scholarly journals Likelihood Inference for Generalized Integer Autoregressive Time Series Models

Econometrics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 43 ◽  
Author(s):  
Harry Joe
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Probability Generating Function ◽  
Likelihood Estimation ◽  
Model Fit ◽  
Likelihood Inference ◽  
Series Data ◽  
Time Series Models ◽  
Autoregressive Time Series ◽  
The Past

For modeling count time series data, one class of models is generalized integer autoregressive of order p based on thinning operators. It is shown how numerical maximum likelihood estimation is possible by inverting the probability generating function of the conditional distribution of an observation given the past p observations. Two data examples are included and show that thinning operators based on compounding can substantially improve the model fit compared with the commonly used binomial thinning operator.

scholarly journals Gaussian and Non-Gaussian Autoregressive Time Series Models with Rainfall Data

2019 ◽  
Vol 9 (1) ◽  
pp. 6699-6704
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Time Series Data ◽  
Autoregressive Models ◽  
Annual Rainfall ◽  
Series Data ◽  
Time Series Models ◽  
Chi Square ◽  
Autoregressive Time Series ◽  
Non Gaussian

The Gaussian and non- Gaussian autoregressive models are used in this paper for analyzing time series data. The autoregressive time series models with various distributions are considered here for analyzing the annual rainfall of Punjab, India. Three different types of autoregressive models are applied here for analyzing data namely autoregressive model with Gaussian, Gamma and Laplace distribution. For the goodness of fit the chi - square test is applied and the best fitted distribution is obtained for the data. Next the stationarity of data is checked, after that models are applied on data for comparing three distributions of AR models and lastly the best fitted model is obtained. The residual checking of selected model is also discussed and forecast the best fitted model based on simulated response comparison.

AN ILLUSTRATION OF GENERALISED ARMA (GARMA) TIME SERIES MODELING OF FOREST AREA IN MALAYSIA

2012 ◽  
Vol 09 ◽  
pp. 390-397 ◽  
Author(s):  
THULASYAMMAL RAMIAH PILLAI ◽  
MAHENDRAN SHITAN
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Likelihood Estimation ◽  
Forest Area ◽  
Series Data ◽  
Tree Plantations ◽  
Time Series Models ◽  
Time Series Modeling ◽  
New Class ◽  
Area Data

Forestry is the art and science of managing forests, tree plantations, and related natural resources. The main goal of forestry is to create and implement systems that allow forests to continue a sustainable provision of environmental supplies and services. Forest area is land under natural or planted stands of trees, whether productive or not. Forest area of Malaysia has been observed over the years and it can be modeled using time series models. A new class of GARMA models have been introduced in the time series literature to reveal some hidden features in time series data. For these models to be used widely in practice, we illustrate the fitting of GARMA (1, 1; 1, δ) model to the Annual Forest Area data of Malaysia which has been observed from 1987 to 2008. The estimation of the model was done using Hannan-Rissanen Algorithm, Whittle's Estimation and Maximum Likelihood Estimation.

Cosinor Analysis for Temperature Time Series Data of Long Duration

2007 ◽  
Vol 9 (1) ◽  
pp. 30-41 ◽  
Author(s):  
Nikhil S. Padhye ◽  
Sandra K. Hanneman
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Model Fit ◽  
Series Data ◽  
Model Parameters ◽  
Cosinor Analysis ◽  
Long Time ◽  
Improved Model ◽  
Data Length ◽  
Cosinor Models

The application of cosinor models to long time series requires special attention. With increasing length of the time series, the presence of noise and drifts in rhythm parameters from cycle to cycle lead to rapid deterioration of cosinor models. The sensitivity of amplitude and model-fit to the data length is demonstrated for body temperature data from ambulatory menstrual cycling and menopausal women and from ambulatory male swine. It follows that amplitude comparisons between studies cannot be made independent of consideration of the data length. Cosinor analysis may be carried out on serial-sections of the series for improved model-fit and for tracking changes in rhythm parameters. Noise and drift reduction can also be achieved by folding the series onto a single cycle, which leads to substantial gains in the model-fit but lowers the amplitude. Central values of model parameters are negligibly changed by consideration of the autoregressive nature of residuals.

A UNIFIED APPROACH TO THE MEASUREMENT ERROR PROBLEM IN TIME SERIES MODELS

2002 ◽  
Vol 18 (2) ◽  
pp. 278-296 ◽  
Author(s):  
Katsuto Tanaka
Keyword(s):  
Time Series ◽  
Random Walk ◽  
Measurement Error ◽  
Long Memory ◽  
Time Series Data ◽  
Series Data ◽  
Time Series Models ◽  
Unified Approach ◽  
Underlying Process ◽  
Short Memory

The measurement error problem that we consider in this paper is concerned with the situation where time series data of various kinds—short memory, long memory, and random walk processes—are contaminated by white noise. We suggest a unified approach to testing for the existence of such noise. It is found that the power of our test crucially depends on the underlying process.

scholarly journals Reconsidering the importance of the past in predator–prey models: both numerical and functional responses depend on delayed prey densities

2013 ◽  
Vol 280 (1768) ◽  
pp. 20131389 ◽  
Author(s):  
Jiqiu Li ◽  
Andy Fenton ◽  
Lee Kettley ◽  
Phillip Roberts ◽  
David J. S. Montagnes
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Prey Abundance ◽  
Series Data ◽  
Functional Responses ◽  
New Approach ◽  
Predator Prey ◽  
The Past ◽  
Predator Prey Models ◽  
Underlying Mechanisms

We propose that delayed predator–prey models may provide superficially acceptable predictions for spurious reasons. Through experimentation and modelling, we offer a new approach: using a model experimental predator–prey system (the ciliates Didinium and Paramecium ), we determine the influence of past-prey abundance at a fixed delay (approx. one generation) on both functional and numerical responses (i.e. the influence of present : past-prey abundance on ingestion and growth, respectively). We reveal a nonlinear influence of past-prey abundance on both responses, with the two responding differently. Including these responses in a model indicated that delay in the numerical response drives population oscillations, supporting the accepted (but untested) notion that reproduction, not feeding, is highly dependent on the past. We next indicate how delays impact short- and long-term population dynamics. Critically, we show that although superficially the standard (parsimonious) approach to modelling can reasonably fit independently obtained time-series data, it does so by relying on biologically unrealistic parameter values. By contrast, including our fully parametrized delayed density dependence provides a better fit, offering insights into underlying mechanisms. We therefore present a new approach to explore time-series data and a revised framework for further theoretical studies.

scholarly journals Empirical Evaluation of Alternative Time-Series Models for COVID-19 Forecasting in Saudi Arabia

2021 ◽  
Vol 18 (16) ◽  
pp. 8660
Author(s):  
Isra Al-Turaiki ◽  
Fahad Almutlaq ◽  
Hend Alrasheed ◽  
Norah Alballa
Keyword(s):  
Time Series ◽  
Saudi Arabia ◽  
Time Series Data ◽  
Arima Model ◽  
Empirical Evaluation ◽  
Cubic Spline ◽  
Exponential Smoothing ◽  
Series Data ◽  
Time Series Models ◽  
Forecasting Models

COVID-19 is a disease-causing coronavirus strain that emerged in December 2019 that led to an ongoing global pandemic. The ability to anticipate the pandemic’s path is critical. This is important in order to determine how to combat and track its spread. COVID-19 data is an example of time-series data where several methods can be applied for forecasting. Although various time-series forecasting models are available, it is difficult to draw broad theoretical conclusions regarding their relative merits. This paper presents an empirical evaluation of several time-series models for forecasting COVID-19 cases, recoveries, and deaths in Saudi Arabia. In particular, seven forecasting models were trained using autoregressive integrated moving average, TBATS, exponential smoothing, cubic spline, simple exponential smoothing Holt, and HoltWinters. The models were built using publicly available daily data of COVID-19 during the period of 24 March 2020 to 5 April 2021 reported in Saudi Arabia. The experimental results indicate that the ARIMA model had a smaller prediction error in forecasting confirmed cases, which is consistent with results reported in the literature, while cubic spline showed better predictions for recoveries and deaths. As more data become available, a fluctuation in the forecasting-accuracy metrics was observed, possibly due to abrupt changes in the data.

scholarly journals Model Rantai Markov dan Model ARIMA serta Kombinasinya dalam Memprediksi Curah Hujan di Kota Makassar

2019 ◽  
Vol 1 (1) ◽  
pp. 8
Author(s):  
Ahmad Zaki ◽  
Wahidah Sanusi ◽  
Saiful Bahri
Keyword(s):  
Time Series ◽  
Markov Chain ◽  
Time Series Data ◽  
Time Sequence ◽  
Monthly Rainfall ◽  
Series Data ◽  
Time Series Models ◽  
Time Series Modeling ◽  
Discrete Variable ◽  
Future Events

Abstrak. Curah hujan merupakan suatu data deret waktu yang bersifat kontinu, namun juga dapat diformulasikan sebagai peubah diskrit yaitu dengan menggolongkan suatu hari menjadi hujan dan tidak hujan. Curah hujan yang dicatat oleh pos hujan dapat digunakan untuk memprediksi curah hujan pada waktu yang akan datang melalui pemodelan deret waktu ARIMA musiman, Rantai Markov atau dengan campuran keduanya. Proses Markov merupakan suatu sistem stokastik di mana kejadian di masa yang akan datang bergantung pada kejadian sesaat sebelumnya Deret waktu merupakan serangkaian data yang disusun menurut urutan waktu Tujuan penelitian ini adalah untuk memodelkan dan memprediksi curah hujan dengan campuran Rantai Markov dan model deret waktu. Data yang digunakan dalam penelitian ini adalah curah hujan bulanan kota Makassar tahun 2007 sampai 2017. Campuran model deret waktu lebih sesuai digunakan untuk memprediksi curah hujan bulanan dibandingkan dengan pemodelan deret waktu saja hal ini dapat dilihat dai nilai MSE.Kata Kunci: Rantai Markov, Deret Waktu, ARIMA MusimanAbstract. Rainfall is a time series data that is continuous, but can also be formulated as a discrete variable that is by classifying one day as rainy and not rainy. Rainfall recorded by rain posts can be used to predict rainfall in the future through seasonal ARIMA time series modeling, Markov Chain or with a mixture of both. The Markov process is a stochastic system in which future events depend on the events of the previous moment. The time series is a series of data arranged in time sequence. The purpose of this study is to model and predict rainfall with a mixture of Markov Chains and time series models. The data used in this study is the monthly rainfall of Makassar city in 2007 to 2017. A mixture of time series models is more suitable to be used to predict monthly rainfall compared to modeling time series. This can be seen from the MSE value.Keywords: Markov chain, Time Series, seasonal ARIMA.

scholarly journals Time-Series Causality with Missing Data

2021 ◽  
Vol 6 (1) ◽  
pp. 1-4
Author(s):  
Bo Yuan Chang ◽  
Mohamed A. Naiel ◽  
Steven Wardell ◽  
Stan Kleinikkink ◽  
John S. Zelek
Keyword(s):  
Time Series ◽  
Missing Data ◽  
Missing Values ◽  
Time Series Data ◽  
Multivariate Time Series ◽  
Gaussian Process Regression ◽  
Series Data ◽  
Causal Relationships ◽  
Sampled Data ◽  
The Past

Over the past years, researchers have proposed various methods to discover causal relationships among time-series data as well as algorithms to fill in missing entries in time-series data. Little to no work has been done in combining the two strategies for the purpose of learning causal relationships using unevenly sampled multivariate time-series data. In this paper, we examine how the causal parameters learnt from unevenly sampled data (with missing entries) deviates from the parameters learnt using the evenly sampled data (without missing entries). However, to obtain the causal relationship from a given time-series requires evenly sampled data, which suggests filling the missing data values before obtaining the causal parameters. Therefore, the proposed method is based on applying a Gaussian Process Regression (GPR) model for missing data recovery, followed by several pairwise Granger causality equations in Vector Autoregssive form to fit the recovered data and obtain the causal parameters. Experimental results show that the causal parameters generated by using GPR data filling offers much lower RMSE than the dummy model (fill with last seen entry) under all missing values percentage, suggesting that GPR data filling can better preserve the causal relationships when compared with dummy data filling, thus should be considered when dealing with unevenly sampled time-series causality learning.

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