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All Journal Square : Journal of Mathematics and Mathematics Education Matematika Sains: Jurnal Ilmu Matematika
Kaigama, Aishatu
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Computer Science & IT Decision Sciences, Operations Research & Management Education Mathematics Other

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Time Series Analysis for The Treatment of Typhoid (Enteric) Fever in Maiduguri: Using Arima Model Kaigama, Aishatu; Madaki, Umar Yusuf
Square : Journal of Mathematics and Mathematics Education Vol 5, No 1 (2023)
Publisher : UIN Walisongo Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21580/square.2023.5.1.18282

Abstract

This research employs the ARIMA model to conduct a thorough time series analysis on the treatment of typhoid (enteric) fever in Maiduguri. The study reveals the presence of both trend and seasonality in the data, with the trend indicating a recent reduction in the recorded data. Using autocorrelation and partial autocorrelation function (ACF and PACF), the data can also be utilized to determine the model's order. The model obtained is subjected to model diagnostics to determine its efficiency and the model is used to forecast the typhoid fever. From the forecast graph shows that there may be a decrease in future years due to the pattern of the series the impression, we obtain from the graph is that predicted series seems to be trend upward and then downward. ARIMA (1,0,0) has the minimum value of AIC therefore it found to be best model. Hence, the model to fit the typhoid fever based on diplomatic test, which is LJung Box test from the family of Box Janks procedure, then our P-value is less than 0.05 level of significant, we reject the null hypothesis and conclude that the typhoid fever is statistically significant at 5% level of significant. Forecast of typhoid fever from February to December 2025 we also conclude that the typhoid fever is stable. Improve Sanitation and Hygiene: Implement measures to improve sanitation and hygiene practices, especially in areas with high disease prevalence. This may include promoting access to clean water, proper waste management, and hygiene education campaigns.Keyword: ARIMA Model, Typhoid fever, Box janks, WHO, Model diagnostic.
MODELING VOLATILITY IN GARCH MODELS WITH SINE STUDENT’S T ERROR INNOVATION Kaigama, Aishatu; Zamani, Farid; Rann, Harun Bakari; Mohammed, Yusuf Abbakar
Matematika Sains Vol 3 No 1 (2025): Jurnal Matematika Sains Volume 3 Nomor 1 Tahun 2025
Publisher : Fakultas Sains Dan Teknologi

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34005/ms.v3i1.4649

Abstract

This study compares the performance of various GARCH models GARCH(1,1), GARCH(1,2), and GARCH(2,1) with different error innovations, focusing on the use of Student’s t-distributions, including sine-modulated, to model financial volatility dynamics. This study offers a novel approach to modeling volatility in financial time series data using GARCH models with sine Student's t error innovation. The analysis uses both simulated data and real-life data from the Nigerian Stock Exchange (NSE). The results reveal that the GARCH(1,1) model with sine-modulated Student’s t error innovation outperforms other models, showing superior model fit (lowest AIC and BIC) and forecasting accuracy (lowest MAE, MSE, and RMSE) in the simulation results. Additionally, GARCH(1,2) with sine-exponentiated Student’s t innovations is found to be the most effective for real-life data, capturing volatility clustering and extreme tail events. The study concludes that advanced error innovations, particularly sine-modulated Student’s t distributions, improve model accuracy by addressing the heavy tails, volatility clustering, and asymmetry typical of financial markets. The study findings also suggest that incorporating the Sine Student's t distribution in GARCH models can provide a more nuanced understanding of financial market dynamics.
Time Series Analysis for The Treatment of Typhoid (Enteric) Fever in Maiduguri: Using Arima Model Kaigama, Aishatu; Madaki, Umar Yusuf
Square : Journal of Mathematics and Mathematics Education Vol. 5 No. 1 (2023)
Publisher : UIN Walisongo Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21580/square.2023.5.1.18282

Abstract

This research employs the ARIMA model to conduct a thorough time series analysis on the treatment of typhoid (enteric) fever in Maiduguri. The study reveals the presence of both trend and seasonality in the data, with the trend indicating a recent reduction in the recorded data. Using autocorrelation and partial autocorrelation function (ACF and PACF), the data can also be utilized to determine the model's order. The model obtained is subjected to model diagnostics to determine its efficiency and the model is used to forecast the typhoid fever. From the forecast graph shows that there may be a decrease in future years due to the pattern of the series the impression, we obtain from the graph is that predicted series seems to be trend upward and then downward. ARIMA (1,0,0) has the minimum value of AIC therefore it found to be best model. Hence, the model to fit the typhoid fever based on diplomatic test, which is LJung Box test from the family of Box Janks procedure, then our P-value is less than 0.05 level of significant, we reject the null hypothesis and conclude that the typhoid fever is statistically significant at 5% level of significant. Forecast of typhoid fever from February to December 2025 we also conclude that the typhoid fever is stable. Improve Sanitation and Hygiene: Implement measures to improve sanitation and hygiene practices, especially in areas with high disease prevalence. This may include promoting access to clean water, proper waste management, and hygiene education campaigns.Keyword: ARIMA Model, Typhoid fever, Box janks, WHO, Model diagnostic.
Co-Authors Madaki, Umar Yusuf Mohammed, Yusuf Abbakar Rann, Harun Bakari Zamani, Farid