scholarly journals Second-Order Least Squares Estimation in Nonlinear Time Series Models with ARCH Errors

Econometrics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 41
Author(s):  
Mustafa Salamh ◽  
Liqun Wang
Keyword(s):  
Time Series ◽  
Real Data ◽  
Error Distribution ◽  
Likelihood Method ◽  
Strong Mixing ◽  
Efficiency Gain ◽  
Economic Time Series ◽  
Mixing Condition ◽  
Conditional Moments ◽  
Dynamic Regression Model

Many financial and economic time series exhibit nonlinear patterns or relationships. However, most statistical methods for time series analysis are developed for mean-stationary processes that require transformation, such as differencing of the data. In this paper, we study a dynamic regression model with nonlinear, time-varying mean function, and autoregressive conditionally heteroscedastic errors. We propose an estimation approach based on the first two conditional moments of the response variable, which does not require specification of error distribution. Strong consistency and asymptotic normality of the proposed estimator is established under strong-mixing condition, so that the results apply to both stationary and mean-nonstationary processes. Moreover, the proposed approach is shown to be superior to the commonly used quasi-likelihood approach and the efficiency gain is significant when the (conditional) error distribution is asymmetric. We demonstrate through a real data example that the proposed method can identify a more accurate model than the quasi-likelihood method.

scholarly journals Forecasting Randomly Distributed Zero-Inflated Time Series

2017 ◽  
Vol 17 (1) ◽  
pp. 7-19
Author(s):  
Mariusz Doszyń
Keyword(s):  
Time Series ◽  
Forecast Error ◽  
Real Data ◽  
Economic Time Series ◽  
Times Series ◽  
Ex Post ◽  
Data Regression ◽  
Economic Time ◽  
The Times ◽  
A Company

Abstract The main aim of the article is to propose a forecasting procedure that could be useful in the case of randomly distributed zero-inflated time series. Many economic time series are randomly distributed, so it is not possible to estimate any kind of statistical or econometric models such as, for example, count data regression models. This is why in the article a new forecasting procedure based on the stochastic simulation is proposed. Before it is used, the randomness of the times series should be considered. The hypothesis stating the randomness of the times series with regard to both sales sequences or sales levels is verified. Moreover, in the article the ex post forecast error that could be computed also for a zero-inflated time series is proposed. All of the above mentioned parts were invented by the author. In the empirical example, the described procedure was applied to forecast the sales of products in a company located in the vicinity of Szczecin (Poland), so real data were analysed. The accuracy of the forecast was verified as well.

scholarly journals Logarithm Transformed Fr´echet Distribution : Properties and Estimation

2018 ◽  
Vol 48 (1) ◽  
pp. 70-93 ◽  
Author(s):  
Sanku Dey ◽  
Mazen Nassar ◽  
Devendra Kumar ◽  
Fahad Alaboud
Keyword(s):  
Maximum Likelihood ◽  
Stochastic Ordering ◽  
Real Data ◽  
Moment Generating Function ◽  
Maximum Likelihood Estimates ◽  
Superior Performance ◽  
Likelihood Method ◽  
Parameter Distribution ◽  
Extended Model ◽  
Conditional Moments

In this paper, a new three-parameter distribution called the Alpha Logarithm Transformed Fr\'{e}chet (ALTF) distribution is introduced which offers a more flexible distribution for modeling lifetime data. Various properties of the proposed distribution, including explicit expressions for the quantiles, moments, incomplete moments, conditional moments, moment generating function R\'{e}nyi and $\delta$-entropies, stochastic ordering, stress-strength reliability and order statistics are derived. The new distribution can have decreasing, reversed J-shaped and upside-down bathtub failure rate functions depending on its parameter values. The maximum likelihood method is used to estimate the distribution parameters. A simulation study is conducted to evaluate the performance of the maximum likelihood estimates. Finally, the proposed extended model is applied on real data sets and the results are given which illustrate the superior performance of the ALTF distribution compared to some other well-known distributions.

scholarly journals Prognozowanie dynamiki gospodarczej Niemiec z pomocą modeli warunkowych (1992-2014)

2016 ◽  
Vol 16 (3) ◽  
pp. 41
Author(s):  
Wiesław Edward Łuczyński
Keyword(s):  
Time Series ◽  
Likelihood Method ◽  
Economic Time Series ◽  
Economic Dynamics ◽  
Ex Post ◽  
Economic Time ◽  
Long Term Forecasting ◽  
Hp Filter ◽  
Mean Square Errors

A great diversity characterizes economic dynamics of Germany over a long period of time. This refers to many time series: in some periods, they show large volatility which then moves into stability and stagnation phase, generating specific difficulties in a long-term forecasting of economic dynamics. The aim of the research is the attempt to determine the prognostic efficiency of conditional modelling and to answer the question whether or not conditional errors are significantly smaller than the unconditional ones in long-term forecasting.The research showed that conditional errors (root mean square errors RMSE) of an ex- post forecast did not differ significantly from the unconditional RMSE. The decreasing RMSE of the ex-post forecast for Germany’s  individual economic processes (with the assumption that an intercept occurs in the ARMA procedure) was correlated more strongly with the procedure of filtering economic time series than with the application of the conditional maximum likelihood method (ML) and robust procedures. The relationship between a decreasing  RMSE of the ex-post forecast and the application  of conditional ML methods occurs in ARMAX forecasts (with exogenous processes) for data filtered with  Hodrick - Prescott (HP) filter. It is worth pointing out that a relatively high prognostic efficiency of the robust (resistant) estimation of quantile regression occurs for the economic series linearized with the help of  the TRAMO/SEATS method.

scholarly journals On the T-X Class of Topp Leone-G Family of Distributions: Statistical Properties and Applications

2021 ◽  
Vol 2 ◽  
pp. 2
Author(s):  
Femi Samuel Adeyinka
Keyword(s):  
Real Data ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Mean Deviation ◽  
Data Sets ◽  
Hazard Functions ◽  
Lorenz Curves ◽  
Conditional Moments ◽  
New Family ◽  
Family Of Distributions

This article investigates the T-X class of Topp Leone- G family of distributions. Some members of the new family are discussed.  The exponential-Topp Leone-exponential distribution (ETLED) which is one of the members of the family is derived and some of its properties which include central and non-central moments, quantiles, incomplete moments, conditional moments, mean deviation, Bonferroni and Lorenz curves, survival and hazard functions, moment generating function, characteristic function and R`enyi entropy are established. The probability density function (pdf) of order statistics of the model is obtained and the parameter estimation is addressed with the maximum likelihood method (MLE). Three real data sets are used to demonstrate its application and the results are compared with two other models in the literature.

scholarly journals A Noncentral Lindley Construction Illustrated in an INAR(1) Environment

Stats ◽  
2022 ◽  
Vol 5 (1) ◽  
pp. 70-88
Author(s):  
Johannes Ferreira ◽  
Ané van der Merwe
Keyword(s):  
Time Series ◽  
Discrete Time ◽  
Count Data ◽  
Structural Characteristics ◽  
Poisson Model ◽  
Real Data ◽  
Error Distribution ◽  
Noncentrality Parameter ◽  
Lindley Distribution ◽  
Count Model

This paper proposes a previously unconsidered generalization of the Lindley distribution by allowing for a measure of noncentrality. Essential structural characteristics are investigated and derived in explicit and tractable forms, and the estimability of the model is illustrated via the fit of this developed model to real data. Subsequently, this model is used as a candidate for the parameter of a Poisson model, which allows for departure from the usual equidispersion restriction that the Poisson offers when modelling count data. This Poisson-noncentral Lindley is also systematically investigated and characteristics are derived. The value of this count model is illustrated and implemented as the count error distribution in an integer autoregressive environment, and juxtaposed against other popular models. The effect of the systematically-induced noncentrality parameter is illustrated and paves the way for future flexible modelling not only as a standalone contender in continuous Lindley-type scenarios but also in discrete and discrete time series scenarios when the often-encountered equidispersed assumption is not adhered to in practical data environments.

A DIFFUSION APPROACH TO ECONOMIC TIME SERIES

2000 ◽  
Vol 03 (03) ◽  
pp. 567-568
Author(s):  
M. CIOGLI ◽  
G. ROTUNDO ◽  
B. TIROZZI
Keyword(s):  
Time Series ◽  
Maximum Likelihood ◽  
Diffusion Equation ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Economic Time Series ◽  
Martingale Theory ◽  
Hedging Strategy ◽  
Economic Time

A diffusion equation for the price evolution of the Italian share "Olivetti" is found by investigating a series of its data. The coefficients of this equation are found by using the maximum likelihood method based on martingale theory. We evaluate pricing and hedging strategy by the Sornette and Bouchaud approach.

scholarly journals The Use of Odd and Even Class Wind Speed Time Series of Distribution Histogram to Estimate Weibull Parameters

2018 ◽  
Vol 7 (2) ◽  
pp. 139-150 ◽  
Author(s):  
Adekunlé Akim Salami ◽  
Ayité Sénah Akoda Ajavon ◽  
Mawugno Koffi Kodjo ◽  
Seydou Ouedraogo ◽  
Koffi-Sa Bédja
Keyword(s):  
Time Series ◽  
Wind Speed ◽  
Time Series Data ◽  
Empirical Method ◽  
Likelihood Method ◽  
Series Data ◽  
New Approach ◽  
Weibull Parameters ◽  
Distribution Histogram ◽  
Mean Wind Speed

In this article, we introduced a new approach based on graphical method (GPM), maximum likelihood method (MLM), energy pattern factor method (EPFM), empirical method of Justus (EMJ), empirical method of Lysen (EML) and moment method (MOM) using the even or odd classes of wind speed series distribution histogram with 1 m/s as bin size to estimate the Weibull parameters. This new approach is compared on the basis of the resulting mean wind speed and its standard deviation using seven reliable statistical indicators (RPE, RMSE, MAPE, MABE, R2, RRMSE and IA). The results indicate that this new approach is adequate to estimate Weibull parameters and can outperform GPM, MLM, EPF, EMJ, EML and MOM which uses all wind speed time series data collected for one period. The study has also found a linear relationship between the Weibull parameters K and C estimated by MLM, EPFM, EMJ, EML and MOM using odd or even class wind speed time series and those obtained by applying these methods to all class (both even and odd bins) wind speed time series. Another interesting feature of this approach is the data size reduction which eventually leads to a reduced processing time.Article History: Received February 16th 2018; Received in revised form May 5th 2018; Accepted May 27th 2018; Available onlineHow to Cite This Article: Salami, A.A., Ajavon, A.S.A., Kodjo, M.K. , Ouedraogo, S. and Bédja, K. (2018) The Use of Odd and Even Class Wind Speed Time Series of Distribution Histogram to Estimate Weibull Parameters. Int. Journal of Renewable Energy Development 7(2), 139-150.https://doi.org/10.14710/ijred.7.2.139-150

Sign in / Sign up

Export Citation Format

Share Document