Predictive data mining on Average Global Temperature using variants of ARIMA models
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This paper analyzes and predicts the Average Global Temperature time series data. Three different variants of ARIMA models: Basic ARIMA, Trend based ARIMA and Wavelet based ARIMA have been used to predict the average global temperature. Out of all the three linear models, it has been observed that Trend based ARIMA method outperforms basic ARIMA method and Wavelet based ARIMA method outperforms Trend based ARIMA method. MAPE (Mean Absolute Percentage Error), MaxAPE (Maximum Absolute Percentage Error) and MAE (Mean Absolute Error) have been used as a performance measures to compare between the models.Keywords:
Mean absolute error
Moving average
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This paper considers the modelling and forecasting of monthly All-items (12 months average change) inflation rates in Nigeria using the Box-Jenkins (ARIMA) model. Time series data used in the study was collected from the Central Bank of Nigeria statistical web database. The data was differenced twice to achieve stationarity in the series as required. Based on the evaluation and diagnostic criteria, the most accurate model is selected. The order of the best ARIMA model was found to be ARIMA (1, 2, 1). The diagnostic analysis of the model residuals showed that they are normally distributed uncorrelated random shocks. The findings in this study showed that the selected ARIMA model captured the dynamics in the series and produced forecasted values which had minimal forecast errors when compared with the actual inflation values in the validation period.
Moving average
Box–Jenkins
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Exponential Smoothing
Moving average
Absolute deviation
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Precise prediction of the streamflow has a significantly importance in water resources management. In this study, two time series models, Autoregressive Moving Average model (ARMA) Autoregressive Integrated Moving Average model (ARIMA) are used for predicting streamflow. In this research, monthly streamflow from 1974 to 2010 were used. The statistics related to first 28 years were used to train the models and last 7 years were used to forecast. The prediction accuracy of both time series models is examined by comparing root mean square error (RMSE), the mean absolute percentage error (MAPE) and the Nash efficiency (NE). According to the results, ARIMA model performs better than the ARMA time series models. Keywords: Streamflow forecasting, Time series models, ARIMA, ARMA
Autoregressive–moving-average model
Moving average
Box–Jenkins
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Univariate
Mean absolute error
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This paper presents electrical load forecasting analysis and forecasted results based on identification of stochastic time series models for short term. Three predictive models namely, the autoregressive moving average (ARMA), autoregressive integrated moving average (ARIMA) and autoregressive integrated moving average model with exogenous variables (ARIMAX) are proposed. The mean absolute percentage errors (MAPE) of these models are computed and compared. Forecasting results show that ARIMA and ARIMAX Models performance is better ensured, thereby improving the forecasting accuracy significantly compared to ARMA Model. Further, it is shown that ARIMAX Model slightly outperforms ARIMA Model. The proposed methodology has been applied, on Karnataka State Demand Data-2019 for short term electrical demand prediction. This approach of time series modeling can accurately predict the practical power system hourly demand considering into account public holidays, weekdays and weekends.
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Autoregressive–moving-average model
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The exchange rates play a vital role in controlling the dynamics of the exchange market. As a result, the appropriate prediction of exchange rate is a crucial factor for the success of many businesses and fund managers. For more than twenty decades, Box Jenkin‟s Auto Regressive Integrated Moving Average (ARIMA) technique is one of the most sophisticated extrapolation method for forecasting. It predicts the values in a time series as a linear combination of its own past values, past errors and current and past values of other time series. Artificial Neural Network (ANN) is a modern non linear technique used for prediction that involves learning and pattern recognition. The historical monthly data for the years 1999-2009 (10 years) for five exchange rates namely US Dollar (USD), Great Britain Pound (GBP), Kuwaiti Dinar (KWD), Japanese Yen (JPY), and Hong Kong Dollar (HKD) were modeled using these two techniques and the Mean Absolute Error (MAE), Mean Square Error (MSE), Root Mean Square Error (RMSE) Mean Absolute Percentage Error (MAPE) are used to evaluate the accuracy of the models. Results show that ANN model performs much better than the traditional ARIMA model. The main focus of this paper is to forecast the monthly exchange rates using various ARIMA models and ANN models and the future exchange rates is forecasted for the succeeding months.
Moving average
Box–Jenkins
Liberian dollar
Mean absolute error
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This paper describes a study that used data collected from the Central Bank statistical web database system in Nigeria to evaluate and compare the forecasting performance of the nonstationary linear state space model and Box-Jenkins (ARIMA) model at different historic time periods. The comparison uses data series on inflation rates (core and non-core) in Nigeria for a specified period. The performances were evaluated based on three metrics: mean absolute error (MAE), mean absolute percentage error (MAPE) and root mean square percentage error (RMSPE). The one-year forecast evaluation results indicated that predictions from the nonstationary linear state space model outperformed the seasonal ARIMA model at different time periods. Furthermore, the proposed nonstationary linear state space model captured the dynamic structure of the inflationary series reasonably and requires no new cycle of identification and model estimation given the availability of new data.
Box–Jenkins
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Modelling and forecasting of volatile data have become the area of interest in financial time series. Volatility refers to a condition where the conditional variance changes between extremely high and extremely low values. In the current study, modelling and forecasting will be carried out using two sets of real data namely crude oil prices and kijang emas prices. The models investigated are Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) model and Generalized Autoregressive Conditionally Heteroscedasticity (GARCH) model. In estimating the parameters for the Box-Jenkins ARIMA model, two estimation methods are used. These are Maximum Likelihood Estimation (MLE) and Ordinary Least Squares Estimation (OLS). The capabilities of these two methods in estimating the ARIMA models are evaluated by using Mean Absolute Percentage Error (MAPE). The modelling performances of ARIMA and GARCH models will be evaluated by using Akaike’s Information Criterion (AIC) while the forecasting performances of both models will be evaluated by using Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE). The processes of modelling and forecasting will be done by using R and Eviews statistical softwares. As a result of the study, it can be concluded that in terms of parameters estimation of ARIMA models, MLE gives more precise forecast for crude oil prices data while OLS gives more precise forecast for kijang emas prices data. In terms of forecasting performances between ARIMA and GARCH models, it can be concluded that GARCH is a better model for kijang emas prices data while ARIMA is a better model for crude oil prices data.
Ordinary least squares
Akaike information criterion
Box–Jenkins
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Forecasting methods of the neural network, ARIMA, ARIMA-GARCH, exponential smoothing and others are introduced. Then using U.S. inflation data, based on the out-of-sample fo recasting test, the paper studies the advantages and disadvantages of these methods by the empirical comparisons. The empirical results show that, firstly, from the superior to the inferior, the ra nking order of the six methods are, the ARIMA-GARCH, ARIMA, neural networks, median method of autoregressive model, least squares method of autoregressive model, exponential smoothing, no matter based on sample mean absolute error or absolute error for one-step forecasting, or absolute error for two-steps forecasting. Secondly, the ARIMA-GARCH method is suitable most to forecast the inflatio n level in the USA and sometimes sophisticated methods such as neural networks can not improve the forecasting results. Thirdly, according to the out-of-sample forecasting, directions of forecasting err ors of these methods are almost the same, indicating that these forecasts have underestimated the inflation level in the USA.
Exponential Smoothing
Moving average
Sample (material)
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