scholarly journals Kalman Filter Algorithm versus Other Methods of Estimating Missing Values: Time Series Evidence

2021 ◽  
Vol 4 (2) ◽  
pp. 1-9
Author(s):  
Adejumo O.A. ◽  
Onifade O.C. ◽  
Albert S.
Keyword(s):  
Time Series ◽  
Kalman Filter ◽  
Missing Values ◽  
Absolute Error ◽  
Additive Models ◽  
Percentage Error ◽  
Sample Sizes ◽  
Linear Quadratic ◽  
Kalman Filter Algorithm ◽  
Accuracy Measures

Ideally, we think data are carefully collected and have regular patterns with no missing values, but in reality, this does not always happen. This study examines four (4) methods—mean imputation (MI), median imputation (MDI), linear imputation (LI) and Kalman filter algorithm (KAL)—of estimating missing values in time series. The study utilized pairs of nine (9) simulated series; each pair constitutes “actual series” and “12% missingness series”. The three (3) sample sizes i.e. small (50), medium (200) and large (1000) were varied over the additive models linear, quadratic and exponential forms of trend. The 12% missingness series were estimated using MI, MDI, LI and KAL. The performances of the method were checked using the root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE), while the overall performances of the estimating methods were accessed using the average of the accuracy measures (RMSE, MAE and MAPE). The results of the average-accuracy measures show that KAL outperformed other methods (MI, MDI and LI) at the three sample sizes when the trend was linear; also, MDI outperformed other methods at the three (3) sample sizes when the trend was exponential. Furthermore, MI outperformed others at small and large sample sizes when the trend was quadratic. However, the Kalman filter algorithm proved better when the sample size was medium. Hence, KAL, MI and MDI methods are recommended to estimate missing data in time series when the trend is linear, quadratic and exponential respectively, until further study proves otherwise.

scholarly journals PERAMALAN JUMLAH KUNJUNGAN WISATAWAN AUSTRALIA YANG BERKUNJUNG KE BALI MENGGUNAKAN MODEL TIME VARYING PARAMETER (TVP)

2016 ◽  
Vol 5 (3) ◽  
pp. 117
Author(s):  
I PUTU GEDE DIAN GERRY SUWEDAYANA ◽  
I WAYAN SUMARJAYA ◽  
NI LUH PUTU SUCIPTAWATI
Keyword(s):  
Kalman Filter ◽  
State Space Model ◽  
Percentage Error ◽  
Time Varying ◽  
Mean Square ◽  
Explanatory Variables ◽  
Space Model ◽  
A Value ◽  
Time Varying Parameter ◽  
Kalman Filter Algorithm

The purpose of this research is to forecast the number of Australian tourists arrival to Bali using Time Varying Parameter (TVP) model based on inflation of Indonesia and exchange rate AUD to IDR from January 2010 – December 2015 as explanatory variables. TVP model is specified in a state space model and estimated by Kalman filter algorithm. The result shows that the TVP model can be used to forecast the number of Australian tourists arrival to Bali because it satisfied the assumption that the residuals are distributed normally and the residuals in the measurement and transition equations are not correlated. The estimated TVP model is . This model has a value of mean absolute percentage error (MAPE) is equal to dan root mean square percentage error (RMSPE) is equal to . The number of Australian tourists arrival to Bali for the next five periods is predicted: ; ; ; ; and (January - May 2016).

scholarly journals Time Series High-Resolution Land Surface Albedo Estimation Based on the Ensemble Kalman Filter Algorithm

2019 ◽  
Vol 11 (7) ◽  
pp. 753 ◽  
Author(s):  
Guodong Zhang ◽  
Hongmin Zhou ◽  
Changjing Wang ◽  
Huazhu Xue ◽  
Jindi Wang ◽  
...  
Keyword(s):  
Time Series ◽  
Kalman Filter ◽  
High Resolution ◽  
Spatial Resolution ◽  
Ensemble Kalman Filter ◽  
Land Surface ◽  
Surface Albedo ◽  
Data Sets ◽  
Broadleaf Forest ◽  
Kalman Filter Algorithm

Continuous, long-term sequence, land surface albedo data have crucial significance for climate simulations and land surface process research. Sensors such as the Moderate-Resolution Imaging Spectroradiometer (MODIS) and Visible Infrared Imaging Radiometer (VIIRS) provide global albedo product data sets with a spatial resolution of 500 m over long time periods. There is demand for new high-resolution albedo data for regional applications. High-resolution observations are often unavailable due to cloud contamination, which makes it difficult to obtain time series albedo estimations. This paper proposes an “amalgamation albedo“ approach to generate daily land surface shortwave albedo with 30 m spatial resolution using Landsat data and the MODIS Bidirectional Reflectance Distribution Functions (BRDF)/Albedo product MCD43A3 (V006). Historical MODIS land surface albedo products were averaged to obtain an albedo estimation background, which was used to construct the albedo dynamic model . The Thematic Mapper (TM) albedo derived via direct estimation approach was then introduced to generate high spatial-temporal resolution albedo data based on the Ensemble Kalman Filter algorithm (EnKF). Estimation results were compared to field observations for cropland, deciduous broadleaf forest, evergreen needleleaf forest, grassland, and evergreen broadleaf forest domains. The results indicated that for all land cover types, the estimated albedos coincided with ground measurements at a root mean squared error (RMSE) of 0.0085–0.0152. The proposed algorithm was then applied to regional time series albedo estimation; the results indicated that it captured spatial and temporal variation patterns for each site. Taken together, our results suggest that the amalgamation albedo approach is a feasible solution to generate albedo data sets with high spatio-temporal resolution.

scholarly journals Hybrid Ensemble Deep Learning-Based Approach for Time Series Energy Prediction

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1942
Author(s):  
Pyae Pyae Phyo ◽  
Yung-Cheol Byun
Keyword(s):  
Time Series ◽  
Deep Learning ◽  
Short Term Memory ◽  
Absolute Error ◽  
Percentage Error ◽  
Ensemble Model ◽  
Load Prediction ◽  
Energy Prediction ◽  
The Times ◽  
One Year

The energy manufacturers are required to produce an accurate amount of energy by meeting the energy requirements at the end-user side. Consequently, energy prediction becomes an essential role in the electric industrial zone. In this paper, we propose the hybrid ensemble deep learning model, which combines multilayer perceptron (MLP), convolutional neural network (CNN), long short-term memory (LSTM), and hybrid CNN-LSTM to improve the forecasting performance. These DL architectures are more popular and better than other machine learning (ML) models for time series electrical load prediction. Therefore, hourly-based energy data are collected from Jeju Island, South Korea, and applied for forecasting. We considered external features associated with meteorological conditions affecting energy. Two-year training and one-year testing data are preprocessed and arranged to reform the times series, which are then trained in each DL model. The forecasting results of the proposed ensemble model are evaluated by using mean square error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). Error metrics are compared with DL stand-alone models such as MLP, CNN, LSTM, and CNN-LSTM. Our ensemble model provides better performance than other forecasting models, providing minimum MAPE at 0.75%, and was proven to be inherently symmetric for forecasting time-series energy and demand data, which is of utmost concern to the power system sector.

scholarly journals Wind Power Short-Term Prediction Based on LSTM and Discrete Wavelet Transform

2019 ◽  
Vol 9 (6) ◽  
pp. 1108 ◽  
Author(s):  
Yao Liu ◽  
Lin Guan ◽  
Chen Hou ◽  
Hua Han ◽  
Zhangjie Liu ◽  
...  
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Wind Power ◽  
Short Term Memory ◽  
Wind Farms ◽  
Absolute Error ◽  
Percentage Error ◽  
Discrete Wavelet ◽  
Short Term

A wind power short-term forecasting method based on discrete wavelet transform and long short-term memory networks (DWT_LSTM) is proposed. The LSTM network is designed to effectively exhibit the dynamic behavior of the wind power time series. The discrete wavelet transform is introduced to decompose the non-stationary wind power time series into several components which have more stationarity and are easier to predict. Each component is dug by an independent LSTM. The forecasting results of the wind power are obtained by synthesizing the prediction values of all components. The prediction accuracy has been improved by the proposed method, which is validated by the MAE (mean absolute error), MAPE (mean absolute percentage error), and RMSE (root mean square error) of experimental results of three wind farms as the benchmarks. Wind power forecasting based on the proposed method provides an alternative way to improve the security and stability of the electric power network with the high penetration of wind power.

scholarly journals An Application of the Kalman Filter Recursive Algorithm to Estimate the Gaussian Errors by Minimizing the Symmetric Loss Function

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 240
Author(s):  
Cristian Busu ◽  
Mihail Busu
Keyword(s):  
Time Series ◽  
Signal Processing ◽  
Kalman Filter ◽  
Loss Function ◽  
Kalman Filtering ◽  
Kinetic Models ◽  
Applied Mathematics ◽  
Recursive Algorithm ◽  
Linear Quadratic ◽  
Symmetric Loss

Kalman filtering is a linear quadratic estimation (LQE) algorithm that uses a time series of observed data to produce estimations of unknown variables. The Kalman filter (KF) concept is widely used in applied mathematics and signal processing. In this study, we developed a methodology for estimating Gaussian errors by minimizing the symmetric loss function. Relevant applications of the kinetic models are described at the end of the manuscript.

scholarly journals Fuzzy Time Series for Forecasting Railway Passengers in Indonesia

2021 ◽  
Vol 2111 (1) ◽  
pp. 012013
Author(s):  
Muhammad Fatih Rizqon ◽  
Handaru Jati
Keyword(s):  
Time Series ◽  
Mean Absolute Error ◽  
Absolute Error ◽  
Fuzzy Time Series ◽  
Percentage Error ◽  
Time Series Models ◽  
Suitable Model ◽  
Arithmetic Operations ◽  
Advantages And Disadvantages ◽  
Absolute Percentage Error

Abstract Some fuzzy time series models have their own advantages and disadvantages. In addition, these models sometimes are complex and claimed to have better forecasting result than each other. The suitable model for forecasting depends on a wide variety of considerations. The models proposed by Chen (1996) applied simplified arithmetic operations and claimed more efficiency than before. The model proposed by Chen was introduced in 1996 and still exists in several previous studies. This research aims to forecast the number of railway passengers in Indonesia using the fuzzy time series. In addition, this research also evaluates the forecasting results based on mean absolute error (MAE) and mean absolute percentage error (MAPE). The results showed the forecasting results in this research has accuracy for 86.6%.

scholarly journals Modification of Recursive Kalman Filter Algorithm for Adaptive Prediction of Cyber Resilience for Industrial Systems

2020 ◽  
Vol 23 (3) ◽  
pp. 270-279
Author(s):  
D.S. Lavrova ◽  
D.P. Zegzhda
Keyword(s):  
Machine Learning ◽  
Time Series ◽  
Kalman Filter ◽  
Prediction Model ◽  
Early Stage ◽  
Classification Algorithm ◽  
Industrial Systems ◽  
Machine Learning Classification ◽  
Adaptive Prediction ◽  
Kalman Filter Algorithm

This paper describes an approach to modification of the recursive Kalman filter algorithm to obtain adaptive prediction of time series from industrial systems. To ensure cyber resilience of modern industrial systems, it is necessary to detect anomalies in their work at an early stage. For this, data from industrial systems are presented as time series, and an adaptive prediction model combined with machine learning classification algorithm applies to identify anomalies. The effectiveness of the proposed approach is confirmed experimentally.

scholarly journals INFANT POLIO IMMUNIZATION

2015 ◽  
Vol 22 (04) ◽  
pp. 507-513
Author(s):  
Muhammad Imran ◽  
Jamal Abdul Nasir ◽  
Syed Arif Ahmed Zaidi
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Immunization Coverage ◽  
Absolute Error ◽  
Percentage Error ◽  
Forecast Errors ◽  
Short Term ◽  
Forecasting Models ◽  
Polio Immunization ◽  
Reported Data

Poliomyelitis is a highly infectious disease but preventable by effective vaccines.Children under five year of age affected by this disease as a result a permanent paralysis.Objectives: To uncover the trend of infant polio immunization coverage through modeling isa significant concern to formulate an adequate vaccination strategies and program after theoutbreak of new cases of polio in a recent year in Pakistan. Design: The reported data ofmonthly infant polio immunization coverage to National Institute of Health, Islamabad, Pakistanfrom January 2008 to July 2013 for the present study has been taken from Pakistan bureau ofstatistics with total time series entities 67. National Institute of Health, Islamabad took the recordof per month number of doses administered ( 0-11 months )children by the registered healthcentre in pakistan. Period: January 2008 - July 2013. Setting: Pakistan bureau of statistics(Statistics House) Methods: A set of various short term time series forecasting models namelyBox-Jenkins, single moving average, double moving average, single parameter exponentialsmoothing, brown, Holts and winter models were carried out to expose the infant polioimmunization coverage trend. Results: Among the several forecasting models ARIMA modelsare chosen due to lower measure of forecast errors namely root mean square error (RMSE),mean absolute error (MAE) and mean absolute percentage error (MAPE). ARIMA (2,1,1), ARIMA(1,0,2), ARIMA (0,1,2) and ARIMA (2,1,1) models are established as an adequate models for theprediction of OPV-0, OPV-1, OPV-2 and OPV-3 respectively. Conclusions: With the exceptionof OPV-1 the infant polio immunization coverage is expected to rise in Pakistan.

FORECASTING FRESH WATER AND MARINE FISH PRODUCTION IN MALAYSIA USING ARIMA AND ARFIMA MODELS

2018 ◽  
Vol 3 (2) ◽  
pp. 81
Author(s):  
P J W Mah ◽  
N A M Ihwal ◽  
N Z Azizan
Keyword(s):  
Time Series ◽  
Marine Fish ◽  
Model Fitting ◽  
Forecast Model ◽  
Absolute Error ◽  
Percentage Error ◽  
Human Consumption ◽  
Fish Production ◽  
Arfima Models ◽  
Time Series Modelling

Malaysia is surrounded by sea, rivers and lakes which provide natural sources of fish for human consumption. Hence, fish is one source of protein supply to the country and fishery is a sub-sector that contribute to the national gross domestic product. Since fish forecasting is crucial in fisheries management for managers and scientists, time series modelling can be one useful tool. Time series modelling have been used in many fields of studies including the fields of fisheries. In a previous research, the ARIMA and ARFIMA models were used to model marine fish production in Malaysia and the ARFIMA model emerged to be a better forecast model. In this study, we consider fitting the ARIMA and ARFIMA to both the marine and freshwater fish production in Malaysia. The process of model fitting was done using the “ITSM 2000, version 7.0” software. The performance of the models were evaluated using the mean absolute error, root mean square error and mean absolute percentage error. It was found in this study that the selection of the best fit model depends on the forecast accuracy measures used.

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