Dynamic Harmonic Regression Model Research Articles

Forecasting the incidence of dengue fever in Malaysia: A comparative analysis of seasonal ARIMA, dynamic harmonic regression, and neural network models

Currently, no vaccines or specific treatments are available to treat or prevent the increasing incidence of dengue worldwide. Therefore, an accurate prediction model is needed to support the anti-dengue control strategy. The primary objective of this study is to develop the most accurate model to predict future dengue cases in the Malaysian environment. This study uses secondary data collected from the weekly reports of the Ministry of Health Malaysia (MOH) website over six years, from 2017 to 2022. Three forecasting techniques, including seasonal autoregressive integrated moving average (SARIMA), dynamic harmonic regression (DHR), and neural network autoregressive model (NNAR), were first fitted to the estimation part of the data. First, several SARIMA models were run, and the best seasonal model identified was SARIMA (0, 1, 2) (1, 1, 1)52. The best DHR model was obtained with a Fourier term of 2, as this corresponds to the lowest Akaike Information Criteria (AIC) value. The NNAR (9, 1, 6)52 was considered the best choice among the NNAR models due to its superior performance in terms of the lowest error measures. The comparison among the three techniques revealed that the DHR model was the best due to its lowest MAPE and RMSE values. Thus, the DHR model was used to generate future forecasts of weekly dengue cases in Malaysia until 2023. The results showed that the model predicted more than a thousand dengue cases around weeks 27 to 32. The results showed an increase in dengue cases after the end of the monsoon season, which lasted about five months. This technique is proving to be valuable for health administrators in improving preparedness.

Time Series Analysis and Prediction of COVID-19 Pandemic Using Dynamic Harmonic Regression Models

Rapidly spreading COVID-19 virus and its variants, especially in metropolitan areas around the world, became a major health public concern. The tendency of COVID-19 pandemic and statistical modelling represents an urgent challenge in the United States for which there are few solutions. In this paper, we demonstrate combining Fourier terms for capturing seasonality with ARIMA errors and other dynamics in the data. Therefore, we have analyzed 156 weeks COVID-19 dataset on national level using Dynamic Harmonic Regression model, including simulation analysis and accuracy improvement from 2020 to 2023. Most importantly, we provide new advanced pathways which may serve as targets for developing new solutions and approaches.

Beyond the beaten paths of forecasting call center arrivals: on the use of dynamic harmonic regression with predictor variables

Modern call centers require precise forecasts of call and e-mail arrivals to optimize staffing decisions and to ensure high customer satisfaction through short waiting times and the availability of qualified agents. In the dynamic environment of multi-channel customer contact, organizational decision-makers often rely on robust but simplistic forecasting methods. Although forecasting literature indicates that incorporating additional information into time series predictions adds value by improving model performance, extant research in the call center domain barely considers the potential of sophisticated multivariate models. Hence, with an extended dynamic harmonic regression (DHR) approach, this study proposes a new reliable method for call center arrivals’ forecasting that is able to capture the dynamics of a time series and to include contextual information in form of predictor variables. The study evaluates the predictive potential of the approach on the call and e-mail arrival series of a leading German online retailer comprising 174 weeks of data. The analysis involves time series cross-validation with an expanding rolling window over 52 weeks and comprises established time series as well as machine learning models as benchmarks. The multivariate DHR model outperforms the compared models with regard to forecast accuracy for a broad spectrum of lead times. This study further gives contextual insights into the selection and optimal implementation of marketing-relevant predictor variables such as catalog releases, mail as well as postal reminders, or billing cycles.

A dynamic harmonic regression approach for bridge structural health monitoring

Structural damage in a bridge is defined as a significant deviation in the structural response from its standard operating conditions, not explainable by variations in external environmental and operational effects. However, environmental effects such as temperature fluctuations can cause significant seasonal variations in the structural response of a bridge and can mask its changes due to structural damage. This poses a challenge for structural health monitoring of bridges where reliable diagnosis of damage or deterioration is often related to isolation of the responses. To address it, a statistical damage-detection methodology is introduced where strain data are modelled using a dynamic harmonic regression time-series model. Prediction intervals of multi-step ahead forecasts from the dynamic harmonic regression model are then used as statistical control limits within which the observed phenomenon should fall under standard operating conditions. This single recursive structural health monitoring framework for automatic fitting and multi-step ahead forecasting of 1-min interval time-series strain data includes recorded temperature values and diurnal trends as regressors in the model to account for environmental variations. The potential of this method as a robust automatic structural health monitoring strategy is demonstrated on strain data sampled at 1-min interval from a full-scale damaged pre-stressed concrete bridge – before, during and after repair. The proposed method can capture both sudden and daily changes in structural response due to temperature effects, and a rolling multi-step ahead interval forecast was able to identify damage on back-cast data transitioning from a healthy state to a damaged state.

Dynamic harmonic regression modeling for monthly mean sea levels at tide gauges within the Arabian Gulf

Time series with strong periodicity and non-stationary character in terms of magnitude and frequency which are changing over measurement period can be decomposed into time-varying trend, seasonal and cyclical components by dynamic harmonic regression (DHR) modeling in the state-space framework. The time-variable parameters of the components are first associated with a generalized random walk process, and then, state parameters are estimated by the recursive Kalman filtering and fixed interval smoothing algorithms. Missed points are filled by the DHR interpolation, and change points are detected by both visual inspection and the Pettitt test. Sea level series at tide gauges, which consist of accelerated trend and strong periodicity, are therefore suitable for DHR modeling. Time-varying trend, seasonal and cyclical components are extracted by the DHR modeling from the monthly mean sea level series longer than 15 years at seven stations within the Arabian Gulf. The DHR model accounts for 90–96% of variation of the monthly series, while the seasonal and cyclical components account for 64–85% and 2–7%, respectively. Average relative sea level rate (RSLR) and absolute sea level rate (ASLR) over the Arabian Gulf are found $$1.67 \pm 0.05$$ mm/year and 1.93 ± 0.05 mm/year, respectively.

Characterization of the Temporal Trends in the Rate of Cattle Carcass Condemnations in the US and Dynamic Modeling of the Condemnation Reasons in California With a Seasonal Component.

Based on the 2016 National Cattlemen's Beef Association statistics, the cattle inventory in the US reached 93.5 million head, from which 30.5 million were commercial slaughter in 2016. California ranked fourth among all the US states that raise cattle and calves, with 5.15 million head and approximately 1.18 million slaughtered animals per year. Approximately 0.5% of cattle carcasses in the US are condemned each year, which has an important economic impact on cattle producers.In this study, we first described and compared the temporal trends of cattle carcass condemnations in all the US states from Jan-2005 to Dec-2014. Then, we focused on the condemnation reasons with a seasonal component in California and used dynamic harmonic regression (DHR) models both to model (from Jan-2005 to Dec-2011) and predict (from Jan-2012 to Dec-2014) the carcass condemnations rate in different time horizons (3 to 12 months).Data consisted of daily reports of 35 condemnation reasons per cattle type reported in 684 federally inspected slaughterhouses in the US from Jan-2005 to Dec-2014 and the monthly slaughtered animals per cattle type per states. Almost 1.5 million carcasses were condemned in the US during the 10 year study period (Jan 2005-Dec 2014), and around 40% were associated with three condemnation reasons: malignant lymphoma, septicemia and pneumonia. In California, emaciation, eosinophilic myositis and malignant lymphoma were the only condemnation reasons presenting seasonality and, therefore, the only ones selected to be modeled using DHRs. The DHR models for Jan-2005 to Dec-2011 were able to correctly model the dynamics of the emaciation, malignant lymphoma and eosinophilic myositis condemnation rates with coefficient of determination () of 0.98, 0.87 and 0.78, respectively. The DHR models for Jan-2012 to Dec-2014 were able to predict the rate of condemned carcasses 3 month ahead of time with mean relative prediction error of 33, 11, and 38%, respectively. The systematic analysis of carcass condemnations and slaughter data in a more real-time fashion could be used to identify changes in carcass condemnation trends and more timely support the implementation of prevention and mitigation strategies that reduce the number of carcass condemnations in the US.

Modeling Seasonal and Spatiotemporal Variation: The Example of Respiratory Prescribing.

Many measures of chronic diseases, including respiratory disease, exhibit seasonal variation together with residual correlation between consecutive time periods and neighboring areas. We demonstrate a strategy for modeling data that exhibit both seasonal trend and spatiotemporal correlation, using an application to respiratory prescribing. We analyzed 55 months (2002–2006) of prescribing data from the northeast of England, in the United Kingdom. We estimated the seasonal pattern of prescribing by fitting a dynamic harmonic regression (DHR) model to salbutamol prescribing in relation to temperature. We compared the output of DHR models to static sinusoidal regression models. We used the DHR-fitted values as an offset in mixed-effects models that aimed to account for the remaining spatiotemporal variation in prescribing rates. As diagnostic checks, we assessed spatial and temporal correlation separately and jointly. Our application of a DHR model resulted in a better fit to the seasonal variation of prescribing than was obtained with a static model. After adjusting for the fitted values from the DHR model, we did not detect any remaining spatiotemporal correlation in the model's residuals. Using a DHR model and temperature data to account for the periodicity of prescribing proved to be an efficient way to capture its seasonal variation. The diagnostic procedures indicated that there was no need to model any remaining correlation explicitly.

Modelling seasonal and spatio-temporal variation in respiratory prescribing

Introduction: Many measures of chronic diseases including respiratory disease exhibit seasonal variation together with residual correlation between consecutive time-periods and neighbouring areas. We demonstrate a modern strategy for modelling data that exhibit both a seasonal trend and spatio-temporal correlation, through an application to respiratory prescribing. Methods: We estimated the seasonal pattern of prescribing by fitting a dynamic harmonic regression (DHR) model to salbutamol prescribing rates in relation to temperature. We compared the output of our DHR models to static sinusoidal regression models. We used the DHR fitted values as an offset in mixed-effects models that aimed to account for the remaining spatio-temporal variation in prescribing rates. As diagnostic checks, we assessed spatial and temporal correlation separately and jointly. Results: Our application of a DHR model resulted in a better fit to the seasonal variation of prescribing, than was obtained with a static model. After adjusting the final model for the fitted values from the DHR model, we did not detect any remaining spatio-temporal correlation in the model's residuals. Conclusions: Using a DHR model and temperature data to account for the periodicity of prescribing proved an efficient way to capture its seasonal variation. The diagnostic procedures indicated that there was no need to model any remaining correlation explicitly.

Short-term solar irradiation forecasting based on Dynamic Harmonic Regression

Solar power generation is a crucial research area for countries that have high dependency on fossil energy sources and is gaining prominence with the current shift to renewable sources of energy. In order to integrate the electricity generated by solar energy into the grid, solar irradiation must be reasonably well forecasted, where deviations of the forecasted value from the actual measured value involve significant costs. The present paper proposes a univariate Dynamic Harmonic Regression model set up in a State Space framework for short-term (1–24 h) solar irradiation forecasting. Time series hourly aggregated as the Global Horizontal Irradiation and the Direct Normal Irradiation will be used to illustrate the proposed approach. This method provides a fast automatic identification and estimation procedure based on the frequency domain. Furthermore, the recursive algorithms applied offer adaptive predictions. The good forecasting performance is illustrated with solar irradiance measurements collected from ground-based weather stations located in Spain. The results show that the Dynamic Harmonic Regression achieves the lowest relative Root Mean Squared Error; about 30% and 47% for the Global and Direct irradiation components, respectively, for a forecast horizon of 24 h ahead.

A Dynamic Harmonic Regression Approach to Power System Modal Identification and Prediction

—Time series models provide a powerful tool to extract nonstationary features from measured data. In this article, a statistical framework based upon a dynamic harmonic regression model for examining modal behavior is provided. In this model, temporal patterns in measured data are modeled within a stochastic state space setting. Estimates of the states or time-varying parameters are then obtained using an optimal estimation method based on the Kalman filter. Techniques to estimate future values of the unobserved signal are also analyzed. The widely applicable technique is illustrated on both simulated and measured data. Factors that affect the performance of the method are discussed, including the effects of non-linear trends, data quality, and sampling design. Connections with other modal identification methods are also investigated.

Modelling seasonal and multi-annual variation in bank vole populations and nephropathia epidemica

Nephropathia epidemica (NE) is a human infection caused by Puumala virus (PUUV), which is naturally carried and shed by bank voles (Myodes glareolus). The objective was to develop a dynamic model of the NE cases and the bank vole population in both Finland and Belgium by defining the periodic components with a dynamic harmonic regression (DHR) model. The defined periodic components can be further used to adapt mechanistic Susceptible and Infective (SI) models regionally. Despite the difference in bank vole population dynamics and NE cases between the Western European temperate zone and boreal zones the DHR model was able to quantify the dynamics of NE cases in Belgium and Central Finland with a coefficient of determination (R2) of 0.70 and 0.82 respectively and to quantify the dynamics of bank vole population in Belgium and Central Finland with R2 of 0.80 and 0.98 respectively. DHR identified 18 month cycles in the bank vole population in Belgium. This approach demonstrated two year cycles in Belgian NE outbreaks. DHR identified three year cycles in Finnish bank vole populations which in turn cause three year cycles in the NE outbreaks in Central Finland. Because the bank vole population data in Finland was contemporary with the data of NE cases, the DHR showed a three month delay between the NE cases and the bank vole population in Central Finland. This approach may help us in our understanding of the spatial and temporal dynamics of NE cases and the bank vole populations in different regions.

Model‐Based Prediction of Nephropathia Epidemica Outbreaks Based on Climatological and Vegetation Data and Bank Vole Population Dynamics

Wildlife-originated zoonotic diseases in general are a major contributor to emerging infectious diseases. Hantaviruses more specifically cause thousands of human disease cases annually worldwide, while understanding and predicting human hantavirus epidemics pose numerous unsolved challenges. Nephropathia epidemica (NE) is a human infection caused by Puumala virus, which is naturally carried and shed by bank voles (Myodes glareolus). The objective of this study was to develop a method that allows model-based predicting 3 months ahead of the occurrence of NE epidemics. Two data sets were utilized to develop and test the models. These data sets were concerned with NE cases in Finland and Belgium. In this study, we selected the most relevant inputs from all the available data for use in a dynamic linear regression (DLR) model. The number of NE cases in Finland were modelled using data from 1996 to 2008. The NE cases were predicted based on the time series data of average monthly air temperature (°C) and bank voles' trapping index using a DLR model. The bank voles' trapping index data were interpolated using a related dynamic harmonic regression model (DHR). Here, the DLR and DHR models used time-varying parameters. Both the DHR and DLR models were based on a unified state-space estimation framework. For the Belgium case, no time series of the bank voles' population dynamics were available. Several studies, however, have suggested that the population of bank voles is related to the variation in seed production of beech and oak trees in Northern Europe. Therefore, the NE occurrence pattern in Belgium was predicted based on a DLR model by using remotely sensed phenology parameters of broad-leaved forests, together with the oak and beech seed categories and average monthly air temperature (°C) using data from 2001 to 2009. Our results suggest that even without any knowledge about hantavirus dynamics in the host population, the time variation in NE outbreaks in Finland could be predicted 3 months ahead with a 34% mean relative prediction error (MRPE). This took into account solely the population dynamics of the carrier species (bank voles). The time series analysis also revealed that climate change, as represented by the vegetation index, changes in forest phenology derived from satellite images and directly measured air temperature, may affect the mechanics of NE transmission. NE outbreaks in Belgium were predicted 3 months ahead with a 40% MRPE, based only on the climatological and vegetation data, in this case, without any knowledge of the bank vole's population dynamics. In this research, we demonstrated that NE outbreaks can be predicted using climate and vegetation data or the bank vole's population dynamics, by using dynamic data-based models with time-varying parameters. Such a predictive modelling approach might be used as a step towards the development of new tools for the prevention of future NE outbreaks.

Exploring the long-term and interannual variability of biogeochemical variables in coastal areas by means of a data assimilation approach

Dynamic Harmonic Regression (DHR) models are applied here to the investigation of the interannual changes in the trend and seasonality of biogeochemical variables monitored in coastal areas. A DHR model can be regarded as a time-series component model, where the phases and amplitudes of the seasonal component, as well as the trend, are parameters that vary with time, reflecting relevant changes in the evolution of the biogeochemical variables. The model parameters and their confidence bounds are estimated by data assimilation algorithms, i.e. the Kalman filter and the Fixed Interval smoother. The DHR model structure is here identified by a preliminary spectral analysis and a subsequent minimization of the Bayesian Information Criterion, thus avoiding subjective choices of the frequencies in the seasonal component. The methodology was applied to the investigation of the long-term and interannual variability of ammonia, nitrate, orthophosphate and chlorophyll-a monitored monthly in the lagoon of Venice (Italy) during the years 1986–2008. It was found that the long-term evolutions of the biogeochemical variables were characterized by non-linear patterns and by statistically significant changes in the trend. The seasonal cycles of all the variables were characterized by a marked interannual variability. In particular, the changes in the seasonality of chlorophyll and nitrate were significantly related to the changes in the seasonality of water temperature at the study site and of nutrient concentrations in river discharges, respectively. These results indicate that the methodology could be a sound alternative to more traditional approaches for investigating the impacts of changes in environmental and anthropogenic forcings on the evolution of biogeochemical variables in coastal areas.

Analysis and prediction of MODIS LAI time series with Dynamic Harmonic Regression model

Analysis and prediction of MODIS LAI time series with Dynamic Harmonic Regression model

Representing time‐varying cyclic dynamics using multiple‐subject state‐space models

Over the last few decades, researchers have become increasingly aware of the need to consider intraindividual variability in the form of cyclic processes. In this paper, we review two contemporary cyclic state-space models: Young and colleagues' dynamic harmonic regression model and Harvey and colleagues' stochastic cycle model. We further derive the analytic equivalence between the two models, discuss their unique strengths and propose multiple-subject extensions. Using data from a study on human postural dynamics and a daily affect study, we demonstrate the use of these models to represent within-person non-stationarities in cyclic dynamics and interindividual differences therein. The use of diagnostic tools for evaluating model fit is also illustrated.

Dynamic Modeling of Space-Time Variation of Black Smoke in an Industrial Urban Setting

ISEE-511 Abstract: This paper presents novel techniques of exposure estimation developed for a large (100,000+ births) study of associations between black smoke (BS) and perinatal health outcomes in an industrial urban setting (population 260,000) for the period 1961 to 1992. An average of 20 monitoring stations recorded BS at a given point in time, but collection periods varied. Objective: Space-time modeling aimed to create estimates of the exposure surface across the city at a resolution of 1 week (for analysis by trimester of pregnancy) and 100 m for all residential areas where births occurred including predictions of error. Material and Methods: We abstracted daily BS readings for the study period (25,000+ weekly observations). We digitized all domestic and industrial chimneys (90,000+) and georeferenced information on slum clearances, phasing in of smokeless zones and industry closures. We created variables for “area of industry within 500 m,” “distance to nearest industry” and “chimney density” for 26,000+ pixels of the map of the study area. Using GIS and R software we developed a 2-stage approach: (1) Modeling temporal variation in spatially-averaged BS levels, and (2) modeling residual spatiotemporal variation about temporal averages. Results: A dynamic harmonic regression model incorporating weekly minimum temperature improved upon a simpler static model in capturing long-term decreasing trends and seasonal variation in spatially-averaged log-BS levels. Spatiotemporal regression modeling, using chimney density and distance to nearest industry as explanatory variables, reduced the space-time dependence of residuals at individual monitoring stations and allowed predictions of BS levels to be made throughout the region of interest. Conclusions: Our dynamic spatiotemporal model, which incorporates monitored pollutant data and detailed georeferenced land-use information, allows exposure estimates for environmental epidemiology studies to gain tremendously both in precision and clarity of error structure.

Linear dynamic harmonic regression

Among the alternative unobserved components formulations within the stochastic state space setting, the dynamic harmonic regression (DHR) model has proven to be particularly useful for adaptive seasonal adjustment, signal extraction, forecasting and back-casting of time series. First, it is shown how to obtain AutoRegressive moving average (ARMA) representations for the DHR components under a generalized random walk setting for the associated stochastic parameters; a setting that includes several well-known random walk models as special cases. Later, these theoretical results are used to derive an alternative algorithm, based on optimization in the frequency domain, for the identification and estimation of DHR models. The main advantages of this algorithm are linearity, fast computational speed, avoidance of some numerical issues, and automatic identification of the DHR model. The signal extraction performance of the algorithm is evaluated using empirical applications and comprehensive Monte Carlo simulation analysis.

Electricity prices forecasting by automatic dynamic harmonic regression models

Abstract The changes experienced by electricity markets in recent years have created the necessity for more accurate forecast tools of electricity prices, both for producers and consumers. Many methodologies have been applied to this aim, but in the view of the authors, state space models are not yet fully exploited. The present paper proposes a univariate dynamic harmonic regression model set up in a state space framework for forecasting prices in these markets. The advantages of the approach are threefold. Firstly, a fast automatic identification and estimation procedure is proposed based on the frequency domain. Secondly, the recursive algorithms applied offer adaptive predictions that compare favourably with respect to other techniques. Finally, since the method is based on unobserved components models, explicit information about trend, seasonal and irregular behaviours of the series can be extracted. This information is of great value to the electricity companies’ managers in order to improve their strategies, i.e. it provides management innovations. The good forecast performance and the rapid adaptability of the model to changes in the data are illustrated with actual prices taken from the PJM interconnection in the US and for the Spanish market for the year 2002.

Resolving the Long-Term Trends of Polycyclic Aromatic Hydrocarbons in the Canadian Arctic Atmosphere

Polycyclic aromatic hydrocarbon (PAH) air concentrations measured over the period 1992-2000 at the Canadian High Arctic station of Alert were subject to time-series analysis using dynamic harmonic regression (DHR). For most of the PAHs, the DHR model fit to the observed data was good, with DHR capable of interpolating over missing data points during periods when air concentrations were below detection limits. As expected, DHR identified seasonal increases in PAH air concentrations. However, it has also identified additional, subtler "seasonal" patterns as a series of harmonics with varying periodicity. For example, a regular summer high in air concentrations was apparent for many PAHs, particularly the lower molecular weight (two- to three-ringed) compounds, which may be attributed to summertime regional combustion events such as forestfires and/or revolatilization from surfaces (e.g., soil and oceans, as well as arctic surfaces). Comparison of wintertime PAH concentrations (where sigmaPAH ranged from 260 to 516 pg m(-3)) with an earlier arctic study did not reveal a reduction in PAH levels. However, removal of the seasonal components by DHR revealed a declining trend in PAH concentrations over the 1992-2000 period. For many lighter PAHs, this was typified by a linear decrease over the whole time series, although, for the higher molecular weight PAHs, a marked reduction was apparent in the first few years of sampling followed by a leveling off in concentrations by the mid/late-1990s. This behavior is similar to reported trends of other air pollutants in the Arctic, may be attributed to the decline in Soviet industry during the early 1990s, and has implications regarding the major PAH sources affecting the Arctic.

An unobserved component model for multi-rate forecasting of telephone call demand: the design of a forecasting support system

An Unobserved Components (UC) Model based on an enhanced version of the Dynamic Harmonic Regression model, including new multi-rate and modulated cycle procedures, is used to develop a customised package for forecasting and signal extraction applied to hourly telephone call numbers made to Barclaycard plc. service centres, with a forecasting horizon of up to several weeks in advance. The paper outlines both the methodological and algorithmic aspects of the modelling, forecasting and signal extraction procedures, including the design and implementation of forecasting support software with a specially designed Graphical User Interface within the Matlab ® computing environment. The forecasting performance is evaluated comprehensively in comparison with the well-known seasonal ARIMA approach.