in spawning phenology and the northward expansion of this species. This study provides evidence that a marine fish species that is able to expand or is forced to shift its distribution as a result of sea warming may take advantage of other environmental conditions of new habitats, contributing to the enhancement of the population's productivity in these areas.

Refined instrumental variable estimation: Maximum likelihood optimization of a unified Box–Jenkins model

For many years, various methods for the identification and estimation of parameters in linear, discrete-time transfer functions have been available and implemented in widely available Toolboxes for Matlab™. This paper considers a unified Refined Instrumental Variable (RIV) approach to the estimation of discrete and continuous-time transfer functions characterized by a unified operator that can be interpreted in terms of backward shift, derivative or delta operators. The estimation is based on the formulation of a pseudo-linear regression relationship involving optimal prefilters that is derived from an appropriately unified Box–Jenkins transfer function model. The paper shows that, contrary to apparently widely held beliefs, the iterative RIV algorithm provides a reliable solution to the maximum likelihood optimization equations for this class of Box–Jenkins transfer function models and so its en bloc or recursive parameter estimates are optimal in maximum likelihood, prediction error minimization and instrumental variable terms.

The impact of newspaper reporting of hydrogen sulfide suicide on imitative suicide attempts in Japan

An analysis model based on monthly or fortnight data is inadequate to precisely evaluate the impact of media reporting of suicide on suicide rates as well as the time lag from exposure to the report of a suicide. Thus, we used daily time-series data and examined the association between newspaper articles on suicide and suicide attempts in Japan. The Box-Jenkins transfer function model was applied to daily time-series data for the period March 27-May 21, 2008. Newspaper articles on suicide using hydrogen sulfide at (t - 1) were related to suicide attempts at (t) (ps < 0.001 and 0.05). Newspaper articles on suicides using hydrogen sulfide on the front page at (t - 1) were related to suicide attempts at (t) (p < 0.00). The magnitude of the impact of newspaper articles about suicide at (t - 1) or (t - 3) on "copy-cat" suicide attempts became greater as the number of news articles violating the media suicide recommendations increased. The time lag between exposure to newspaper reports of suicide and attempts was 1 or 3 days, and the magnitude of the impact of front page articles was about four times as great as that of suicide articles in general.

Refined Instrumental Variable Identification of Continuous-time OE and BJ Models from Irregularly Sampled Data

This paper looks at the problem of system identification from non-uniformly sampled input-output data. It describes how refined instrumental variable estimators can be derived to directly identify the parameters of continuous-time output error and Box-Jenkins transfer function models from irregularly sampled data. Monte Carlo simulation analysis is used to illustrate the properties of the proposed estimation schemes.

Effects of media reports and the subsequent voluntary withdrawal from sale of suicide-related products on the suicide rate in Japan

Media reports of suicides have an impact on suicide rates. However, countermeasures to this media effect have not been evaluated. We examined the association between media reports of suicides accomplished with the use of hydrogen sulfide, the voluntary stoppage of sales of suicide-related products, and suicide rates for people in their 20s, 30s, and 40s in Japan. The Box-Jenkins transfer function model was applied to monthly time series data from February 2003 to December 2009 (83 months). In the male suicide time series, media reports of suicide were not related to suicide counts (ω((R)) = 8.988, P = 0.694). Similarly, stopping the sale of bath salts was not related to the number of suicides (ω((S)) = -7.344, P = 0.694). However, in the female suicide time series, media reports of suicide were related to the number of suicides (ω((R)) = 17.225, P = 0.049). Similarly, stopping the sale of bath salts was related to the number of suicides (ω((S)) = -18.545, P = 0.040). The results suggest that stopping the sale of bath salts might be effective in reducing the number of copycat suicides among the women in their 20s, 30s, and 40s. In practice, stopping the sale of suicide-related products might be a potentially effective countermeasure to prevent copycat suicides triggered by media coverage of suicides.

Seasonal Variations in Clostridium difficile Infections Are Associated with Influenza and Respiratory Syncytial Virus Activity Independently of Antibiotic Prescriptions: a Time Series Analysis in Québec, Canada

Seasonal variations in Clostridium difficile-associated diarrhea (CDAD), with a higher incidence occurring during winter months, have been reported. Although winter epidemics of respiratory viruses may be temporally associated with an increase in CDAD morbidity, we hypothesized that this association is mainly due to increased antibiotic use for respiratory infections. The objective of this study was to evaluate the effect of the two most frequent respiratory viruses (influenza virus and respiratory syncytial virus [RSV]) and antibiotics prescribed for respiratory infections (fluoroquinolones and macrolides) on the CDAD incidence in hospitals in the province of Québec, Canada. A multivariable Box-Jenkins transfer function model was built to relate monthly CDAD incidence to the monthly percentage of positive tests for influenza virus and RSV and monthly fluoroquinolone and macrolide prescriptions over a 4-year period (January 2005 to December 2008). Analysis showed that temporal variations in CDAD incidence followed temporal variations for influenza virus (P = 0.043), RSV (P = 0.004), and macrolide prescription (P = 0.05) time series with an average delay of 1 month and fluoroquinolone prescription time series with an average delay of 2 months (P = 0.01). We conclude that influenza virus and RSV circulation is independently associated with CDAD incidence after controlling for fluoroquinolone and macrolide use. This association was observed at an aggregated level and may be indicative of other phenomena occurring during wintertime.

Internet suicide searches and the incidence of suicide in young people in Japan

Although several case reports have suggested a relationship between accessing Internet suicide sites and the incidence of suicide, the influence of the Internet on the incidence of suicide is not known. Thus, we examined the association between Internet suicide-related searches and the incidence of suicide in 20- and 30-year-old individuals in Japan. The Box-Jenkins transfer function model was applied to monthly time series data from January 2004 to May 2010 (77months). The terms "hydrogen sulfide," "hydrogen sulfide suicide," and "suicide hydrogen sulfide suicide" at (t-11) were related to the incidence of suicide among people aged in their 20s (P=0.005, 0.005, and 0.006, respectively) and people aged in their 30s (P=0.013, 0.011, and 0.012, respectively). "BBS on suicide" at (t-5) and "suicide by jumping" at (t-6) were related to the incidence of suicide in people aged 30-39 (P=0.006 and 0.001, respectively). Internet searches for specific suicide-related terms are related to the incidence of suicide among 20- and 30-year-old individuals in Japan. Routine interrogation by a clinician about visiting Internet suicide websites and stricter regulation of these websites may reduce the incidence of suicide among young people.

Discussion on: “Why Is Resorting to Fate Wise? A Critical Look at Randomized Algorithms in Systems and Control”

For many years, various methods for the identification and estimation of parameters in linear, discrete-time transfer functions have been available and implemented in widely available Toolboxes for Matlab™. This paper considers a unified Refined Instrumental Variable (RIV) approach to the estimation of discrete and continuous-time transfer functions characterized by a unified operator that can be interpreted in terms of backward shift, derivative or delta operators. The estimation is based on the formulation of a pseudo-linear regression relationship involving optimal prefilters that is derived from an appropriately unified Box–Jenkins transfer function model. The paper shows that, contrary to apparently widely held beliefs, the iterative RIV algorithm provides a reliable solution to the maximum likelihood optimization equations for this class of Box–Jenkins transfer function models and so its en bloc or recursive parameter estimates are optimal in maximum likelihood, prediction error minimization and instrumental variable terms.

전이함수를 통한 광릉 산림 유역의 토양수분 모델링

토양수분은 사면에서의 수문학적 과정의 가장 중요한 요소이며, 불포화대에서의 흐름을 결정하는 중요요소이다. 본 연구는 전이함수모형을 이용하여 토양수분의 시간적 공간적 분포 양상을 인지하고자 한다. 이를 위하여, 광릉 수목원 슈퍼사이트 원두부 소유역 내에서 TDR을 이용하여 2시간 간격으로 연속 측정한 10cm 깊이의 토양수분 결과를 전이함수를 통하여 분석하였다. 강우 자료를 입력변수로, 지표면으로부터 10cm 깊이의 실측 토양수분 자료를 출력변수로 선정하여 단일 입출력 전이함수를 전개하였다. 토양수분의 계절적인 변화를 분석하기 위해 5월과 9월의 전이함수를 비교하였다. 시계열 전이 함수는 크게 자료의 전처리, 모형구조의 규명, 후보 모형군의 구성, 모수추정, 모형진단 등의 과정을 통해서 전개되며 10cm 깊이의 토양수분과 강우의 상관관계를 보여준다. 도출한 전이함수 시계열 모형에서 10cm 깊이의 토양수분은 강우에 의한 영향이 지배적이었으며, 지점별 경사에 따라 토양수분의 변동성이 크게 차이를 나타내지 않았다. 이는 10cm 깊이의 토양수분 변동량은 각 지점의 경사보다 강우에 의한 반응이 우세하다는 것을 시사한다. 계절별로 상이한 모의 결과는 식생의 활동이 활발한 5월에는 식생이 토양수분 이동에 많은 영향을 미치며 식생이 토양수분을 해석하는데 중요한 변수로 작용함을 나타낸다. 본 연구 결과는 광릉 산림과 같은 복잡 경관에서 토양수분의 분포를 이해하는 기반자료가 될 것으로 기대된다. Soil moisture is one of the important components in hydrological processes and also controls the subsurface flow mechanism at a hillslope scale. In this study, time series of soil moisture were measured at a hillslope located in Gwangneung National Arboretum, Korea using a multiplex Time Domain Reflectometry(TDR) system measuring soil moisture with bi-hour interval. The Box-Jenkins transfer function and noise model was used to estimate spatial distributions of soil moisture histories between May and September, 2007. Rainfall was used as an input parameter and soil moisture at 10 cm depth was used as an output parameter in the model. The modeling process consisted of a series of procedures(e.g., data pretreatment, model identification, parameter estimation, and diagnostic checking of selected models), and the relationship between soil moisture and rainfall was assessed. The results indicated that the patterns of soil moisture at different locations and slopes along the hillslope were similar with those of rainfall during the measurment period. However, the spatial distribution of soil moisture was not associated with the slope of the monitored location. This implies that the variability of the soil moisture was determined more by rainfall than by the slope of the site. Due to the influence of vegetation activity on soil moisture flow in spring, the soil moisture prediction in spring showed higher variability and complexity than that in early autumn did. This indicates that vegetation activity is an important factor explaining the patterns of soil moisture for an upland forested hillslope.

A new national smokefree law increased calls to a national quitline

BackgroundA law making all indoor workplaces including bars and restaurants smokefree became operational in New Zealand in December 2004. New Zealand has a national free-phone Quitline Service which has been operational since 1999. Previous work has shown that the number of calls to the Quitline are influenced by marketing of the service through media campaigns. We set out to investigate if the smokefree law increased calls to the Quitline.MethodsFor 24 months prior to the law, and 12 months after the law, data were collected on: (i) Quitline caller registrations and the issuing of nicotine replacement therapy (NRT) vouchers by the Quitline Service; (ii) expenditure on Quitline-related television advertising; (iii) expenditure on other smokefree television advertising; and (iv) print media coverage of smoking in major New Zealand newspapers. These data were inputs to a time series analysis using a Box-Jenkins transfer function model. This used the law change as the intervention variable, with the response series being the monthly Quitline caller rates and monthly first time NRT voucher issue rates.ResultsThe monthly rates of Quitline caller registrations and NRT voucher issues were observed to increase in the months after the law change. The increase in both these outcomes was even greater when considered in terms of per level of Quitline advertising expenditure (though these patterns may have partly reflected marked reductions in advertising expenditure at the time of the law change and hence are of limited validity).In the more robust time series analyses, the law change (intervention variable) had a significant effect (p = 0.025) on increasing the monthly caller registration rate in December 2004. This was after adjusting for the possible effects of Quitline advertising expenditure, print media coverage, and other smoking-related advertising expenditure.ConclusionThe new national smokefree law resulted in increased quitting-related behaviour. This would suggest there is an extra opportunity for health agencies to promote quitting at such times.

Automatic fuzzy model identification for short-term load forecast

The conventional fuzzy modelling of short-term load forecasting has a drawback in that the fuzzy rules or the fuzzy membership functions are determined by trial and error. An automatic model identification procedure is proposed to construct the fuzzy model for short-term load forecast. An analysis of variance is used to identify the influential variables of the system load. To set up the fuzzy rules, a cluster estimation method is adopted to determine the number of rules and the membership functions of variables involved in the premises of the rules. A recursive least squares method is then used to determine the coefficients in the concluding parts of the rules. None of these steps involves nonlinear optimisation and all steps have well bounded computation time. This method was tested on the Taiwan Power Company's (Taipower) load data and the performance of the proposed method is compared to those of Box-Jenkins (B-J) transfer function and artificial neural network (ANN) models.

Modelling Thermohaline Properties in an Estuarine Upwelling Ecosystem (Rı́a de Vigo: NW Spain) Using Box-Jenkins Transfer Function Models

Since 1987, twice weekly, hydrological variables have been monitored at a fixed station in the Rı́a de Vigo (NW Spain), aiming to examine the time scales of variability and the relationships to meteorological conditions. The present paper analyses: (1) the advantage of Box-Jenkins transfer function (TF) models (single output–multiple input), a type of linear stochastic model, to describe the dynamic behaviour of the system; and (2) the coupling between the Rı́a and meteorological events at the time scale of autonomy of this coastal inlet affected by the Iberian coastal upwelling, approximately a fortnightly period. In order to achieve these objectives, thermohaline properties have been used to characterize the estuarine ecosystem (output variables), while wind regime, runoff in the drainage basin and incoming solar radiation have been considered as the main forcing variables (input variables). The use of the amplitude time series, derived from principal component analysis (PCA) applied to the deseasonalized meteorological variables, is also explored as a different set of input variables.When compared with standard regression models, all TF models built to describe thermohaline behaviour had reduced residual variance. Similar TF models, as well as percentage of explained variance, were also obtained when meteorological variables or the amplitude time series were used as input variables. The fitted TF models provided an insight into the ‘inertial’ behaviour of the system and the time scales of coupling of the system with the forcing variables. The plausible physical mechanisms which link the response of the system with the observed meteorological variability are also discussed. As could be expected, bottom thermohaline properties show a stronger inertial behaviour than the surface ones, which is particularly marked for bottom temperature. Besides, the shelf domain, by means of upwelling-downwelling events, strongly influences surface and bottom temperature, as well as bottom salinity; by contrast, surface salinity is mainly influenced by the effect of wind along the main axis of the Rı́a and runoff. In relation to the time scales of coupling between the system and the forcing variables, thermohaline properties show a dependance with the meteorological conditions in, at least, the immediately preceding fortnight period. It was concluded that: (1) TF models that incorporate meteorological information described the dynamic behaviour of the system adequately; and (2) this type of model can be useful as a first approximation to develop more sophisticated (deterministic) models, since, with the purpose of modelling any state variable of the system, both the coupling between different domains and the time scales of the interactions must be taken into account.

Environmental Factors Associated with Long-Term Changes in Chlorophyll Concentration in the Sacramento-San Joaquin Delta and Suisun Bay, California

Long-term changes in chlorophyll concentration were predicted from environmental variables using Box-Jenkins transfer function models for the Sacramento and San Joaquin rivers and Suisun Bay. Data used for the analyses were collected continuously on a semimonthly or monthly basis over the 17-yr period between 1971 and 1987. Groups of highly correlated environmental variables were summarized along three environmental axes using principal component analysis. The first environmental axis summarized river flow and specific conductance. The second environmental axis summarized water transparency and the third environmental axis summarized air and water temperature. Chlorophyll concentration was significantly corss-correlated with environmental axes and individual environmental variables. Transfer function models developed to describe changes in chlorophyll concentration over time were characterized by lag responses and described between 41% and 51% of the data variation. Significant cross-correlations between environmental axes and the California climate index (CA SLP) were used to develop a conceptual model of the link between regional climate and estuarine production.

Forecasting for business planning: A case study of IBM product sales

This is a case study of a closely managed product. Its purpose is to determine whether time-series methods can be appropriate for business planning. By appropriate, we mean two things: whether these methods can model and estimate the special events or features that are often present in sales data; and whether they can forecast accurately enough one, two and four quarters ahead to be useful for business planning. We use two time-series methods, Box-Jenkins modeling and Holt-Winters adaptive forecasting, to obtain forecasts of shipments of a closely managed product. We show how Box-Jenkins transfer-function models can account for the special events in the data. We develop criteria for choosing a final model which differ from the usual methods and are specifically directed towards maximizing the accuracy of next-quarter, next-half-year and next-full-year forecasts. We find that the best Box-Jenkins models give forecasts which are clearly better than those obtained from Holt-Winters forecast functions, and are also better than the judgmental forecasts of IBM's own planners. In conclusion, we judge that Box-Jenkins models can be appropriate for business planning, in particular for determining at the end of the year baseline business-as-usual annual and monthly forecasts for the next year, and in mid-year for resetting the remaining monthly forecasts.

Automatic forecasting using explanatory variables: A comparative study

Automatic model selection techniques can be an effective and efficient method of forecasting in certain business situations. The purpose of this study is to examine the potential of these automated methods for developing multivariate forecasting models; univariate models are utilized as benchmarks by which to evaluate the performance of the multivariate schemes. For the multivariate cases, ex ante and ex post forecasts for the input series are compared. Ten pairs of selected indicator, industry, and international macroeconomic series are used to evaluate forecasting performance. The results of this research show that overall the Box-Jenkins transfer function models perform more accurately. Also, it is found that misspecification of the transfer function component often produces poorer forecasts than simple univariate methods that ignore the explanatory variables altogether.

Sequential estimation of a time dependent advertising effectiveness model

A commonly used model for the relationship between advertising awareness and weight of advertising is that of Simon Broadbent (1979), One way TV advertisements work. In the paper Short-term modelling of advertising effectiveness: A confirmation of Broadbent's Model (Jex, 1985), it was found that from the very general class of Box-Jenkins Transfer Function models the Broadbent type model was indicated as being the most appropriate for National Girobank data. The present paper extends this work to cover the possibility that the parameters of the Broadbent model may change in time. Discount Weighted Estimation has been used to track parameter changes. These changes may be slow, due to decay of effectiveness or ‘ageing’ of a campaign, or they may be sudden, due for example to competitor activity.

Ridge estimation of transfer function weights

In this paper ridge estimators are used to obtain preliminary estimates of the impulse response weights in the Box-Jenkins transfer function model. Five ridge estimators and the Equity estimator are evaluated in a Monte Carlo study covering 5000 different transfer function models. The results show that although the differences between the estimators in most cases are rather small, the Dempster et al estimator RIDGM and the estimator by Lawless and Wang are best in terms of low average and median squared deviations from the true coefficient vector. The k values by these estimators are most closely correlated with the optimal k (computed from known true values) and also give the highest frequency of lowest squared error and lowest frequency of highest squared error among the investigated estimators.