scholarly journals دراسة مقارنة لمعايير المعلومات لتحديد رتبة نماذج الانحدار الذاتي

2012 ◽  
Vol 18 (65) ◽  
pp. 323
Author(s):  
جنان عباس ناصر
Keyword(s):  
Autoregressive Model ◽  
Error Term ◽  
Information Criterion ◽  
Information Criteria ◽  
Autoregressive Models ◽  
Sample Sizes ◽  
Data Generating Process ◽  
The Mean ◽  
Normally Distributed

In this study, we compare between the traditional Information Criteria (AIC, SIC, HQ, FPE) with The Modified Divergence Information Criterion (MDIC) which used to determine the order of Autoregressive model (AR) for the data generating process, by using the simulation by generating data from several of Autoregressive models, when the error term is normally distributed with different values for its parameters (the mean and the variance),and for different sample  sizes.

scholarly journals Model Selection Procedures in Bounds Test of Cointegration: Theoretical Comparison and Empirical Evidence

Economies ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 49 ◽  
Author(s):  
Waqar Badshah ◽  
Mehmet Bulut
Keyword(s):  
Model Selection ◽  
Akaike Information Criterion ◽  
Bayesian Information Criterion ◽  
Selection Process ◽  
Information Criterion ◽  
Small Sample ◽  
Information Criteria ◽  
Path Model ◽  
Sample Sizes ◽  
Bounds Test

Only unstructured single-path model selection techniques, i.e., Information Criteria, are used by Bounds test of cointegration for model selection. The aim of this paper was twofold; one was to evaluate the performance of these five routinely used information criteria {Akaike Information Criterion (AIC), Akaike Information Criterion Corrected (AICC), Schwarz/Bayesian Information Criterion (SIC/BIC), Schwarz/Bayesian Information Criterion Corrected (SICC/BICC), and Hannan and Quinn Information Criterion (HQC)} and three structured approaches (Forward Selection, Backward Elimination, and Stepwise) by assessing their size and power properties at different sample sizes based on Monte Carlo simulations, and second was the assessment of the same based on real economic data. The second aim was achieved by the evaluation of the long-run relationship between three pairs of macroeconomic variables, i.e., Energy Consumption and GDP, Oil Price and GDP, and Broad Money and GDP for BRICS (Brazil, Russia, India, China and South Africa) countries using Bounds cointegration test. It was found that information criteria and structured procedures have the same powers for a sample size of 50 or greater. However, BICC and Stepwise are better at small sample sizes. In the light of simulation and real data results, a modified Bounds test with Stepwise model selection procedure may be used as it is strongly theoretically supported and avoids noise in the model selection process.

scholarly journals Mean number of real zeros of a random trigonometric polynomial. III

1995 ◽  
Vol 8 (3) ◽  
pp. 299-317
Author(s):  
J. Ernest Wilkins ◽  
Shantay A. Souter
Keyword(s):  
Trigonometric Polynomial ◽  
Approximate Formula ◽  
Error Term ◽  
Random Variables ◽  
Real Zeros ◽  
Number Of Zeros ◽  
Number Of Real Zeros ◽  
Random Trigonometric Polynomial ◽  
The Mean ◽  
Normally Distributed

If a1,a2,…,an are independent, normally distributed random variables with mean 0 and variance 1, and if vn is the mean number of zeros on the interval (0,2π) of the trigonometric polynomial a1cosx+2½a2cos2x+…+n½ancosnx, then vn=2−½{(2n+1)+D1+(2n+1)−1D2+(2n+1)−2D3}+O{(2n+1)−3}, in which D1=−0.378124, D2=−12, D3=0.5523. After tabulation of 5D values of vn when n=1(1)40, we find that the approximate formula for vn, obtained from the above result when the error term is neglected, produces 5D values that are in error by at most 10−5 when n≥8, and by only about 0.1% when n=2.

scholarly journals Markov Switching Intercept Vector Autoregressive Model (MSI(2)-VAR(2)) of Nigeria Inflation Rate and Crude Oil Price (Using Views 11)

2021 ◽  
Vol 4 (2) ◽  
pp. 88-100
Author(s):  
Wiri L. ◽  
Sibeate P.U. ◽  
Isaac D.E.
Keyword(s):  
Crude Oil ◽  
Regime Switching ◽  
Autoregressive Model ◽  
Inflation Rate ◽  
Markov Switching ◽  
Information Criterion ◽  
Information Criteria ◽  
Vector Autoregressive Model ◽  
Vector Autoregressive ◽  
Crude Oil Prices

To model inflation rate and crude oil prices, we used Markov Switching intercept heteroscedasticity Vector Autoregressive models. The data for this analysis was gathered from the Central Bank of Nigeria Statistical Bulletin monthly. The upward and downward movement in the series revealed by the time plot suggests that the series exhibit a regime-switching pattern: the period of expansion and contraction. The variable was stationary at first differences, the Augmented Dickey-Fuller test was used to screen for stationarity. The information criteria were used to test the number of regime and regime two were selected. Eight models were estimated for the MSI-VAR model. The best model was chosen based on the criterion of least information criterion, Markov-switching intercept heteroscedasticity – Vector Autoregressive model (MSIH(2)-VAR(2)) with AIC (8.596641) and SC (8.973119). The model was used to predict the series' values over a one-year cycle (12 months).

scholarly journals Normalized Information Criteria and Model Selection in the Presence of Missing Data

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2474
Author(s):  
Nitzan Cohen ◽  
Yakir Berchenko
Keyword(s):  
Missing Data ◽  
Model Selection ◽  
Missing Values ◽  
Model Averaging ◽  
Information Criterion ◽  
Current Theory ◽  
Information Criteria ◽  
Alternative Methods ◽  
Sample Sizes ◽  
Statistical Efficiency

Information criteria such as the Akaike information criterion (AIC) and Bayesian information criterion (BIC) are commonly used for model selection. However, the current theory does not support unconventional data, so naive use of these criteria is not suitable for data with missing values. Imputation, at the core of most alternative methods, is both distorted as well as computationally demanding. We propose a new approach that enables the use of classic well-known information criteria for model selection when there are missing data. We adapt the current theory of information criteria through normalization, accounting for the different sample sizes used for each candidate model (focusing on AIC and BIC). Interestingly, when the sample sizes are different, our theoretical analysis finds that AICj/nj is the proper correction for AICj that we need to optimize (where nj is the sample size available to the jth model) while −(BICj−BICi)/(nj−ni) is the correction of BIC. Furthermore, we find that the computational complexity of normalized information criteria methods is exponentially better than that of imputation methods. In a series of simulation studies, we find that normalized-AIC and normalized-BIC outperform previous methods (i.e., normalized-AIC is more efficient, and normalized BIC includes only important variables, although it tends to exclude some of them in cases of large correlation). We propose three additional methods aimed at increasing the statistical efficiency of normalized-AIC: post-selection imputation, Akaike sub-model averaging, and minimum-variance averaging. The latter succeeds in increasing efficiency further.

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".

The Estimation of Blood Platelet Survival

1972 ◽  
Vol 28 (03) ◽  
pp. 447-456 ◽  
Author(s):  
E. A Murphy ◽  
M. E Francis ◽  
J. F Mustard
Keyword(s):  
Standard Deviation ◽  
Least Squares ◽  
Experimental Error ◽  
Blood Platelet ◽  
Least Squares Estimation ◽  
Systematic Relationship ◽  
Platelet Survival ◽  
The Mean ◽  
Normally Distributed

SummaryThe characteristics of experimental error in measurement of platelet radioactivity have been explored by blind replicate determinations on specimens taken on several days on each of three Walker hounds.Analysis suggests that it is not unreasonable to suppose that error for each sample is normally distributed ; and while there is evidence that the variance is heterogeneous, no systematic relationship has been discovered between the mean and the standard deviation of the determinations on individual samples. Thus, since it would be impracticable for investigators to do replicate determinations as a routine, no improvement over simple unweighted least squares estimation on untransformed data suggests itself.

scholarly journals Modeling of Lake Malombe Annual Fish Landings and Catch per Unit Effort (CPUE)

Forecasting ◽  
2021 ◽  
Vol 3 (1) ◽  
pp. 39-55
Author(s):  
Rodgers Makwinja ◽  
Seyoum Mengistou ◽  
Emmanuel Kaunda ◽  
Tena Alemiew ◽  
Titus Bandulo Phiri ◽  
...  
Keyword(s):  
Time Series ◽  
Information Criterion ◽  
Coefficient Of Determination ◽  
Series Data ◽  
Efficiency Coefficient ◽  
Arima Models ◽  
Catch Per Unit Effort ◽  
Annual Fish ◽  
Unit Effort ◽  
The Mean

Forecasting, using time series data, has become the most relevant and effective tool for fisheries stock assessment. Autoregressive integrated moving average (ARIMA) modeling has been commonly used to predict the general trend for fish landings with increased reliability and precision. In this paper, ARIMA models were applied to predict Lake Malombe annual fish landings and catch per unit effort (CPUE). The annual fish landings and CPUE trends were first observed and both were non-stationary. The first-order differencing was applied to transform the non-stationary data into stationary. Autocorrelation functions (AC), partial autocorrelation function (PAC), Akaike information criterion (AIC), Bayesian information criterion (BIC), square root of the mean square error (RMSE), the mean absolute error (MAE), percentage standard error of prediction (SEP), average relative variance (ARV), Gaussian maximum likelihood estimation (GMLE) algorithm, efficiency coefficient (E2), coefficient of determination (R2), and persistent index (PI) were estimated, which led to the identification and construction of ARIMA models, suitable in explaining the time series and forecasting. According to the measures of forecasting accuracy, the best forecasting models for fish landings and CPUE were ARIMA (0,1,1) and ARIMA (0,1,0). These models had the lowest values AIC, BIC, RMSE, MAE, SEP, ARV. The models further displayed the highest values of GMLE, PI, R2, and E2. The “auto. arima ()” command in R version 3.6.3 further displayed ARIMA (0,1,1) and ARIMA (0,1,0) as the best. The selected models satisfactorily forecasted the fish landings of 2725.243 metric tons and CPUE of 0.097 kg/h by 2024.

ON A NEW CIRCLE PROBLEM

2016 ◽  
Vol 103 (2) ◽  
pp. 231-249
Author(s):  
JUN FURUYA ◽  
MAKOTO MINAMIDE ◽  
YOSHIO TANIGAWA
Keyword(s):  
Asymptotic Formula ◽  
Error Term ◽  
Dirichlet Character ◽  
Arithmetical Function ◽  
Circle Problem ◽  
The Riemann Zeta Function ◽  
Primitive Dirichlet Character ◽  
Riemann Zeta ◽  
The Mean ◽  
Voronoi Formula

We attempt to discuss a new circle problem. Let $\unicode[STIX]{x1D701}(s)$ denote the Riemann zeta-function $\sum _{n=1}^{\infty }n^{-s}$ ($\text{Re}\,s>1$) and $L(s,\unicode[STIX]{x1D712}_{4})$ the Dirichlet $L$-function $\sum _{n=1}^{\infty }\unicode[STIX]{x1D712}_{4}(n)n^{-s}$ ($\text{Re}\,s>1$) with the primitive Dirichlet character mod 4. We shall define an arithmetical function $R_{(1,1)}(n)$ by the coefficient of the Dirichlet series $\unicode[STIX]{x1D701}^{\prime }(s)L^{\prime }(s,\unicode[STIX]{x1D712}_{4})=\sum _{n=1}^{\infty }R_{(1,1)}(n)n^{-s}$$(\text{Re}\,s>1)$. This is an analogue of $r(n)/4=\sum _{d|n}\unicode[STIX]{x1D712}_{4}(d)$. In the circle problem, there are many researches of estimations and related topics on the error term in the asymptotic formula for $\sum _{n\leq x}r(n)$. As a new problem, we deduce a ‘truncated Voronoï formula’ for the error term in the asymptotic formula for $\sum _{n\leq x}R_{(1,1)}(n)$. As a direct application, we show the mean square for the error term in our new problem.

scholarly journals The Probability That a Measurement Falls within a Range of Standard Deviations from an Estimate of the Mean

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Louis M. Houston
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
General Equation ◽  
Sample Sizes ◽  
The Mean ◽  
Standard Deviations ◽  
Intermediate Value ◽  
Theoretical Results

We derive a general equation for the probability that a measurement falls within a range of n standard deviations from an estimate of the mean. So, we provide a format that is compatible with a confidence interval centered about the mean that is naturally independent of the sample size. The equation is derived by interpolating theoretical results for extreme sample sizes. The intermediate value of the equation is confirmed with a computational test.

scholarly journals A mixture autoregressive model based on Gaussian and Student’s t-distributions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Savi Virolainen
Keyword(s):  
Interest Rate ◽  
Autoregressive Model ◽  
Autoregressive Models ◽  
Federal Funds ◽  
Treasury Bill ◽  
Federal Funds Rate ◽  
Empirical Application ◽  
Model Based ◽  
Interest Rate Spread ◽  
Student’S T

Abstract We introduce a new mixture autoregressive model which combines Gaussian and Student’s t mixture components. The model has very attractive properties analogous to the Gaussian and Student’s t mixture autoregressive models, but it is more flexible as it enables to model series which consist of both conditionally homoscedastic Gaussian regimes and conditionally heteroscedastic Student’s t regimes. The usefulness of our model is demonstrated in an empirical application to the monthly U.S. interest rate spread between the 3-month Treasury bill rate and the effective federal funds rate.

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