Automatic forecasting with a modified exponential smoothing state space framework

A new automatic forecasting procedure is proposed based on a recent exponential smoothing framework which incorporates a Box-Cox transformation and ARMA residual corrections. The procedure is complete with well-defined methods for initialization, estimation, likelihood evaluation, and analytical derivation of point and interval predictions under a Gaussian error assumption. The algorithm is examined extensively by applying it to single seasonal and non-seasonal time series from the M and the M3 competitions, and is shown to provide competitive out-of-sample forecast accuracy compared to the best methods in these competitions and to the traditional exponential smoothing framework. The proposed algorithm can be used as an alternative to existing automatic forecasting procedures in modeling single seasonal and non-seasonal time series. In addition, it provides the new option of automatic modeling of multiple seasonal time series which cannot be handled using any of the existing automatic forecasting procedures. The proposed automatic procedure is further illustrated by applying it to two multiple seasonal time series involving call center data and electricity demand data.Exponential smoothing, state space models, automatic forecasting, Box-Cox transformation, residual adjustment, multiple seasonality, time series

Forecasting time series with complex seasonal patterns using exponential smoothing

A new innovations state space modeling framework, incorporating Box-Cox transformations, Fourier series with time varying coefficients and ARMA error correction, is introduced for forecasting complex seasonal time series that cannot be handled using existing forecasting models. Such complex time series include time series with multiple seasonal periods, high frequency seasonality, non-integer seasonality and dual-calendar effects. Our new modelling framework provides an alternative to existing exponential smoothing models, and is shown to have many advantages. The methods for initialization and estimation, including likelihood evaluation, are presented, and analytical expressions for point forecasts and interval predictions under the assumption of Gaussian errors are derived, leading to a simple, comprehensible approach to forecasting complex seasonal time series. Our trigonometric formulation is also presented as a means of decomposing complex seasonal time series, which cannot be decomposed using any of the existing decomposition methods. The approach is useful in a broad range of applications, and we illustrate its versatility in three empirical studies where it demonstrates excellent forecasting performance over a range of prediction horizons. In addition, we show that our trigonometric decomposition leads to the identification and extraction of seasonal components, which are otherwise not apparent in the time series plot itself.Exponential smoothing, Fourier series, prediction intervals, seasonality, state space models, time series decomposition

Genomic prediction of coronary heart disease

Aims Genetics plays an important role in coronary heart disease (CHD) but the clinical utility of genomic risk scores (GRSs) relative to clinical risk scores, such as the Framingham Risk Score (FRS), is unclear. Our aim was to construct and externally validate a CHD GRS, in terms of lifetime CHD risk and relative to traditional clinical risk scores. Methods and results We generated a GRS of 49 310 SNPs based on a CARDIoGRAMplusC4D Consortium meta-analysis of CHD, then independently tested it using five prospective population cohorts (three FINRISK cohorts, combined n = 12 676, 757 incident CHD events; two Framingham Heart Study cohorts (FHS), combined n = 3406, 587 incident CHD events). The GRS was associated with incident CHD (FINRISK HR = 1.74, 95% confidence interval (CI) 1.61-1.86 per S.D. of GRS; Framingham HR = 1.28, 95% CI 1.18-1.38), and was largely unchanged by adjustment for known risk factors, including family history. Integration of the GRS with the FRS or ACC/AHA13 scores improved the 10 years risk prediction (meta-analysis C-index: +1.5-1.6%, P = 60 years old (meta-analysis C-index: +4.6-5.1%, P <0.001). Importantly, the GRS captured substantially different trajectories of absolute risk, with men in the top 20% of attaining 10% cumulative CHD risk 12-18 y earlier than those in the bottom 20%. High genomic risk was partially compensated for by low systolic blood pressure, low cholesterol level, and non-smoking. Conclusions A GRS based on a large number of SNPs improves CHD risk prediction and encodes different trajectories of lifetime risk not captured by traditional clinical risk scores.Peer reviewe

Longitudinal Associations of Modifiable Lifestyle Factors With Positive Depression-Screen Over 2.5-Years in an International Cohort of People Living With Multiple Sclerosis

Background: Depression is common and has a significant impact on quality of life for many people with multiple sclerosis (MS). A preventive management approach via modification of lifestyle risk factors holds potential benefits. We examined the relationship between modifiable lifestyle factors and depression risk and the change in depression over 2.5 years.Methods: Sample recruited using online platforms. 2,224 (88.9%) at baseline and 1,309 (93.4%) at 2.5 years follow up completed the necessary survey data. Depression risk was measured by the Patient Health Questionnaire-2 (PHQ-2) at baseline and Patient Health Questionniare-9 (PHQ-9) at 2.5-years follow-up. Multivariable regression models assessed the relationships between lifestyle factors and depression risk, adjusted for sex, age, fatigue, disability, antidepressant medication use, and baseline depression score, as appropriate.Results: The prevalence of depression risk at 2.5-years follow-up in this cohort was 14.5% using the PHQ-2 and 21.7% using the PHQ-9. Moderate alcohol intake, being a non-smoker, diet quality, no meat or dairy intake, vitamin D supplementation, omega 3 supplement use, regular exercise, and meditation at baseline were associated with lower frequencies of positive depression-screen 2.5 years later. Moderate alcohol intake was associated with greater likelihood of becoming depression-free and a lower likelihood of becoming depressed at 2.5-years follow-up. Meditating at least once a week was associated with a decreased frequency of losing depression risk, against our expectation. After adjusting for potential confounders, smoking, diet, physical activity, and vitamin D and omega-3 supplementation were not associated with a change in risk for depression.Conclusion: In a large prospective cohort study of people with MS and depression, in line with the emerging treatment paradigm of early intervention, these results suggest a role for some lifestyle factors in depression risk. Further studies should endeavor to explore the impact of positive lifestyle change and improving depression in people living with MS

Modeling time series with complex seasonal patterns using exponential smoothing

New innovations state space modeling tools, incorporating Box-Cox transformations, Fourier series with time varying coefficients and ARMA error correction, are introduced for modeling complex seasonal time series. Such complex seasonal time series include those with multiple seasonal periods, high frequency seasonality, non-integer seasonality and dual-calendar effects. It is demonstrated that the new modeling practices provide alternatives to existing exponential smoothing approaches, but are shown to have several key advantages. The new approaches are complete with well-defined methods for initialization and estimation, including likelihood evaluation and the derivation of analytical expressions for point forecasts and interval predictions under the assumption of Gaussian errors, leading to simple, comprehensible approaches to modeling complex seasonal time series. The new approaches are capable of forecasting and decomposing non-seasonal, single seasonal and complex seasonal time series, and are useful in a broad range of applications. Their versatility is illustrated in various empirical studies, and it is also shown that the new approaches lead to the identification and extraction of seasonal components, which are otherwise not apparent in the time series plot itself. In addition, the new procedures are demonstrated as automated algorithms, and are shown to provide competitive forecast accuracy compared to the existing methods with several options. Relevant R software programs have been developed, and the implementation is presented using real life time series

Modeling time series with complex seasonal patterns using exponential smoothing

New innovations state space modeling tools, incorporating Box-Cox transformations, Fourier series with time varying coefficients and ARMA error correction, are introduced for modeling complex seasonal time series. Such complex seasonal time series include those with multiple seasonal periods, high frequency seasonality, non-integer seasonality and dual-calendar effects. It is demonstrated that the new modeling practices provide alternatives to existing exponential smoothing approaches, but are shown to have several key advantages. The new approaches are complete with well-defined methods for initialization and estimation, including likelihood evaluation and the derivation of analytical expressions for point forecasts and interval predictions under the assumption of Gaussian errors, leading to simple, comprehensible approaches to modeling complex seasonal time series. The new approaches are capable of forecasting and decomposing non-seasonal, single seasonal and complex seasonal time series, and are useful in a broad range of applications. Their versatility is illustrated in various empirical studies, and it is also shown that the new approaches lead to the identification and extraction of seasonal components, which are otherwise not apparent in the time series plot itself. In addition, the new procedures are demonstrated as automated algorithms, and are shown to provide competitive forecast accuracy compared to the existing methods with several options. Relevant R software programs have been developed, and the implementation is presented using real life time series