scholarly journals Asymptotic expansions of econometric estimators in time series models

2011 ◽  
Author(s):  
Δήμητρα Κυριακοπούλου
Keyword(s):  
Time Series ◽  
Asymptotic Expansions ◽  
Bias Correction ◽  
Mean Squared Error ◽  
Asymptotic Properties ◽  
Second Order ◽  
Supremum Norm ◽  
Time Series Models ◽  
True Parameter ◽  
The Mean

Techniques for approximating probability distributions like the Edgeworth expansion have a long history in time series models. The purpose of this thesis is to give a detailed study of the asymptotic properties of the Moving Average (MA) and the Exponential GARCH (EGARCH) models. Extending the results in Sargan (1976) [80] and Tanaka (1984) [87], we derive the asymptotic expansions of the distribution, the bias and the mean squared error of the MM and QML estimators of the first order autocorrelation and the MA parameter for the MA(1) model. It turns out that the asymptotic properties of the estimators depend on whether the mean of the process is known or estimated. A comparison of the moment expansions, either in terms of bias or MSE, reveals that there is not uniform superiority of neither of the estimators, when the mean of the process is estimated. This is also confirmed by simulations. In the zero-mean case, and on theoretical grounds, the QMLEs are superior to the MM ones in both bias and MSE terms. The results are important for bias correction and increasing the efficiency of the estimators. Next, we derive the bias approximations of the ML and QML estimators of the EGARCH(1,1) parameters and we check our theoretical results through simulations. With the approximate bias expressions up to O(1/T), we are then able to correct the bias of all estimators. To this end, a Monte Carlo exercise is conducted and the results are presented and discussed. We conclude that, for given sets of parameters values, the bias correction works satisfactory for all parameters. The results for the bias expressions can be used to formulate the approximate Edgeworth distribution of the estimators. Moreover, the asymptotic properties of EGARCH models are still largely unexplored and are considered difficult tasks (see e.g. Straumann and Mikosch, 2006) [83]. There is still no complete answer to the following questions: under which conditions do EGARCH processes have bounded first and second order variance derivatives? And under which conditions is the expectation of the supremum norm of the second order log-likelihood derivative finite, in a neighborhood around the true parameter value? These questions are important because the existence of such moment bounds permits the establishment of large sample statistical properties, such as the asymptotic normality of the QMLEs.

scholarly journals An Analysis of Time-Series Models for Age-Specific Mortality Rates in India

2020 ◽  
Vol 5 (8) ◽  
pp. 1133-1140
Author(s):  
Aritra Sen ◽  
Shalmoli Dutta
Keyword(s):  
Time Series ◽  
Mean Squared Error ◽  
Current Trend ◽  
Mortality Rates ◽  
Percentage Error ◽  
Time Series Models ◽  
Annual Data ◽  
Registration System ◽  
The Mean ◽  
Best Fit

Mortality is a continuous force of attrition, tending to reduce the population, a prime negative force in the balance of vital processes (Bhasin and Nag, 2004). Sample Registration System (SRS) serves as the only source of annual data on vital events on a full scale from 1969-70 in India. Few studies have examined the trends and patterns of mortality across time and regions in India (Preston and Bhat, 1984). The Under 5 Mortality Rates (U5MR) can be seen to decrease by more than half from 1970 to 2017 but in contrast little is known about the mortality patterns of the older children (5-9) and young adolescents (10-14), and not many studies have been done on their changing trends (Masquelier et al., 2018). Using the annual data for the 5-14 age, the trend of decline in the mortality patterns is studied from 1970 to 2013. The linear trend in the time series plot suggests analysis using time series models AR(p), MA(q), ARMA(p,q), Box- Jenkins ARIMA(p,d,q) and Random Walk with drift models to get the best fit to the trend of the data. The order of the time series models have been calculated by studying the ACF, PACF plots and the coefficients have been derived using the Yule-Walker equation matrix. An in-sample forecast of the years 2014-17 are taken. The Mean Squared Error (MSE) and the Mean Absolute Percentage Error (MAPE) as a measure of accuracy is used to determine the best fit model. ARIMA(3,1,1) produced lower values making it the best-fit model. Out-of-sample forecasting was done for 2018-2025. The forecast value shows that at the current trend, India would have 0.03 deaths per 1000 population in the 5-14 age group in 2025 showing that the government’s policies and health care interventions towards realization of the MDG4 goal is working positively.

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

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

<p align="justify">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 <span>a principal component</span> 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 <span>a</span> 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 <span>proposed</span> 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.</p>

Forecasting Technique for the Production Plan of the Local Earthenware Industries of Thailand

2014 ◽  
Vol 577 ◽  
pp. 1279-1282
Author(s):  
Weerapol Namboonruang ◽  
N Amdee
Keyword(s):  
Time Series ◽  
Classical Model ◽  
Mean Absolute Percentage Error ◽  
Percentage Error ◽  
Time Series Models ◽  
Production Plan ◽  
Absolute Percentage Error ◽  
The Mean

The purpose of this work is to compare the forecasting of time series models between two different models. One is the classical model and another is the Box-Jenkins model. The data are calculated using the circulation of Angbuaand Ahongwhich are the local earthenware products from Ratchaburi province, Thailand. Results show that the mean absolute percentage error (MAPE) of Angbua and Ahong are 17.80, 36.12 and 16.38,17.21 respectively. Also,prediction using the Box-Jenkins Model by ARIMA form of both products are (1, 0, 0) and (1, 1, 1). From this work the Box-Jenkins Model shows more appropriate method than the classical model considered by the less error.

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