Kumaraswamy autoregressive moving average models for double bounded environmental data

Bayer, Fábio M.; Bayer, Débora Missio; Pumi, Guilherme

doi:10.1016/j.jhydrol.2017.10.006

Cited by 55 publications

(49 citation statements)

References 47 publications

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“…is the r-dimensional explanatory variables vector, = ( 1 , … , p ) ⊤ and = ( 1 , … , q ) ⊤ are the autoregressive and moving average coefficients respectively, r t is a random error, and is an intercept. In this article, we consider the errors measured on the predictor scale r t = g(y t ) − g( t ) as in Rocha and Cribari-Neto (2009), Bayer et al (2017), and Benjamin et al (2003). The proposed CMP-ARMA(p, q) model is defined by (3) and (5).…”

Section: The Proposed Modelmentioning

confidence: 99%

“…One of the advantages of time series models based on GLM is that they straightforwardly describe covariate effects and negative autocorrelations (Liboschik et al ). In addition to the GARMA model, several time series models based on GLM with different distributions have been considered in the literature (Li, ; ; Fokianos and Kedem, ; Rocha and Cribari‐Neto, ; Bayer et al ).…”

Section: Introductionmentioning

confidence: 99%

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Conway–Maxwell–Poisson Autoregressive Moving Average Model for Equidispersed, Underdispersed, and Overdispersed Count Data

Melo

Alencar

2020

Journal Time Series Analysis

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In this work, we propose a dynamic regression model based on the Conway-Maxwell-Poisson (CMP) distribution with time-varying conditional mean depending on covariates and lagged observations. This new class of Conway-Maxwell-Poisson autoregressive moving average (CMP-ARMA) models is suitable for the analysis of time series of counts. The CMP distribution is a two-parameter generalization of the Poisson distribution that allows the modeling of underdispersed, equidispersed, and overdispersed data. Our main contribution is to combine this dispersion flexibility with the inclusion of lagged terms to model the conditional mean response, inducing an autocorrelation structure, usually relevant in time series. We present the conditional maximum likelihood estimation, hypothesis testing inference, diagnostic analysis, and forecasting along with their asymptotic properties. In particular, we provide closed-form expressions for the conditional score vector and conditional Fisher information matrix. We conduct a Monte Carlo experiment to evaluate the performance of the estimators in finite sample sizes. Finally, we illustrate the usefulness of the proposed model by exploring two empirical applications.

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Section: The Proposed Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Conway–Maxwell–Poisson Autoregressive Moving Average Model for Equidispersed, Underdispersed, and Overdispersed Count Data

Melo

Alencar

2020

Journal Time Series Analysis

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“…An extension of the model that incorporates seasonal dynamics, the β SARMA model, was recently proposed by Bayer, Cintra, and Cribari‐Neto (), and an extension of the model for compositional data, the DARMA model (“D” stands for Dirichlet), was developed by Zheng and Chen (). A dynamic model for doubly bounded random variables based on an alternative law—the Kumaraswamy law—was introduced by Bayer, Bayer, and Pumi (). In what follows, we shall focus on the standard, baseline β ARMA model.…”

Section: The Modelmentioning

confidence: 99%

“…The latter two models were selected based on the AIC using the auto.arima function of the forecast package (Hyndman & Khandakar, ) of the R statistical computing environment (R Core Team, ). We also used the KARMA(1,1) model (Bayer et al, ); again, model selection was performed using the AIC. Finally, we considered the Holt exponential smoothing algorithm, as implemented in the holt function of the R forecast package.…”

Section: Empirical Hydrological Applicationmentioning

confidence: 99%

Goodness‐of‐fit tests forβARMA hydrological time series modeling

et al. 2019

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We address the issue of performing portmanteau testing inference using time series data that assume values in the standard unit interval. The motivation involves modeling the time series dynamics of the proportion of stocked hydroelectric energy in the South of Brazil. Our focus lies in the class of beta autoregressive moving average (βARMA) models. In particular, we wish to test the goodness‐of‐fit of such models. We consider several testing criteria that have been proposed for Gaussian time series models and introduce two new tests. We derive the asymptotic null distribution of the two proposed test statistics in two different scenarios, namely, when the tests are applied to an observed time series and when they are applied to the residuals from a fitted βARMA model. It is worth noticing that our results imply the asymptotic validity of standard portmanteau tests in the class of βARMA models that are, under the null hypothesis, asymptotically equivalent to our test statistics. We use Monte Carlo simulation to assess the relative merits of the different portmanteau tests when used with fitted βARMA models. The simulation results we present show that the new tests are typically more powerful than a well‐known test whose test statistic is also based on residual partial autocorrelations. Overall, the tests we propose perform quite well. Finally, we model the dynamics of the proportion of stocked hydroelectric energy in Brazil. The results show that the βARMA model outperforms three alternative models and an exponential smoothing algorithm.

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“…In general, stochastic time series models can be classified into two kinds: univariate and multivariate models. Univariate models consist of single variable series which can be modeled by autoregressive moving average (ARMA), autoregressive integrated moving average (ARIMA) group of models (Young 1999;Ahn 2000;Bidwell 2005;Adamowski & Chan 2011;Pektas & Cigizoglu 2013;Bayer et al 2017), or traditional decomposition-based time series models (Peng & Liu 2000;Yang et al 2009;Lu et al 2013;Moeeni et al 2017). On the other hand, multivariate models involve two or more input variables and their dynamic relationships with the output can be modeled by transfer function-noise (TFN) modeling technique.…”

Section: Introductionmentioning

confidence: 99%

A novel deseasonalized time series model with an improved seasonal estimate for groundwater level predictions

2019

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Groundwater level prediction and forecasting using univariate time series models are useful for effective groundwater management under data limiting conditions. The seasonal autoregressive integrated moving average (SARIMA) models are widely used for modeling groundwater level data as the groundwater level signals possess the seasonality pattern. Alternatively, deseasonalized autoregressive and moving average models (Ds-ARMA) can be modeled with deseasonalized groundwater level signals in which the seasonal component is estimated and removed from the raw groundwater level signals. The seasonal component is traditionally estimated by calculating long-term averaging values of the corresponding months in the year. This traditional way of estimating seasonal component may not be appropriate for non-stationary groundwater level signals. Thus, in this study, an improved way of estimating the seasonal component by adopting a 13-month moving average trend and corresponding confidence interval approach has been attempted. To test the proposed approach, two representative observation wells from Adyar basin, India were modeled by both traditional and proposed methods. It was observed from this study that the proposed model prediction performance was better than the traditional model's performance with R2 values of 0.82 and 0.93 for the corresponding wells' groundwater level data.

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Kumaraswamy autoregressive moving average models for double bounded environmental data

Cited by 55 publications

References 47 publications

Conway–Maxwell–Poisson Autoregressive Moving Average Model for Equidispersed, Underdispersed, and Overdispersed Count Data

Conway–Maxwell–Poisson Autoregressive Moving Average Model for Equidispersed, Underdispersed, and Overdispersed Count Data

Goodness‐of‐fit tests forβARMA hydrological time series modeling

A novel deseasonalized time series model with an improved seasonal estimate for groundwater level predictions

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