Comparative Analysis of Univariate SARIMA and Multivariate VAR Models for Time Series Forecasting: A Case Study of Climate Variables in Ninahvah City, Iraq
Mathematical problems of computer science, Jun 1, 2024
International journal of statistics in medical research, Nov 9, 2023
Objective: This research aims to compare two nonparametric functional regression models, the Kern... more Objective: This research aims to compare two nonparametric functional regression models, the Kernel Model and the K-Nearest Neighbor (KNN) Model, with a focus on predicting scalar responses from functional covariates. Two semi-metrics, one based on second derivatives and the other on Functional Principle Component Analysis, are employed for prediction. The study assesses the accuracy of these models by computing Mean Square Errors (MSE) and provides practical applications for illustration. Method: The study delves into the realm of nonparametric functional regression, where the response variable (Y) is scalar, and the covariate variable (x) is a function. The Kernel Model, known as funopare.kernel.cv, and the KNN Model, termed funopare.knn.gcv, are used for prediction. The Kernel Model employs automatic bandwidth selection via Cross-Validation, while the KNN Model employs a global smoothing parameter. The performance of both models is evaluated using MSE, considering two different semi-metrics. Results: The results indicate that the KNN Model outperforms the Kernel Model in terms of prediction accuracy, as supported by the computed MSE. The choice of semi-metric, whether based on second derivatives or Functional Principle Component Analysis, impacts the model's performance. Two real-world applications, Spectrometric Data for predicting fat content and Canadian Weather Station data for predicting precipitation, demonstrate the practicality and utility of the models. Conclusion: This research provides valuable insights into nonparametric functional regression methods for predicting scalar responses from functional covariates. The KNN Model, when compared to the Kernel Model, offers superior predictive performance. The selection of an appropriate semi-metric is essential for model accuracy. Future research may explore the extension of these models to cases involving multivariate responses and consider interactions between response components.
In nonparametric analyses, many authors indicate that the kernel density functions work well when... more In nonparametric analyses, many authors indicate that the kernel density functions work well when the variable is close to the Gaussian shape. This chapter interest is on the improvement the forecastability of the functional nonparametric time series by using a new approach of the parametric power transformation. The choice of the power parameter in this approach is based on minimizing the mean integrated square error of kernel estimation. Many authors have used this criterion in estimating density under the assumption that the original data follow a known probability distribution. In this chapter, the authors assumed that the original data were of unknown distribution and set the theoretical framework to derive a criterion for estimating the power parameter and proposed an application algorithm in two-time series of temperature monthly averages.
Comparison Between Forecasting ARIMA and ARIMAX Method
ZANCO Journal of Pure and Applied Sciences, Dec 15, 2016
The aim of this paper is Comparison between ARIMA and ARIMAX method includes the application of s... more The aim of this paper is Comparison between ARIMA and ARIMAX method includes the application of some statistical techniques for studying the time series of the average monthly discharge balinda river - duhok governorate which is measured at the General Directorate of irrigation in Duhok. The techniques used are the modeling by an (ARIMA), ARIMAX model to check a goodness of fit we use mean square error ,AIC , t, p to test the best mode significant . The result show that ARIMAX method is better than ARIMA method in accuracy level of testing, and next time forecasting processes. There are minimum fourteen variables have to include in ARIMAX model in order to make accuracy level is not decrease.
The aim of this paper is Comparison between models with and without intercept and Statement the b... more The aim of this paper is Comparison between models with and without intercept and Statement the beast one, and applying the method leverage point when we added the new point to the original data. We are testing the significant intercept by using (t) test.
Outliers are data points or observations that stand out significantly from the rest of the group ... more Outliers are data points or observations that stand out significantly from the rest of the group in terms of size or frequency. They are also referred to as "abnormal data". Before fitting a forecasting model, outliers are often eliminated from the data set, or if not removed, the forecasting model is altered to account for the presence of outliers. The first scenario covered in the study is the detection of outliers when the parameters have been established. Second, where there are unidentified parameters. This article mentions a number of causes for outlier correction and detection in time series analysis and forecasting. For the objective of the study, a time series of the volume of water entering the Dohuk dam reservoir in Dohuk city was used. The study arrived at the following conclusions after conducting their research: first, whenever the critical value increased, the value of residual standard error (with outlier adjustment) increased. Second, the quantity of outlier values dropped each time the critical value was raised. Third, forecasts with outlier correction perform better than forecasts without outlier adjustment when outliers are present.
The aim of this article is to apply the adjusted residuals to analysis of (two-way) contingency t... more The aim of this article is to apply the adjusted residuals to analysis of (two-way) contingency tables to determine the cells which affected to the significance of chi-square statistic
Outliers are data points or observations that stand out significantly from the rest of the group ... more Outliers are data points or observations that stand out significantly from the rest of the group in terms of size or frequency. They are also referred to as "abnormal data". Before fitting a forecasting model, outliers are often eliminated from the data set, or if not removed, the forecasting model is altered to account for the presence of outliers. The first scenario covered in the study is the detection of outliers when the parameters have been established. Second, where there are unidentified parameters. This article mentions a number of causes for outlier correction and detection in time series analysis and forecasting. For the objective of the study, a time series of the volume of water entering the Dohuk dam reservoir in Dohuk city was used. The study arrived at the following conclusions after conducting their research: first, whenever the critical value increased, the value of residual standard error (with outlier adjustment) increased. Second, the quantity of outlier values dropped each time the critical value was raised. Third, forecasts with outlier correction perform better than forecasts without outlier adjustment when outliers are present.
Statistics, Optimization & Information Computing
The aim of this paper is to select an appropriate ARIMA model for the time series after transform... more The aim of this paper is to select an appropriate ARIMA model for the time series after transforming the original responses. Box-Cox and Yeo-Johnson power transformation models were used on the response variables of two time series datasets of average temperatures and then diagnosed and built the appropriate ARIMA models for each time-series. The authors treat the results of the model fitting as a package in an attempt to decide and choose the best model by diagnosing the effect of the data transformation on the response normality, significant of estimated model parameters, forecastability and the behavior of the residuals. The authors conclude that the Yeo-Johnson model was more flexible in smoothing the data and contributedto accessing a simple model with good forecastability.
A New Approach of Power Transformations in Functional Non-Parametric Temperature Time Series
Time Series Analysis - New Insights [Working Title]
In nonparametric analyses, many authors indicate that the kernel density functions work well when... more In nonparametric analyses, many authors indicate that the kernel density functions work well when the variable is close to the Gaussian shape. This chapter interest is on the improvement the forecastability of the functional nonparametric time series by using a new approach of the parametric power transformation. The choice of the power parameter in this approach is based on minimizing the mean integrated square error of kernel estimation. Many authors have used this criterion in estimating density under the assumption that the original data follow a known probability distribution. In this chapter, the authors assumed that the original data were of unknown distribution and set the theoretical framework to derive a criterion for estimating the power parameter and proposed an application algorithm in two-time series of temperature monthly averages.
The aim of this paper is Comparison between models with and without intercept and Statement the b... more The aim of this paper is Comparison between models with and without intercept and Statement the beast one, and applying the method leverage point when we added the new point to the original data. W e are testing the significant intercept by using (t) test.
The aim of this article is to apply the adjusted residuals to analysis of (two-way) contingency t... more The aim of this article is to apply the adjusted residuals to analysis of (two-way) contingency tables to determine the cells which affected to the significance of chi-square statistic
In this article, Box-Cox and Yeo-Johnson transformation models are applied to two time series dat... more In this article, Box-Cox and Yeo-Johnson transformation models are applied to two time series datasets of monthly temperature averages to improve the forecast ability. An application algorithm was proposed to transform the positive original responses using the first model and the stationary responses using the second model to improve the nonparametric estimation of the functional time series. The Box-Cox model contributed to improving the results of the nonparametric estimation of the original data, but the results become somewhat confusing after attempting to make the transformed response variable stationary in the mean, while the functional time series predictions were more accurate using the transformed stationary datasets using the Yeo-Johnson model.
Multiple Linear regression (MLR) is a method used to model the linear relationship between a depe... more Multiple Linear regression (MLR) is a method used to model the linear relationship between a dependent variable and one or more independent variables. The dependent variable is sometimes also called Predict and, and the independent variables the predictors. The aim of this paper to use stepwise regression and other method to know the best method when the model contains intercept and without intercept, and contain the important definition of the regression and the most important relationship and the equation that are used to solve example about the Multiple linear regression of least squares and estimation and test of hypothesis due to the parameters, and so the most important application the theoretical of blood pressure (dependent variable Y) and height, weight, age sugar, sex, hereditary factor social status (independent variable) .
Comparison Between Forecasting ARIMA and ARIMAX Method
ZANCO Journal of Pure and Applied Sciences, Dec 15, 2016
The aim of this paper is Comparison between ARIMA and ARIMAX method includes the application of s... more The aim of this paper is Comparison between ARIMA and ARIMAX method includes the application of some statistical techniques for studying the time series of the average monthly discharge balinda river - duhok governorate which is measured at the General Directorate of irrigation in Duhok. The techniques used are the modeling by an (ARIMA), ARIMAX model to check a goodness of fit we use mean square error ,AIC , t, p to test the best mode significant . The result show that ARIMAX method is better than ARIMA method in accuracy level of testing, and next time forecasting processes. There are minimum fourteen variables have to include in ARIMAX model in order to make accuracy level is not decrease.
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