The k-factor GARMA Process with Infinite Variance Innovations

The ever-increasing amount of network traffic generated by various devices and applications has made it crucial to have efficient methods for analyzing and managing network traffic. Traditional approaches, such as statistical modeling, have yet to be proven enough due to network traffic's complex nature and dynamic characteristics. Recent research has shown the effectiveness of complex network analysis techniques for understanding network traffic patterns. This paper proposes multilayer seasonal autoregressive integrated moving average models for analyzing and predicting network traffic. This approach considers the seasonal patterns and interdependencies between different layers of network traffic, allowing for a more accurate and comprehensive representation of the data. The Multilayer Seasonal Autoregressive Integrated Moving Average (MSARIMA) model consists of multiple layers, each representing a different aspect of network traffic, such as time of day, day of week, or type of traffic. Each layer is modeled separately using SARIMA, a popular time series forecasting technique. The models for different layers are combined to capture the overall behavior of network traffic. The proposed approach has several benefits over traditional statistical approaches. It can capture network traffic's complex and dynamic nature, including short-term and long-term seasonal patterns. It also allows for the detection of anomalies and the prediction of future traffic patterns with high accuracy.

Definitive evidence regarding a rapid mean reversion of the real exchange rate is not present when using standard linear methodology, including unit root tests and fractional integration. To consider the robustness of these results, we use an encompassing model, the Gegenbauer AutoRegressive Moving Average (GARMA) model, which nests as special cases the existing linear methods. The GARMA model accommodates a complete notion of persistence and allows shocks to dissipate slowly in a cyclical manner. We find evidence supporting a weak version of purchasing power parity, where equilibrium errors are long memory with strongly persistent cycles. However, this new form of cyclical mean reversion is likely too slow to be economically meaningful. The inability to find a strong equilibrium attractor process, using a very general encompassing linear methodology provides support for the recent models that allow for a nonlinear attraction process and for shifting real exchange rate equilibria.

Even though several reports over the past few decades indicate an increasing aridity over West Africa, attempts to establish the controlling factor(s) have not been successful. The traditional belief of the position of the Inter-tropical Convergence Zone (ITCZ) as the predominant factor over the region has been refuted by recent findings. Changes in major atmospheric circulations such as African Easterly Jet (AEJ) and Tropical Easterly Jet (TEJ) are being cited as major precipitation driving forces over the region. Thus, any attempt to predict long term precipitation events over the region using Global Circulation or Local Circulation Models could be flawed as the controlling factors are not fully elucidated yet. Successful prediction effort may require models which depend on past events as their inputs as in the case of time series models such as Autoregressive Integrated Moving Average (ARIMA) model. In this study, historical precipitation data was imported as time series data structure into an R programming language and was used to build appropriate Seasonal Multiplicative Autoregressive Integrated Moving Average model, ARIMA (p, d, q)*(P, D, Q). The model was then used to predict long term precipitation events over the Ghanaian segment of the Volta Basin which could be used in planning and implementation of development policies.

This paper investigated Bitcoin daily closing price using time series approach to predict future values for financial managers and investors. Daily data were sourced from CoinDesk, with Bitcoin Price Index (BPI) for 5 years (January 1, 2016 to May 31, 2021) extracted. Data analysis and modelling of price trend using Autoregressive Integrated Moving Average (ARIMA) model was carried out, and a suitable model for forecasting was proposed. Results showed that ARIMA(6,1,12) model was the most suitable based on a combination of number of significant coefficients and values of volatility, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). A two-month test window was used for forecasting and prediction. Results showed a decline in prediction accuracy as number of days of the test period increased; from 99.94% for the first 7 days, to 99.59 % for 14 days and 95.84% for 30 days. For the two-month test period, percentage accuracy was 84.75%. The study confirms that the ARIMA model is a veritable planning tool for financial managers, investors and other stakeholders; especially for short-term forecasting. It is however imperative that the influence of external factors, such as investors’/influencers’ comments and government intervention, that may affect forecasting be taken into consideration.

Background: This study intends to identify the best model for predicting the incidence of hand, foot and mouth disease (HFMD) in Ningbo by comparing Autoregressive Integrated Moving Average (ARIMA) and Long Short-Term Memory Neural Network (LSTM) models combined and uncombined with exogenous meteorological variables. Methods: The data of daily HFMD incidence in Ningbo from January 2014 to November 2017 were set as the training set, and the data of December 2017 were set as the test set. ARIMA and LSTM models combined and uncombined with exogenous meteorological variables were adopted to fit the daily incidence of HFMD by using the data of the training set. The forecasting performances of the four fitted models were verified by using the data of the test set. Root mean square error (RMSE) was selected as the main measure to evaluate the performance of the models. Results: The RMSE for multivariate LSTM, univariate LSTM, ARIMA and ARIMAX (Autoregressive Integrated Moving Average Model with Exogenous Input Variables) was 10.78, 11.20, 12.43 and 14.73, respectively. The LSTM model with exogenous meteorological variables has the best performance among the four models and meteorological variables can increase the prediction accuracy of LSTM model. For the ARIMA model, exogenous meteorological variables did not increase the prediction accuracy but became the interference factor of the model. Conclusions: Multivariate LSTM is the best among the four models to fit the daily incidence of HFMD in Ningbo. It can provide a scientific method to build the HFMD early warning system and the methodology can also be applied to other communicable diseases.

This paper investigates the application of the Autoregressive Integrated Moving Average (ARIMA) model to predict future trends in Chinese housing prices. The Chinese real estate market, characterized by its volatility, especially during the post-COVID-19 period, presents a complex environment for buyers and investors. The paper investigates how the ARIMA model is employed to make informed predictions in this uncertain market. Although it has some limitations, such as a heavy reliance on historical data and insensitivity to unexpected macroeconomic shifts, the ARIMA model offers a structure for understanding and anticipating housing price trends. The paper integrates various data sources, including long-term housing price statistics, to build a comprehensive ARIMA model tailored to the nuances of China’s housing market. This essay demonstrates the ARIMA model's utility in aiding stakeholders to make more confident and informed decisions in an increasingly complex and unpredictable market. The analysis further suggests refinements to the ARIMA model, considering the multifaceted nature of the housing market, influenced by macroeconomic factors and public perception. The final goal is to enhance the model's accuracy and reliability, making it an indispensable tool in economic and policy decision-making in China's evolving real estate landscape.

Nowadays , nonlinear time series and artificial neural networks (ANN) models are used for forecasting in the field of business, agriculture and soon. Recent studies have shown, ANN have been successfully used for forecasting of financial and agriculture data series The classical methods used for time series prediction like Box-Jenkins or ARIMA assumes that there is a linear relationship between inputs and outputs. ANN have more advantages that can approximate to model both linear and nonlinear structures in time series, they are not able to handling both structures equally well. The autoregressive integrated moving average (ARIMA) model and two ANN models namely, Radial basis function neural networks (RBFNN), and Elman recurrent neural networks (ERNN) methods were applied to Hyderabad airport traffic data. The data obtained for 15 years from 2002–2003 to 2016–2017 about domestic and international passenger of International Airport of Hyderabad, India. In this research paper, we compared the performances of ARIMA, RBFNN and ERNN were based on three measures: mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE). The results showed that RBFNN obtained the smallest MAE, MAPE and RMSE in both the modeling and forecasting processes. The performances of the three models ranked in ascending order were: ARIMA, ERNN and the RBFNN model. Keywords: T ime series, forecasting, artificial neural networks, ARIMA models, radial basis function neural networks, and Elman recurrent neural networks Cite this Article R. Ramakrishna, Berhe Aregay, Tewodros Gebregergs. The Comparison in Time Series Forecasting of Air Traffic Data by Autoregressive Integrated Moving Average Model, Radial Basis Function and Elman Recurrent Neural Networks. Research & Reviews: Journal of Statistics . 2018; 7(3): 75–90p.

Under the background of mass entrepreneurship and innovation, it is of great practical and theoretical significance to predict the Shenzhen Growth Enterprise Market (GEM) price index. In view of the nonlinearity and the non-stationarity of GEM price index a prediction method based on empirical mode decomposition (EMD) and Autoregressive Integrated Moving Average (ARIMA) model is studied. Firstly, the EMD is used to stabilize GEM price index data to make GEM price index data more regular and improve the non-linear and non-stationary characteristics of GEM price index data. Then, the ARIMA model is used to model and predict the decomposed data. The model accuracy evaluation index results of the EMD-ARIMA model in this paper are lower than that of the ARIMA model and the average error rate of the prediction results is also lower than the ARIMA model. The results show that the method proposed in this paper is more accurate than that of direct prediction by only using ARIMA model, which indicates that the EMD-ARIMA method proposed in this paper has higher generalization ability and prediction accuracy.

The present study was carried out to estimate the trends of area, production and productivity of wheat in North Gujarat. Yearly time series data on area, production and productivity of wheat of North Gujarat for the period of 1991-92 to 2021-22 were collected from the published reports by Directorate of Agriculture, Gujarat state, Gandhinagar. Polynomial and Autoregressive Integrated Moving Average (ARIMA) models were applied to analyze the area, production and productivity of wheat in North Gujarat. First, second and third-degree polynomial models were fitted to the original data and moving averages, with the best model selected based on adjusted R², Root Mean Square Error (RMSE), Mean Absolute Error (MAE), normality by the Shapiro-Wilk (1965) test and randomness of residuals by the Run test. ARIMA models were evaluated for stationarity and different orders (p, d, q) were assessed using autocorrelation function (ACF), partial autocorrelation function (PACF) and the models were selected on the basis of significant autoregressive and moving average term, lower value of Akaike’s Information Criteria (AIC) and Schwartz-Bayesian Criteria (SBC) and normality of residuals by Shapiro-Wilk (1965) test and Box-Ljung (1978) test. The cubic polynomial model on a four year moving average was most suitable for wheat production trends, while ARIMA (0, 2, 1) and ARIMA (0, 2, 2) were optimal for wheat area and production patterns.

Nowadays, Saudi government has established several strategic tactics such as Saudi Vision 2030 to predict the future of the country. In order to accomplish a superior growth in the economy of the country, mathematical model and forecasting techniques are important tools. In this study, total annual exports and imports of the Kingdom of Saudi Arabia are forecasted using Artificial Neural Network (ANN) and Autoregressive Integrated Moving Average (ARIMA) models. This paper tries to predict a time series data using ANN and ARIMA models on total annual exports and imports of Kingdom of Saudi Arabia from the year 1968 to the year 2017 with the help of statistical software XLSTAT. The applied models are used to predict some future values of total annual exports and imports of the Kingdom of Saudi Arabia. It is found that the ANN and ARIMA (1, 1, 2) and ARIMA (0, 1, 1) models are suitable for predicting the total annual exports and imports of the Kingdom of Saudi Arabia.

Gold investment is one of the favorite investments during the Covid-19 pandemic because the price of gold is relatively volatile but shows an increasing trend. Savvy investors investing in gold need to be able to predict future opportunities. Therefore, price estimation is needed to develop a buying and selling strategy to maximize profits. The Autoregressive Integrated Moving Average (ARIMA) model is a suitable method for predicting time series data, so the best ARIMA model will be applied for forecasting world gold prices. The best ARIMA model is selected based on the Akaike Information Criterion (AIC) and Mean Absolute Percentage Error (MAPE) criteria. Monthly world gold price data for 146 periods are applied in this study and will be used to predict gold prices for the following six periods. ARIMA(0,1,1) is the best model obtained from the analysis results, with AIC and MAPE values ​​of 1264.731 and 11.972%, respectively. Forecasting results show that world gold prices will increase for the next periods.

The Covid-19 pandemic has caused severe economic depression and has disrupted the supply chains of various industries. The automobile industry which contributes significantly to the Indian economy was gravely hit due to the lockdowns, semiconductor shortage and the uncertainty associated with the pandemic. This research paper analyses the effect of Covid-19 on the automobile sales in India using the time series modelling approach. The data recorded by SIAM from 2012 to 2019 was used to develop the Autoregressive Integrated Moving Average (ARIMA) model following the Box-Jenkins methodology. ARIMA model (2, 1, 3) was chosen as it had the lowest AIC and BIC criteria. This model was used to forecast the sales from 2020 to 2021 to give a picture of the expected automobile sales had the pandemic not occurred. The forecasted data from the model developed has then been compared with actual automobile sales data during the pandemic to gauge the level of impact Covid-19 had on the Indian automobile industry. The paper also explores the associated challenges that the automobile industry had to face due to the pandemic.

Coronavirus disease 2019 (COVID-19) has been considered a global threat spreading to Nigeria and posing major public health threats and concerns. This led to the introduction of internationally acceptable non-pharmaceutical interventions (NPI) such as lockdowns, social distancing, and mandatory use of face masks by the Nigerian government to curtail the disease. This study aims to develop an Autoregressive Integrated Moving Average (ARIMA) model to predict COVID-19 cases vis Total Confirmed Cases (TCC) and Total Discharged Cases (TDC) in Nigeria based on the daily data obtained from the Nigeria Centre for Diseases Control (NCDC) from 27th February 2020 to 6th June 2020. The autocorrelation function (ACF), and partial autocorrelation function (PACF) were used to determine the constructed model. An ARIMA model was developed to predict the trend of TCC and TDC for the next 200 days. Forecasting was done using the constructed models. The finding shown that TCC increased to 50,225 with a CI between 29,425 to 100,450 and TDC to 20,186 with CI between 11,106 to 40,366 approximately. The result shows a significant increase in both TCC and TDC from COVID-19 which should guide the government roll out and management of the different NPI and policies to contain the virus.

This paper investigates the comparison between Autoregressive Integrated Moving Average (ARIMA) model and Ordinary Least Square (OLS) model. As two good ways to deal with time series datas, these two methods have been widely used in the economic world. Based on these phenomenon, it has a significant research value in the field of finance. Since ARIMA model and OLS model are fit the historical datas and make prediction, it is important to know about the charateristics of them. In this paper, basic information of ARIMA model and OLS model are mainly discussed, including the definition, modeling process and summary of the main protries. Then, the paper will do comparison from three parts: applicable data types, treatment of errors, validity. And it is concluded that both models take a good fitting effects. Finally, this paper derives the practical applicability of ARIMA and OLS models to be provided to research members as a reference.

Modelling and predicting rainfallRainfall in research are essential because the inferences from the study will assist decision-makers, planners, and policymakers in mitigating the effects of droughtDrought or floodingFlooding in the environmentEnvironment. This chapter aims to fit time series models to rainfallRainfall data from seven states in the Nigerian north-central region. The data used for this research was obtained from NIMET (Jan 1989–Dec 2019). The rainfall data set was modelled and predicted using the conventional seasonal Autoregressive Integrated Moving Average (ARIMA)Autoregressive Integrated Moving Average (ARIMA) and Neural Network Times Series Autoregressive (NNETAR)Neural Network Times Series Autoregressive (NNETAR) models. The time plot sequence shows the time series data is stationary, and the Augmented Dick Fuller (ADF) test did not suggest otherwise. Furthermore, the Hegy and Canova-Hansen tests indicate seasonalitySeasonality in the data with order 1. When the ARIMAAutoregressive Integrated Moving Average (ARIMA) and NNETARNeural Network Times Series Autoregressive (NNETAR) models were applied to the rainfallRainfall data set, the analysis revealed that the NNETAR model outperformed the ARIMA model in modelling and predicting the Ilorin, Jos, Lafia, Lokoja, and Minna rainfall data sets. In contrast, the ARIMAAutoregressive Integrated Moving Average (ARIMA) model outperformed the NNETARNeural Network Times Series Autoregressive (NNETAR) model for predicting rainfallRainfall in Abuja and Makurdi. The fitted models were used to predict monthly rainfall in the north-central region for the next five years. The forecast suggests an expected increase in rainfallRainfall in Lafia, Abuja, and Minna. At the same time, an expected decrease in rainfall in Ilorin, Lokoja, Jos, and Makurdi states in the north-central region of NigeriaNigeria.