scholarly journals Regime-Switching Discrete ARMA Models for Categorical Time Series

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 458
Author(s):  
Christian H. Weiß
Keyword(s):  
Time Series ◽  
Regime Switching ◽  
Moving Average ◽  
Model Fitting ◽  
Real Data ◽  
Future Research ◽  
Arma Models ◽  
Categorical Time Series ◽  
Ordinal Time Series ◽  
Stochastic Properties

For the modeling of categorical time series, both nominal or ordinal time series, an extension of the basic discrete autoregressive moving-average (ARMA) models is proposed. It uses an observation-driven regime-switching mechanism, leading to the family of RS-DARMA models. After having discussed the stochastic properties of RS-DARMA models in general, we focus on the particular case of the first-order RS-DAR model. This RS-DAR ( 1 ) model constitutes a parsimoniously parameterized type of Markov chain, which has an easy-to-interpret data-generating mechanism and may also handle negative forms of serial dependence. Approaches for model fitting are elaborated on, and they are illustrated by two real-data examples: the modeling of a nominal sequence from biology, and of an ordinal time series regarding cloudiness. For future research, one might use the RS-DAR ( 1 ) model for constructing parsimonious advanced models, and one might adapt techniques for smoother regime transitions.

Continuous Autoregressive Moving Average Models

2021 ◽  
pp. 118-141
Author(s):  
Yakup Ari
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Discrete Time ◽  
Moving Average ◽  
Likelihood Estimation ◽  
Real Data ◽  
Autoregressive Moving Average ◽  
The Difference

The financial time series have a high frequency and the difference between their observations is not regular. Therefore, continuous models can be used instead of discrete-time series models. The purpose of this chapter is to define Lévy-driven continuous autoregressive moving average (CARMA) models and their applications. The CARMA model is an explicit solution to stochastic differential equations, and also, it is analogue to the discrete ARMA models. In order to form a basis for CARMA processes, the structures of discrete-time processes models are examined. Then stochastic differential equations, Lévy processes, compound Poisson processes, and variance gamma processes are defined. Finally, the parameter estimation of CARMA(2,1) is discussed as an example. The most common method for the parameter estimation of the CARMA process is the pseudo maximum likelihood estimation (PMLE) method by mapping the ARMA coefficients to the corresponding estimates of the CARMA coefficients. Furthermore, a simulation study and a real data application are given as examples.

scholarly journals Study of the forecasting problem of energy consumption of water pumping station

2019 ◽  
Vol 102 ◽  
pp. 03001
Author(s):  
Aleksandr V. Alekseev
Keyword(s):  
Energy Consumption ◽  
Moving Average ◽  
Real Data ◽  
Future Research ◽  
Wholesale Market ◽  
Pumping Station ◽  
Water Pumping ◽  
Object Properties ◽  
Forecasting Methods ◽  
City Water

The article describes the study of the energy consumption forecasting of city water pumping station. The review of the existing approaches for technical systems energy consumption forecasting is made. The shot description of the studied object properties including hourly energy consumption is presented. Two often used forecasting methods exponential smoothing and the autoregression of the integrated moving average methods was tested on real data. The results of predict calculations shows that the autoregression of the integrated moving average methods is suitable for energy consumption planning and can be used to submit an hourly bid for the required amount of the electricity in the wholesale market. Directions for future research is also presented.

scholarly journals Statistical Methods for Predicting Malaria Incidences Using Data from Sudan

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Hamid H. Hussien ◽  
Fathy H. Eissa ◽  
Khidir E. Awadalla
Keyword(s):  
Time Series ◽  
Malaria Incidence ◽  
Moving Average ◽  
Forecast Accuracy ◽  
Transformation Method ◽  
Transformation Model ◽  
Future Research ◽  
Incidence Data ◽  
Moving Average Model ◽  
Using Data

Malaria is the leading cause of illness and death in Sudan. The entire population is at risk of malaria epidemics with a very high burden on government and population. The usefulness of forecasting methods in predicting the number of future incidences is needed to motivate the development of a system that can predict future incidences. The objective of this paper is to develop applicable and understood time series models and to find out what method can provide better performance to predict future incidences level. We used monthly incidence data collected from five states in Sudan with unstable malaria transmission. We test four methods of the forecast: (1) autoregressive integrated moving average (ARIMA); (2) exponential smoothing; (3) transformation model; and (4) moving average. The result showed that transformation method performed significantly better than the other methods for Gadaref, Gazira, North Kordofan, and Northern, while the moving average model performed significantly better for Khartoum. Future research should combine a number of different and dissimilar methods of time series to improve forecast accuracy with the ultimate aim of developing a simple and useful model for producing reasonably reliable forecasts of the malaria incidence in the study area.

scholarly journals A Fuzzy Set-Valued Autoregressive Moving Average Model and Its Applications

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 324 ◽  
Author(s):  
Dabuxilatu Wang ◽  
Liang Zhang
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Empirical Analysis ◽  
Moving Average ◽  
Arma Model ◽  
Autoregressive Moving Average ◽  
Complex Data ◽  
Arma Models ◽  
Linguistic Data ◽  
Series Analysis

Autoregressive moving average (ARMA) models are important in many fields and applications, although they are most widely applied in time series analysis. Expanding the ARMA models to the case of various complex data is arguably one of the more challenging problems in time series analysis and mathematical statistics. In this study, we extended the ARMA model to the case of linguistic data that can be modeled by some symmetric fuzzy sets, and where the relations between the linguistic data of the time series can be considered as the ordinary stochastic correlation rather than fuzzy logical relations. Therefore, the concepts of set-valued or interval-valued random variables can be employed, and the notions of Aumann expectation, Fréchet variance, and covariance, as well as standardized process, were used to construct the ARMA model. We firstly determined that the estimators from the least square estimation of the ARMA (1,1) model under some L2 distance between two sets are weakly consistent. Moreover, the justified linguistic data-valued ARMA model was applied to forecast the linguistic monthly Hang Seng Index (HSI) as an empirical analysis. The obtained results from the empirical analysis indicate that the accuracy of the prediction produced from the proposed model is better than that produced from the classical one-order, two-order, three-order autoregressive (AR(1), AR(2), AR(3)) models, as well as the (1,1)-order autoregressive moving average (ARMA(1,1)) model.

scholarly journals A New Strategy of Hybrid Models using ARIMA, ANN, and DWT in Time Series Modelling

2021 ◽  
Vol 25 (1) ◽  
pp. 27-50
Author(s):  
Tsung-Lin Li ◽  
◽  
Chen-An Tsai ◽  
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Arima Model ◽  
Real Data ◽  
Hybrid Models ◽  
Discrete Wavelet ◽  
Data Sets ◽  
Model Combining ◽  
Time Series Modelling ◽  
Significant Difference

Time series forecasting is a challenging task of interest in many disciplines. A variety of techniques have been developed to deal with the problem through a combination of different disciplines. Although various researches have proved successful for hybrid models, none of them carried out the comparisons with solid statistical test. This paper proposes a new stepwise model determination method for artificial neural network (ANN) and a novel hybrid model combining autoregressive integrated moving average (ARIMA) model, ANN and discrete wavelet transformation (DWT). Simulation studies are conducted to compare the performance of different models, including ARIMA, ANN, ARIMA-ANN, DWT-ARIMA-ANN and the proposed method, ARIMA-DWT-ANN. Also, two real data sets, Lynx data and cabbage data, are used to demonstrate the applications. Our proposed method, ARIMA-DWT-ANN, outperforms other methods in both simulated datasets and Lynx data, while ANN shows a better performance in the cabbage data. We conducted a two-way ANOVA test to compare the performances of methods. The results showed a significant difference between methods. As a brief conclusion, it is suggested to try on ANN and ARIMA-DWT-ANN due to their robustness and high accuracy. Since the performance of hybrid models may vary across data sets based on their ARIMA alike or ANN alike natures, they should all be considered when encountering a new data to reach an optimal performance.

scholarly journals COVID-19 pandemic control using restrictions and vaccination

2021 ◽  
Vol 19 (2) ◽  
pp. 1355-1372
Author(s):  
Vinicius Piccirillo ◽  
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Real Data ◽  
The United States ◽  
Prevention Policy ◽  
Autoregressive Integrated Moving Average ◽  
Infected People ◽  
Marquardt Algorithm ◽  
The Impact ◽  
Methods Numerical

<abstract><p>This work deals with the impact of the vaccination in combination with a restriction parameter that represents non-pharmaceutical interventions measures applied to the compartmental SEIR model in order to control the COVID-19 epidemic. This restriction parameter is used as a control parameter, and the univariate autoregressive integrated moving average (ARIMA) is used to forecast the time series of vaccination of all individuals of a specific country. Having in hand the time series of the population fully vaccinated (real data + forecast), the Levenberg–Marquardt algorithm is used to fit an analytic function that models this evolution over time. Here, it is used two time series of real data that refer to a slow vaccination obtained from India and Brazil, and two faster vaccination as observed in Israel and the United States of America. Together with vaccination, two different control approaches are presented in this paper, which enable reduces the infected people successfully: namely, the feedback and nonfeedback control methods. Numerical results predict that vaccination can reduce the peaks of infections and the duration of the pandemic, however, a better result is achieved when the vaccination is combined with any restrictions or prevention policy.</p></abstract>

scholarly journals Multi-scale CO2

2021 ◽  
Author(s):  
Xiaomeng Gu ◽  
Andrew Viggo Metcalfe ◽  
Gary Glonek
Keyword(s):  
Time Series ◽  
Seasonal Variation ◽  
Industrial Revolution ◽  
Moving Average ◽  
Arima Models ◽  
Arma Models ◽  
Deterministic Models ◽  
Increasing Trend ◽  
Exponential Trend ◽  
Sampling Intervals

Abstract Five time series of estimated atmospheric CO 2 with sampling intervals ranging from 0.5 million years to the relatively high frequency of one week are analysed. The yearly series shows a clear increasing trend since the beginning of the first Industrial Revolution around 1760. The weekly series shows a clear increasing trend and also seasonal variation. In both cases, the trend is fitted by a conceptual model that consists of a baseline value with an exponential trend superimposed. For the weekly series, the seasonal variation is modelled as an exponential of a sum of sine and cosine terms. The deviations from these deterministic models are treated as detrended and deseasonalised time series.Then,threesub-categoriesof autoregressive integrated moving average (ARIMA) models are fitted to the five time series: ARMA models which are stationary; FARIMA models which are stationary but have long memory and are fractal processes, and ARIMA models which are variations on a random walk and so non-stationary in the variance.The FARIMA and ARIMA models provide better fits to the data than the corresponding ARMA models. All the fitted models are close to the boundary of stability, and are consistent with claims that climate change due to an increase in atmospheric CO 2 may not quickly be reversed even if CO 2 emissions are stopped.

Modeling and Prediction of Great Salt Lake Elevation Time Series Based on ARFIMA

2007 ◽  
Author(s):  
Rongtao Sun ◽  
YangQuan Chen ◽  
Qianru Li
Keyword(s):  
Time Series ◽  
Salt Lake ◽  
Moving Average ◽  
Great Salt Lake ◽  
Estimation Methods ◽  
Arma Models ◽  
Modeling And Prediction ◽  
The People ◽  
Arfima Model ◽  
Parameter Estimation Methods

The elevation of Great Salt Lake (GSL) has a great impact on the people of Utah. The flood of GSL in 1982 has caused a loss of millions of dollars. Therefore, it is very important to predict the GSL levels as precisely as possible. This paper points out the reason why conventional methods failed to describe adequately the rise and fall of the GSL levels — the long-range dependence (LRD) property. The LRD of GSL elevation time series is characterized by some most commonly used Hurst parameter estimation methods in this paper. Then, according to the revealed LRD, the autoregressive fractional integrated moving average (ARFIMA) model is applied to analyze the data and predict the future levels. We have shown that the prediction results has a better performance compared to the conventional ARMA models.

TIME-SERIES MODEL WITH PERIODIC STOCHASTIC REGIME SWITCHING

2000 ◽  
Vol 4 (4) ◽  
pp. 467-486 ◽  
Author(s):  
Eric Ghysels
Keyword(s):  
Time Series ◽  
Regime Switching ◽  
Transition Probabilities ◽  
Time Series Model ◽  
Time Series Models ◽  
Seasonal Cycles ◽  
Arma Processes ◽  
Regime Switching Models ◽  
Switching Models ◽  
Stochastic Properties

We present a class of stochastic regime-switching models. The time-series models may have periodic transition probabilities and the drifts may be seasonal. In the latter case, the model exhibits seasonal dummy variation that may change with the regime. The processes entail nontrivial interactions between so-called business and seasonal cycles. We discuss the stochastic properties as well as their relationship with periodic ARMA processes. Estimation and testing are also discussed in detail.

scholarly journals Measures of Dispersion and Serial Dependence in Categorical Time Series

Econometrics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 17 ◽  
Author(s):  
Christian H. Weiß
Keyword(s):  
Time Series ◽  
Real Data ◽  
Asymptotic Distributions ◽  
Serial Dependence ◽  
Finite Sample ◽  
Categorical Time Series ◽  
Dispersion Measures ◽  
Measures Of Dispersion ◽  
Dependence Measures ◽  
Economics And Biology

The analysis and modeling of categorical time series requires quantifying the extent of dispersion and serial dependence. The dispersion of categorical data is commonly measured by Gini index or entropy, but also the recently proposed extropy measure can be used for this purpose. Regarding signed serial dependence in categorical time series, we consider three types of κ -measures. By analyzing bias properties, it is shown that always one of the κ -measures is related to one of the above-mentioned dispersion measures. For doing statistical inference based on the sample versions of these dispersion and dependence measures, knowledge on their distribution is required. Therefore, we study the asymptotic distributions and bias corrections of the considered dispersion and dependence measures, and we investigate the finite-sample performance of the resulting asymptotic approximations with simulations. The application of the measures is illustrated with real-data examples from politics, economics and biology.

Sign in / Sign up

Export Citation Format

Share Document