Fuzzy Time Series for Projecting School Enrolment in Malaysia

There are a variety of approaches to the problem of predicting educational enrolment. However, none of them can be used when the historical data are linguistic values. Fuzzy time series is an efficient and effective tool to deal with such problems. In this paper, the forecast of the enrolment of pre-primary, primary, secondary, and tertiary schools in Malaysia is carried out using fuzzy time series approaches. A fuzzy time series model is developed using historical dataset collected from the United Nations Educational, Scientific, and Cultural Organization (UNESCO) from the year 1981 to 2018. A complete procedure is proposed which includes: fuzzifying the historical dataset, developing a fuzzy time series model, and calculating and interpreting the outputs. The accuracy of the model are also examined to evaluate how good the developed forecasting model is. It is tested based on the value of the mean squared error (MSE), Mean Absolute Percent Error (MAPE) and Mean Absolute Deviation (MAD). The lower the value of error measure, the higher the accuracy of the model. The result shows that fuzzy time series model developed for primary school enrollments is the most accurate with the lowest error measure, with the MSE value being 0.38, MAPE 0.43 and MAD 0.43 respectively.

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A Comparative Simulation Study of ARIMA and Fuzzy Time Series Model for Forecasting Time Series Data

International Journal of Scientific Research in Science Engineering and Technology ◽

10.32628/ijsrset1184112 ◽

2018 ◽

pp. 49-56

Author(s):

Haji A. Haji ◽

Kusman Sadik ◽

Agus Mohamad Soleh

Keyword(s):

Time Series ◽

Simulation Study ◽

Time Series Data ◽

Mean Squared Error ◽

Time Series Model ◽

Fuzzy Time Series ◽

Series Data ◽

Percentage Error ◽

Data Generation ◽

Data Set

Simulation study is used when real world data is hard to ﬁnd or time consuming to gather and it involves generating data set by specific statistical model or using random sampling. A simulation of the process is useful to test theories and understand behavior of the statistical methods. This study aimed to compare ARIMA and Fuzzy Time Series (FTS) model in order to identify the best model for forecasting time series data based on 100 replicates on 100 generated data of the ARIMA (1,0,1) model.There are 16 scenarios used in this study as a combination between 4 data generation variance error values (0.5, 1, 3,5) with 4 ARMA(1,1) parameter values. Furthermore, The performances were evaluated based on three metric mean absolute percentage error (MAPE),Root mean squared error (RMSE) and Bias statistics criterion to determine the more appropriate method and performance of model. The results of the study show a lowest bias for the chen fuzzy time series model and the performance of all measurements is small then other models. The results also proved that chen method is compatible with the advanced forecasting techniques in all of the consided situation in providing better forecasting accuracy.

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The Sailor-diagram. An extension of the Taylor diagram to two-dimensional variables for verification of model data.

10.5194/egusphere-egu2020-315 ◽

2020 ◽

Author(s):

Jon Saenz ◽

Sheila Carreno-Madinabeitia ◽

Ganix Esnaola ◽

Santos J. González-Rojí ◽

Gabriel Ibarra-Berastegi ◽

...

Keyword(s):

Time Series ◽

Wind Velocity ◽

Mean Squared Error ◽

Cmip5 Models ◽

Two Dimensional ◽

Error Matrix ◽

Squared Error ◽

Taylor Diagram ◽

The Mean ◽

The Individual

A new diagram is proposed for the verification of vector quantities generated by individual or multiple models against a set of observations. It has been designed with the idea of extending the Taylor diagram to two-dimensional vector such as currents, wind velocity, or horizontal fluxes of water vapour, salinity, energy and other geophysical variables. The diagram is based on a principal component analysis of the two-dimensional structure of the mean squared error matrix between model and observations. This matrix is separated in two parts corresponding to the bias and the relative rotation of the empirical orthogonal functions of the data. We test the performance of this new diagram identifying the differences amongst a reference dataset and different model outputs using examples wind velocities, current, vertically integrated moisture transport and wave energy flux time series. An alternative setup is also proposed with an application to the time-averaged spatial field of surface wind velocity in the Northern and Southern Hemispheres according to different reanalyses and realizations of an ensemble of CMIP5 models. The examples of the use of the Sailor diagram show that it is a tool which helps identifying errors due to the bias or the orientation of the simulated vector time series or fields. An implementation of the algorithm in form of an R package (sailoR) is already publicly available from the CRAN repository, and besides the ability to plot the individual components of the error matrix, functions in the package also allow to easily retrieve the individual components of the mean squared error.

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The Sailor diagram – A new diagram for the verification of two-dimensional vector data from multiple models

Geoscientific Model Development ◽

10.5194/gmd-13-3221-2020 ◽

2020 ◽

Vol 13 (7) ◽

pp. 3221-3240

Author(s):

Jon Sáenz ◽

Sheila Carreno-Madinabeitia ◽

Ganix Esnaola ◽

Santos J. González-Rojí ◽

Gabriel Ibarra-Berastegi ◽

...

Keyword(s):

Time Series ◽

Mean Squared Error ◽

Cmip5 Models ◽

Multiple Models ◽

Two Dimensional ◽

Vector Data ◽

Reference Dataset ◽

Error Matrix ◽

Squared Error ◽

The Mean

Abstract. A new diagram is proposed for the verification of vector quantities generated by multiple models against a set of observations. It has been designed with the objective, as in the Taylor diagram, of providing a visual diagnostic tool which allows an easy comparison of simulations by multiple models against a reference dataset. However, the Sailor diagram extends this ability to two-dimensional quantities such as currents, wind, horizontal fluxes of water vapour and other geophysical variables by adding features which allow us to evaluate directional properties of the data as well. The diagram is based on the analysis of the two-dimensional structure of the mean squared error matrix between model and observations. This matrix is separated in a part corresponding to the bias and the relative rotation of the two orthogonal directions (empirical orthogonal functions; EOFs) which best describe the vector data. Since there is no truncation of the retained EOFs, these orthogonal directions explain the total variability of the original dataset. We test the performance of this new diagram to identify the differences amongst the reference dataset and a series of model outputs by using some synthetic datasets and real-world examples with time series of variables such as wind, current and vertically integrated moisture transport. An alternative setup for spatially varying time-fixed fields is shown in the last examples, in which the spatial average of surface wind in the Northern and Southern Hemisphere according to different reanalyses and realizations from ensembles of CMIP5 models are compared. The Sailor diagrams presented here show that it is a tool which helps in identifying errors due to the bias or the orientation of the simulated vector time series or fields. The R implementation of the diagram presented together with this paper allows us also to easily retrieve the individual diagnostics of the different components of the mean squared error and additional diagnostics which can be presented in tabular form.

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MSE of the best linear predictor in nonorthogonal models

Mathematica Slovaca ◽

10.2478/s12175-007-0015-6 ◽

2007 ◽

Vol 57 (1) ◽

Author(s):

František Štulajter

Keyword(s):

Time Series ◽

White Noise ◽

Mean Squared Error ◽

Linear Predictor ◽

Squared Error ◽

Additive White Noise ◽

Best Linear Predictor ◽

The Mean ◽

Finite Observation ◽

Noise Models

AbstractThe problem of computing the mean squared error (MSE) of the best linear predictor (BLP) in finite discrete spectrum with an additive white noise models(FDSWNMs) for an observed time series is considered. This is done under the assumption that the corresponding vectors in models for finite observation of this time series are not orthogonal.

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The mean squared error of Geweke and Porter-Hudak's estimator of the memory parameter of a long-memory time series

Journal of Time Series Analysis ◽

10.1111/1467-9892.00075 ◽

1998 ◽

Vol 19 (1) ◽

pp. 19-46 ◽

Cited By ~ 189

Author(s):

Clifford M. Hurvich ◽

Rohit Deo ◽

Julia Brodsky

Keyword(s):

Time Series ◽

Long Memory ◽

Mean Squared Error ◽

Squared Error ◽

Memory Time ◽

The Mean ◽

Memory Parameter

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The Sailor diagram. An extension of Taylor’s diagram to two-dimensional vector data

10.5194/gmd-2019-289 ◽

2019 ◽

Author(s):

Jon Sáenz ◽

Sheila Carreno-Madinabeitia ◽

Ganix Esnaola ◽

Santos J. González-Rojí ◽

Gabriel Ibarra-Berastegi ◽

...

Keyword(s):

Time Series ◽

Mean Squared Error ◽

Empirical Orthogonal Functions ◽

Cmip5 Models ◽

Spatial Average ◽

Two Dimensional ◽

Error Matrix ◽

Squared Error ◽

Taylor Diagram ◽

The Mean

Abstract. A new diagram is proposed for the verification of vector quantities generated by multiple models against a set of observations. It has been designed with the idea of extending the Taylor diagram to two dimensional quantities such as currents, wind, or horizontal fluxes of water vapour, salinity, energy and other geophysical variables. The diagram is based on the analysis of the two-dimensional structure of the mean squared error matrix between model and observations. This matrix is separated in a part corresponding to the bias and the relative rotation of the empirical orthogonal functions of the data. We test the performance of this new diagram to identify the differences amongst the reference dataset and the different model outputs by using examples with wind, current, vertically integrated moisture transport and wave energy flux time series. An alternative setup is shown in the last examples, where the spatial average of surface wind in the Northern and Southern Hemispheres according to different reanalyses and realizations of CMIP5 models are compared. The examples of use of the Sailor diagram presented show that it is a tool which helps in identifying errors due to the bias or the orientation of the simulated vector time series or fields. The R implementation of the diagram presented together with this paper allows also to easily retrieve the individual diagnostics of the different components of the mean squared error.

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Using Laboratory Data to Aid Early Warning in Prospective Influenza Mortality Surveillance

Online Journal of Public Health Informatics ◽

10.5210/ojphi.v8i1.6557 ◽

2016 ◽

Vol 8 (1) ◽

Author(s):

Aye M. Moa ◽

David J. Muscatello ◽

Robin Turner ◽

C Raina MacIntyre

Keyword(s):

Time Series ◽

Mean Squared Error ◽

Laboratory Data ◽

Time Series Model ◽

Attributable Mortality ◽

Influenza Surveillance ◽

Seasonal Time Series ◽

Squared Error ◽

Laboratory Surveillance ◽

Mortality Surveillance

Many countries prospectively monitor influenza-attributable mortality using a variation of the Serfling seasonal time series model. Our aim is to demonstrate use of routine laboratory-confirmed influenza surveillance data to forecast predicted influenza-attributable deaths during the current influenza season. The two models provided a reasonable forecast for 2012. The model forecasts of weekly deaths during 2012 were compared against observed deaths using root mean squared error (RMSE). The results shown that the model including influenza type A and B provided a better fit. Here, we demonstrated a time series model for influenza-attributable mortality surveillance based on laboratory surveillance information.

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