Fractional Arima Models

A class of univariate fractional ARIMA models with a continuous time parameter is developed for the purpose of modeling long-memory time series. The spectral density of discretely observed data is derived for both point observations (stock variables) and integral observations (flow variables). A frequency domain maximum likelihood method is proposed for estimating the longmemory parameter and is shown to be consistent and asymptotically normally distributed, and some issues associated with the computation of the spectral density are explored.

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A new architecture based on ARIMA models for the safety classification of inter-city routes using meteorological metrics

Proceedings of the 4th International Conference on Smart City Applications - SCA '19 ◽

10.1145/3368756.3369067 ◽

2019 ◽

Author(s):

Samir Allach ◽

Badr Benamrou ◽

Mohamed Ben Ahmed ◽

Anouar Abdelhakim Boudhir ◽

Mustapha Ouardouz

Keyword(s):

Arima Models

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Hybrid Model for Time Series of Complex Structure with ARIMA Components

Mathematics ◽

10.3390/math9101122 ◽

2021 ◽

Vol 9 (10) ◽

pp. 1122

Author(s):

Oksana Mandrikova ◽

Nadezhda Fetisova ◽

Yuriy Polozov

Keyword(s):

Neural Network ◽

Time Series ◽

Hybrid Model ◽

Complex Structure ◽

Arima Model ◽

Ionospheric Parameter ◽

Arima Models ◽

Complicated Structure ◽

Threshold Functions ◽

Anomalous Component

A hybrid model for the time series of complex structure (HMTS) was proposed. It is based on the combination of function expansions in a wavelet series with ARIMA models. HMTS has regular and anomalous components. The time series components, obtained after expansion, have a simpler structure that makes it possible to identify the ARIMA model if the components are stationary. This allows us to obtain a more accurate ARIMA model for a time series of complicated structure and to extend the area for application. To identify the HMTS anomalous component, threshold functions are applied. This paper describes a technique to identify HMTS and proposes operations to detect anomalies. With the example of an ionospheric parameter time series, we show the HMTS efficiency, describe the results and their application in detecting ionospheric anomalies. The HMTS was compared with the nonlinear autoregression neural network NARX, which confirmed HMTS efficiency.

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Modeling of Lake Malombe Annual Fish Landings and Catch per Unit Effort (CPUE)

Forecasting ◽

10.3390/forecast3010004 ◽

2021 ◽

Vol 3 (1) ◽

pp. 39-55

Author(s):

Rodgers Makwinja ◽

Seyoum Mengistou ◽

Emmanuel Kaunda ◽

Tena Alemiew ◽

Titus Bandulo Phiri ◽

...

Keyword(s):

Time Series ◽

Information Criterion ◽

Coefficient Of Determination ◽

Series Data ◽

Efficiency Coefficient ◽

Arima Models ◽

Catch Per Unit Effort ◽

Annual Fish ◽

Unit Effort ◽

The Mean

Forecasting, using time series data, has become the most relevant and effective tool for fisheries stock assessment. Autoregressive integrated moving average (ARIMA) modeling has been commonly used to predict the general trend for fish landings with increased reliability and precision. In this paper, ARIMA models were applied to predict Lake Malombe annual fish landings and catch per unit effort (CPUE). The annual fish landings and CPUE trends were first observed and both were non-stationary. The first-order differencing was applied to transform the non-stationary data into stationary. Autocorrelation functions (AC), partial autocorrelation function (PAC), Akaike information criterion (AIC), Bayesian information criterion (BIC), square root of the mean square error (RMSE), the mean absolute error (MAE), percentage standard error of prediction (SEP), average relative variance (ARV), Gaussian maximum likelihood estimation (GMLE) algorithm, efficiency coefficient (E2), coefficient of determination (R2), and persistent index (PI) were estimated, which led to the identification and construction of ARIMA models, suitable in explaining the time series and forecasting. According to the measures of forecasting accuracy, the best forecasting models for fish landings and CPUE were ARIMA (0,1,1) and ARIMA (0,1,0). These models had the lowest values AIC, BIC, RMSE, MAE, SEP, ARV. The models further displayed the highest values of GMLE, PI, R2, and E2. The “auto. arima ()” command in R version 3.6.3 further displayed ARIMA (0,1,1) and ARIMA (0,1,0) as the best. The selected models satisfactorily forecasted the fish landings of 2725.243 metric tons and CPUE of 0.097 kg/h by 2024.

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