Piecewise autoregression for general integer-valued time series

Diop, Mamadou Lamine; Kengne, William

doi:10.1016/j.jspi.2020.07.003

Cited by 12 publications

(5 citation statements)

References 28 publications

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“…This result is consistent with the results of a study by Walker et al [ 21 ] showing that a declining population-level Ct value preceded increases in SARS-CoV-2 positivity tests. Another study showed a negative association between individual Ct values and severity of symptoms of COVID-19 [ 25 ].…”

Section: Discussionsupporting

confidence: 93%

“…If the time series has a seasonal trend, seasonal differences are used to stabilize the series. The AR parameter p represents the linear correlation of the current value of the time series Y t with the previous values Y t–1 , Y t–2 ,... and current residuals ε t [ 21 ]. The MA parameter q shows the linear correlation of the current value of the time series Y t with the current and previous residuals of the time series ε t , ε t–1 ,… [ 22 ].…”

Section: Methodsmentioning

confidence: 99%

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The Relationship Between Population-Level SARS-CoV-2 Cycle Threshold Values and Trend of COVID-19 Infection: Longitudinal Study

Dehesh¹,

Baradaran²,

Eshrati³

et al. 2022

JMIR Public Health Surveill

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Background The distribution of population-level real-time reverse transcription-polymerase chain reaction (RT-PCR) cycle threshold (Ct) values as a proxy of viral load may be a useful indicator for predicting COVID-19 dynamics. Objective The aim of this study was to determine the relationship between the daily trend of average Ct values and COVID-19 dynamics, calculated as the daily number of hospitalized patients with COVID-19, daily number of new positive tests, daily number of COVID-19 deaths, and number of hospitalized patients with COVID-19 by age. We further sought to determine the lag between these data series. Methods The samples included in this study were collected from March 21, 2021, to December 1, 2021. Daily Ct values of all patients who were referred to the Molecular Diagnostic Laboratory of Iran University of Medical Sciences in Tehran, Iran, for RT-PCR tests were recorded. The daily number of positive tests and the number of hospitalized patients by age group were extracted from the COVID-19 patient information registration system in Tehran province, Iran. An autoregressive integrated moving average (ARIMA) model was constructed for the time series of variables. Cross-correlation analysis was then performed to determine the best lag and correlations between the average daily Ct value and other COVID-19 dynamics–related variables. Finally, the best-selected lag of Ct identified through cross-correlation was incorporated as a covariate into the autoregressive integrated moving average with exogenous variables (ARIMAX) model to calculate the coefficients. Results Daily average Ct values showed a significant negative correlation (23-day time delay) with the daily number of newly hospitalized patients (P=.02), 30-day time delay with the daily number of new positive tests (P=.02), and daily number of COVID-19 deaths (P=.02). The daily average Ct value with a 30-day delay could impact the daily number of positive tests for COVID-19 (β=–16.87, P<.001) and the daily number of deaths from COVID-19 (β=–1.52, P=.03). There was a significant association between Ct lag (23 days) and the number of COVID-19 hospitalizations (β=–24.12, P=.005). Cross-correlation analysis showed significant time delays in the average Ct values and daily hospitalized patients between 18-59 years (23-day time delay, P=.02) and in patients over 60 years old (23-day time delay, P<.001). No statistically significant relation was detected in the number of daily hospitalized patients under 5 years old (9-day time delay, P=.27) and aged 5-17 years (13-day time delay, P=.39). Conclusions It is important for surveillance of COVID-19 to find a good indicator that can predict epidemic surges in the community. Our results suggest that the average daily Ct value with a 30-day delay can predict increases in the number of positive confirmed COVID-19 cases, which may be a useful indicator for the health system.

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Section: Discussionsupporting

confidence: 93%

Section: Methodsmentioning

confidence: 99%

The Relationship Between Population-Level SARS-CoV-2 Cycle Threshold Values and Trend of COVID-19 Infection: Longitudinal Study

Dehesh¹,

Baradaran²,

Eshrati³

et al. 2022

JMIR Public Health Surveill

View full text Add to dashboard Cite

show abstract

“…Box-Jenkins (ARMA) forecasting model is very popular as it has high prediction efficiency in the stationary time series analysis [ 23 ]. An autoregression AR is a known time series method used to predict the future value by using observations from previous -time steps as inputs to the regression equation multiplied by the appropriate coefficients of AR [ 24 , 25 ]. Besides, the sum is extended by adding the mean of the series and white noise that is a random error.…”

Section: Methodsmentioning

confidence: 99%

ARIMA models for predicting the end of COVID-19 pandemic and the risk of second rebound

Malki

Atlam

Ewis

et al. 2020

Neural Comput & Applic

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Globally, many research works are going on to study the infectious nature of COVID-19 and every day we learn something new about it through the flooding of the huge data that are accumulating hourly rather than daily which instantly opens hot research avenues for artificial intelligence researchers. However, the public’s concern by now is to find answers for two questions; (1) When this COVID-19 pandemic will be over? and (2) After coming to its end, will COVID-19 return again in what is known as a second rebound of the pandemic? In this work, we developed a predictive model that can estimate the expected period that the virus can be stopped and the risk of the second rebound of COVID-19 pandemic. Therefore, we have considered the SARIMA model to predict the spread of the virus on several selected countries and used it for predicting the COVID-19 pandemic life cycle and its end. The study can be applied to predict the same for other countries as the nature of the virus is the same everywhere. The proposed model investigates the statistical estimation of the slowdown period of the pandemic which is extracted based on the concept of normal distribution. The advantages of this study are that it can help governments to act and make sound decisions and plan for future so that the anxiety of the people can be minimized and prepare the mentality of people for the next phases of the pandemic. Based on the experimental results and simulation, the most striking finding is that the proposed algorithm shows the expected COVID-19 infections for the top countries of the highest number of confirmed cases will be manifested between Dec-2020 and Apr-2021. Moreover, our study forecasts that there may be a second rebound of the pandemic in a year time if the currently taken precautions are eased completely. We have to consider the uncertain nature of the current COVID-19 pandemic and the growing inter-connected and complex world, that are ultimately demanding flexibility, robustness and resilience to cope with the unexpected future events and scenarios.

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“…Two recent studies, Weiß and Feld (2020) and Weiß et al (2019), partially follow the direction outlined by Jung et al (2016), but concentrate on the case of unbounded counts. Diop and Kenge (2020) propose a penalized criterion relying on a Poisson quasi-likelihood approach for some INGARCH-type processes of counts, and they prove its consistency under certain regularity conditions. We also point out the work by Katz (1981), but this cannot be applied here, because it focuses on the order selection of general finite Markov processes, that is, without the parametric relations implied by the models in Sect.…”

Section: Using Information Criteria For Model Selectionmentioning

confidence: 99%

Models for autoregressive processes of bounded counts: How different are they?

2020

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We focus on purely autoregressive (AR)-type models defined on the bounded range {0, 1, . . . , n} with a fixed upper limit n ∈ N. These include the binomial AR model, binomial AR conditional heteroscedasticity (ARCH) model, binomial-variation AR model with their linear conditional mean, nonlinear max-binomial AR model, and binomial logit-ARCH model. We consider the key problem of identifying which of these AR-type models is the true data-generating process. Despite the volume of the literature on model selection, little is known about this procedure in the context of nonnested and nonlinear time series models for counts. We consider the most popular approaches used for model identification, Akaike's information criterion and the Bayesian information criterion, and compare them using extensive Monte Carlo simulations. Furthermore, we investigate the properties of the fitted models (both the correct and wrong models) obtained using maximum likelihood estimation. A real-data example demonstrates our findings.

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Piecewise autoregression for general integer-valued time series

Cited by 12 publications

References 28 publications

The Relationship Between Population-Level SARS-CoV-2 Cycle Threshold Values and Trend of COVID-19 Infection: Longitudinal Study

The Relationship Between Population-Level SARS-CoV-2 Cycle Threshold Values and Trend of COVID-19 Infection: Longitudinal Study

ARIMA models for predicting the end of COVID-19 pandemic and the risk of second rebound

Models for autoregressive processes of bounded counts: How different are they?

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