On Consistency of Tests for Stationarity in Autoregressive and Moving Average Models of Different Orders

Akeyede, Imam; Habiba, Danjuma; Atanda, Bature Tajudeen

doi:10.11648/j.ajtas.20160503.20

Cited by 10 publications

(5 citation statements)

References 9 publications

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“…Pengujian dilakukan menggunakan Augmented Dicky Fuller (ADF). Hasil uji ADF bernilai negatif, semakin besar nilai negatif maka semakin kuat penolakan terhadap hipotesis yang menyatakan bahwa terdapat unit root (tidak stasioner) pada beberapa level pengujian (Imam, Habiba, & Atanda, 2016). Adapun aturan dalam pengambilan keputusan stasioneritas data sebagai berikut: 1.…”

Section: Uji Stasioneritas Dataunclassified

Analisis Efisiensi Pemasaran Jagung di Provinsi Gorontalo

Ashari

Syamsir²

2021

J. Indones. Agribus

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Price fluctuations at the producer and consumer levels determine the performance of the maize market in Gorontalo Province. This will affect the decisions and ability of the corn marketing agencies involved in responding to price changes. The slow response of marketing agencies to changes in maize prices indicates inefficient market conditions in terms of prices. In addition, differences in market power between marketing agencies indicate inefficiencies in marketing maize from an operational perspective. Therefore, this research was conducted with the aim of 1) analyzing market integration and transmission of maize prices between producers and consumers, 2) analyzing the distribution of marketing margins in the maize marketing channels in Gorontalo Province. The research data used is in the form of weekly price data at the producer and consumer levels for 148 weeks, from March 2016 to March 2019 and added data from direct interviews with the marketing actors involved, namely farmers as many as 30 people, while sampling of traders was carried out by snowball sampling technique. Data analysis used the Asymmetric Error Correction Model (AECM), marketing margin and farmer share for each channel. The results showed that the transmission of maize prices at the producer and consumer level is symmetrical in the long run indicating market integration. The smallest marketing margin and the largest farmer share are in Channel III, where marketing is done directly to an exporter. Corn marketing in Gorontalo Province shows price transmission and market integration as well as high farmer share value in each channel, so it can be concluded that marketing is efficient.

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Section: Uji Stasioneritas Dataunclassified

Analisis Efisiensi Pemasaran Jagung di Provinsi Gorontalo

Ashari

Syamsir²

2021

J. Indones. Agribus

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“…In this study a significance level of 5% was maintained for all hypothesis tests. Imam [18]. According to the tests performed, first the series was normal but nonstationary.…”

Section: Procedures Followedmentioning

confidence: 99%

Application of Time Series Analysis to Annual Rainfall Values in Debre Markos Town, Ethiopia

Abebe¹

2018

CWEEE

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For many years planning and management of water resources involved modeling and simulation of temporally sequenced and stochastic hydrologic events. Rainfall process is one of such hydrologic events which calls for time series analysis to better understand interesting features contained in it. Many statistics-based methods are available to simulate and predict such a kind of time series. Autoregressive (AR), moving average (MA), autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) models are among those methods. In this study a search was conducted to identify and examine a capable stochastic model for annual rainfall series (over the period 1954-2015) of Debre Markos town, Ethiopia. For the historical series, normality and stationarity tests were conducted to check if the time series was from a normally distributed and stationary process. Shapiro-Wilk (SW), Anderson-Darling (AD) and Kolmogorov-Smirnov (KS) tests were among the normality tests conducted whereas, Augmented Dickey-Fuller (ADF), Phillips-Perron (PP) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests were among the stationarity tests. Based on the test results, logarithmic transformation and first order differencing were performed to bring the original series to a normal and stationary series. Results of model fitting showed that three models namely, AR (2), MA (1) and ARMA (2,1) were capable in describing the annual rainfall series. A diagnostic check was performed on model residuals and ARMA (2,1) was found to be the best model among the candidates. Furthermore, three information criteria: Akaike Information Criterion (AIC), the corrected Akaike Information Criterion (AICc) and Bayesian Information Criterion (BIC) were used to select the best model. In this regard, too, the least information discrepancy between the underlying process and the fitted model was obtained from ARMA (2,1) model. Hence, this model was considered as a better representative of the annual rainfall values and was used to predict five years ahead values. The mean absolute percentage error (MAPE) of the prediction was found to be less than 10%. Thus, ARMA (2,1) model could be used for forecasting and simulation of annual rainfall for How to cite this paper: Abebe, S.A.

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“…Or import and export data can be predicted by using information on how many is imported and exported in the past few months. Many examples can be given and these ARMA-models work pretty well in modeling the time series (Imam, 2020). One special class of time series model is ARIMA models which are often associated with Box and Jenkins (1976) for their effort to systematize the whole methodology of estimating, checking and forecasting using ARIMA models (Mahesh, 2005).…”

Section: Introductionmentioning

confidence: 99%

“…The results indicated variation in precision, M 3 performed best in one-week ahead and 9-12 weeks ahead while M4 performed better in 2-8 weeks and also for 13 weeks and above, M 1 was the weak model in forecasting. Imam (2020) investigated the best ARIMA model for forecasting average daily share price indices of the series of square pharmaceuticals limited (SPL). After stationary test, the data was found to be not stationary; a differencing was carried out to obtain stationarity.…”

Section: Introductionmentioning

confidence: 99%

Modeling Time Series Poison Count Data: An Application to COVID 19 Confirmed Cases in Nigeria

Alhaji Mustapha

2023

AJBAR

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Time series events are counted within time intervals usually for convenience and practical reasons. Time series data involving counts frequently follows Poison distribution. Integrated Autoregressive Moving Average (ARIMA) models were studied on simulated Poison data of different parameter and sample sizes. These models were used to capture Poison data with different phenomena. Data set were simulated from Poison process with ARIMA (p, d, q) were then fitted to the simulated data so as to examine the effect of the changes in parameter value of the Poison on the models’ performance across the sample size. Thereafter, the same models were used to fit and forecast the daily Covid-19 data, confirmed cases from inception to February 2023. It was concluded that ARIMA (2, 1, 2) and ARIMA (1, 1, 1) are obviously the best Models at different sample sizes respectively. Based on the Covid-19 analysis, the estimated coefficient values of all ARIMA (p,d,q) strictly conforms to the bounds of the parameter between -1 and 1 and this had made the model to be stationary comparing the ARIMA models in terms of the AIC, BIC and MSE. It is clearly preferred ARIMA (1, 0, 2) to other models since their estimated AIC, BIC and MSE are smaller as compared to other models. The forecast is quite accurate, and hereby confirms what was expected. It seems that ARIMA (1, 0, 2) does a very good job in capturing the dynamic nature of the data and forecasting. It was observed that the confirmed cases increase, and then keep stationary throughout the future times.

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On Consistency of Tests for Stationarity in Autoregressive and Moving Average Models of Different Orders

Cited by 10 publications

References 9 publications

Analisis Efisiensi Pemasaran Jagung di Provinsi Gorontalo

Analisis Efisiensi Pemasaran Jagung di Provinsi Gorontalo

Application of Time Series Analysis to Annual Rainfall Values in Debre Markos Town, Ethiopia

Modeling Time Series Poison Count Data: An Application to COVID 19 Confirmed Cases in Nigeria

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