Computing the mean square error of unobserved components extracted by misspecified time series models

2009 ◽  
Vol 33 (2) ◽  
pp. 283-295 ◽  
Author(s):  
Andrew C. Harvey ◽  
Davide Delle Monache
Keyword(s):  
Time Series ◽  
Mean Square Error ◽  
Time Series Models ◽  
Mean Square ◽  
Unobserved Components ◽  
The Mean

scholarly journals The Mean Square Error of Prediction in the Chain Ladder Reserving Method (Mack and Murphy Revisited)

2006 ◽  
Vol 36 (02) ◽  
pp. 521-542 ◽  
Author(s):  
Markus Buchwalder ◽  
Hans Bühlmann ◽  
Michael Merz ◽  
Mario V. Wüthrich
Keyword(s):  
Time Series ◽  
Mean Square Error ◽  
Time Series Model ◽  
Mean Square ◽  
Chain Ladder Method ◽  
The Mean ◽  
Chain Ladder

We revisit the famous Mack formula [2], which gives an estimate for the mean square error of prediction MSEP of the chain ladder claims reserving method: We define a time series model for the chain ladder method. In this time series framework we give an approach for the estimation of the conditional MSEP. It turns out that our approach leads to results that differ from the Mack formula. But we also see that our derivation leads to the same formulas for the MSEP estimate as the ones given in Murphy [4]. We discuss the differences and similarities of these derivations.

scholarly journals Financial Time Series Image Algorithm Based on Wavelet Analysis and Data Fusion

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Wuwei Liu ◽  
Jingdong Yan
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Mean Square Error ◽  
Financial Time Series ◽  
Prediction Method ◽  
Mean Square ◽  
Rbf Network ◽  
Network Prediction ◽  
The Mean ◽  
Hidden Layer

In recent years, people are more and more interested in time series modeling and its application in prediction. This paper mainly discusses a financial time series image algorithm based on wavelet analysis and data fusion. In this research, we conducted an in-depth study on the scale decomposition sequence and wavelet transform sequence in different scale domains of wavelet transform according to the scale change rule based on wavelet transform. We use wavelet neural network with different input neurons and hidden neurons to predict, respectively. Finally, the prediction results are integrated into the final prediction results based on the original time series by using wavelet reconstruction technology. Using RBF algorithm in neural network and SPSS Clementine, the wavelet transform sequences on five scales are modeled. Each network model has three layers: one input layer, one hidden layer, and one output layer, and each output layer has only one output element. In order to compare the prediction effect of the model proposed in this study, the ordinary RBF network is used to model and predict the log yield itself. When the input sample is 5, the minimum mean square error is obtained when the hidden layer is 6, and the mean square error is 1.6349. The mean square error of the training phase is 0.0209, and the validation error is 1.6141. The results show that the prediction results of the wavelet prediction method combined with the RBF network prediction method are better than those of wavelet prediction or RBF network prediction.

scholarly journals Modeling of COVID-19 Outbreak Indicators in China Between January and June

2020 ◽  
pp. 1-9
Author(s):  
Senol Celik ◽  
Handan Ankarali ◽  
Ozge Pasin
Keyword(s):  
Time Series ◽  
Mean Square Error ◽  
Bayesian Information Criterion ◽  
Linear Trend ◽  
Growth Curves ◽  
Information Criterion ◽  
Time Series Models ◽  
Cumulative Number ◽  
Mean Square ◽  
Nonlinear Growth

ABSTRACT Objectives: The objective of this study is to compare the various nonlinear and time series models in describing the course of the coronavirus disease 2019 (COVID-19) outbreak in China. To this aim, we focus on 2 indicators: the number of total cases diagnosed with the disease, and the death toll. Methods: The data used for this study are based on the reports of China between January 22 and June 18, 2020. We used nonlinear growth curves and some time series models for prediction of the number of total cases and total deaths. The determination coefficient (R2), mean square error (MSE), and Bayesian Information Criterion (BIC) were used to select the best model. Results: Our results show that while the Sloboda and ARIMA (0,2,1) models are the most convenient models that elucidate the cumulative number of cases; the Lundqvist-Korf model and Holt linear trend exponential smoothing model are the most suitable models for analyzing the cumulative number of deaths. Our time series models forecast that on 19 July, the number of total cases and total deaths will be 85,589 and 4639, respectively. Conclusion: The results of this study will be of great importance when it comes to modeling outbreak indicators for other countries. This information will enable governments to implement suitable measures for subsequent similar situations.

scholarly journals Prediksi Kedatangan Turis Asing ke Indonesia Menggunakan Backpropagation Neural Networks

2016 ◽  
Vol 4 (4) ◽  
pp. 485
Author(s):  
Haviluddin Haviluddin ◽  
Zainal Arifin ◽  
Awang Harsa Kridalaksana ◽  
Dedy Cahyadi
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Mean Square Error ◽  
Time Series Data ◽  
Alternative Methods ◽  
Series Data ◽  
Mean Square ◽  
Backpropagation Neural Network ◽  
Forecasting Accuracy ◽  
The Mean

In this paper, a backpropagation neural network (BPNN) method with time series data have been explored. The BPNN method to predict the foreign tourist’s arrival to Indonesia datasets have been implemented. The foreign tourist’s arrival datasets were taken from the center agency on statistics (BPS) Indonesia. The experimental results showed that the BPNN method with two hidden layers were able to forecast foreign tourist’s arrival to Indonesia. Where, the mean square error (MSE) as forecasting accuracy has been indicated. In this study, the BPNN method is able and recommended to be alternative methods for predicting time series datasets. Also, the BPNN method showed that effective and easy to use. In other words, BPNN method is capable to producing good value of forecasting.Keywords - BPNN; foreign tourists; BPS; MSEPemanfaatan backpropagation neural network (BPNN) dengan data deret waktu telah digunakan dalam paper ini. Metode BPNN telah digunakan untuk memprediksi data kedatangan turis asing ke Indonesia, dimana data turis tersebut diambil dari badan pusat statistik Indonesia (BPS). Hasil pengujian menunjukkan bahwa metode BPNN dengan dua lapisan tersembunyi mampu memodelkan dan meramalkan data kedatangan turis asing ke Indonesia yang diindikasikan dengan nilai mean square error (MSE). Penelitian ini merekomendasikan bahwa metode BPNN mampu menjadi alternative metode dalam memprediksi data yang berjenis deret waktu karena metode BPNN efektif dan lebih mudah digunakan serta mampu menghasilkan akurasi nilai peramalan yang baik.

scholarly journals A Comparison Study on Fuzzy Time Series and Holt-Winter Model in Forecasting Tourist Arrival in Langkawi, Kedah

2020 ◽  
Vol 5 (1) ◽  
pp. 34-43
Author(s):  
Nur Fatihah Fauzi ◽  
Nurul Shahiera Ahmadi ◽  
Nor Hayati Shafii ◽  
Huda Zuhrah Ab Halim
Keyword(s):  
Time Series ◽  
Mean Square Error ◽  
Tourism Industry ◽  
Fuzzy Time Series ◽  
Mean Square ◽  
Comparison Study ◽  
Microsoft Excel ◽  
A Value ◽  
The Mean ◽  
Major Donors

The tourism industry in Malaysia has been growing significantly over the years. Tourism has been one of the major donors to Malaysia’s economy. Based on the report from the Department of Statistics, a total of domestic visitors in Malaysia were recorded at about 221.3 million in 2018 with an increase of 7.7% alongside a higher record in visitor arrivals and tourism expenditure.  This study aims to make a comparison between two methods, which are Fuzzy Time Series and Holt-Winter in forecasting the number of tourist arrival in Langkawi based on the monthly tourist arrival data from January 2015 to December 2019. Both models were generated using Microsoft Excel in obtaining the forecast value.  The Mean Square Error (MSE) has been calculated in this study to get the best model by looking at the lowest value. The result found that Holt-Winter has the lowest value that is 713524285 compared to the Fuzzy Time Series with a value of 2625517469. Thus, the Holt-Winter model is the best method and has been used to forecast the tourist arrival for the next 2 years. The forecast value for the years 2020 and 2021 are displayed by month.

scholarly journals AUTOREGRESSION MODELS OF SPACE OBJECTS MOVEMENT REPRESENTED BY TLE ELEMENTS

2020 ◽  
Vol 2 (127) ◽  
pp. 103-116
Author(s):  
Aleksandr Sarichev ◽  
Bogdan Perviy
Keyword(s):  
Time Series ◽  
Mean Square Error ◽  
Autoregressive Model ◽  
Autoregressive Models ◽  
Mean Square ◽  
Element Determination ◽  
Training Samples ◽  
Space Objects ◽  
The Mean

The developed method, which is a modification of the previously developed methods for constructing autoregressive models, is used to simulate the motion of space objects in the time series of their TLE elements. The modeling system has been developed that includes: determining the optimal volume of training samples in modeling time series of TLE elements; determination of the autoregression order for each variable (TLE element); determination of the optimal structure and identification of the parameters of the autoregressive model for each variable; identification of patterns of evolution of the mean square error of autoregressive models in time based on the modeling of time series of TLE elements according to the principle of "moving interval".

scholarly journals Prediction Error of the Chain Ladder Reserving Method applied to Correlated Run-off Triangles

2007 ◽  
Vol 2 (1) ◽  
pp. 25-50 ◽  
Author(s):  
M. Merz ◽  
M. V. Wüthrich
Keyword(s):  
Time Series ◽  
Mean Square Error ◽  
Prediction Error ◽  
Time Series Model ◽  
Mean Square ◽  
Run Off ◽  
Chain Ladder Method ◽  
The Mean ◽  
Chain Ladder ◽  
Special Case

ABSTRACTIn Buchwalder et al. (2006) we revisited Mack's (1993) and Murphy's (1994) estimates for the mean square error of prediction (MSEP) of the chain ladder claims reserving method. This was done using a time series model for the chain ladder method. In this paper we extend the time series model to determine an estimate for the MSEP of a portfolio of N correlated run-off triangles. This estimate differs in the special case N = 2 from the estimate given by Braun (2004). We discuss the differences between the estimates.

scholarly journals The Mean Square Error of Prediction in the Chain Ladder Reserving Method (Mack and Murphy Revisited)

2006 ◽  
Vol 36 (2) ◽  
pp. 521-542 ◽  
Author(s):  
Markus Buchwalder ◽  
Hans Bühlmann ◽  
Michael Merz ◽  
Mario V. Wüthrich
Keyword(s):  
Time Series ◽  
Mean Square Error ◽  
Time Series Model ◽  
Mean Square ◽  
Chain Ladder Method ◽  
The Mean ◽  
Chain Ladder

We revisit the famous Mack formula [2], which gives an estimate for the mean square error of prediction MSEP of the chain ladder claims reserving method: We define a time series model for the chain ladder method. In this time series framework we give an approach for the estimation of the conditional MSEP. It turns out that our approach leads to results that differ from the Mack formula. But we also see that our derivation leads to the same formulas for the MSEP estimate as the ones given in Murphy [4]. We discuss the differences and similarities of these derivations.

The Bordeaux Automatic Meridian Circle

1978 ◽  
Vol 48 ◽  
pp. 227-228
Author(s):  
Y. Requième
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Meridian Circle ◽  
The Mean ◽  
Full Automation

In spite of important delays in the initial planning, the full automation of the Bordeaux meridian circle is progressing well and will be ready for regular observations by the middle of the next year. It is expected that the mean square error for one observation will be about ±0.”10 in the two coordinates for declinations up to 87°.

Limit tolerances for sums of measurement errors

2018 ◽  
Vol 934 (4) ◽  
pp. 59-62
Author(s):  
V.I. Salnikov
Keyword(s):  
Normal Distribution ◽  
Mean Square Error ◽  
Gaussian Distribution ◽  
Measurement Errors ◽  
Theory And Practice ◽  
Mean Square ◽  
The Mean ◽  
Limiting Values ◽  
Limiting Value

The question of calculating the limiting values of residuals in geodesic constructions is considered in the case when the limiting value for measurement errors is assumed equal to 3m, ie ∆рred = 3m, where m is the mean square error of the measurement. Larger errors are rejected. At present, the limiting value for the residual is calculated by the formula 3m√n, where n is the number of measurements. The article draws attention to two contradictions between theory and practice arising from the use of this formula. First, the formula is derived from the classical law of the normal Gaussian distribution, and it is applied to the truncated law of the normal distribution. And, secondly, as shown in [1], when ∆рred = 2m, the sums of errors naturally take the value equal to ?pred, after which the number of errors in the sum starts anew. This article establishes its validity for ∆рred = 3m. A table of comparative values of the tolerances valid and recommended for more stringent ones is given. The article gives a graph of applied and recommended tolerances for ∆рred = 3m.

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