scholarly journals New Estimator for AR (1) Model with Missing Observations

2021 ◽  
Vol 23 (09) ◽  
pp. 147-159
Author(s):  
Mohamed Khalifa Ahmed Issa ◽  
Keyword(s):  
Time Series ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Least Squares ◽  
Unit Root ◽  
Constant Term ◽  
Ordinary Least Squares ◽  
Missing Observations ◽  
New Form ◽  
Near Unit Root

In this paper, new form of the parameters of AR(1) with constant term with missing observations has been derived by using Ordinary Least Squares (OLS) method, Also, the properties of OLS estimator are discussed, moreover, an extension of Youssef [18]has been suggested for AR(1) with constant with missing observations. A comparative study between (OLS), Yule-Walker (YW) and modification of the ordinary least squares (MOLS) is considered in the case of stationary and near unit root time series, using Monte Carlo simulation.

Using limited dependent variable estimators for estimating percent decay

1993 ◽  
Vol 23 (2) ◽  
pp. 266-274 ◽  
Author(s):  
Valerie M. Lemay ◽  
Antal Kozak ◽  
Peter L. Marshall
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Least Squares ◽  
Ordinary Least Squares ◽  
Unexpected Result ◽  
Data Set ◽  
A Value ◽  
Wide Range ◽  
Truncated Normal ◽  
Tobit Estimator

The data used for the estimation of percent decay are bounded by zero and 100. Because a value of 100% indicates that the tree is completely decayed, this value is not observable in nature. However, a value of zero percent is often observed over a wide range of the independent variables. The distribution of percent decay is a combination of a truncated continuous distribution for percent decay greater than zero and a discrete component for the zero percents. The use of ordinary least squares with this type of data results in biased and inconsistent estimates of the coefficients of a percent decay equation. An alternative is the tobit estimator (a combined regression and probit estimator based on a maximum likelihood equation), which results in consistent estimates of the coefficients if the error terms of the model are independent and identically distributed as the truncated normal distribution. A Monte Carlo simulation using data for three species with different proportions of zero percents was performed to compare the ordinary least squares and tobit estimators. As expected, the tobit estimator resulted in quite different estimates of the coefficients of the equations than did ordinary least squares. An unexpected result was that the estimated expected percent decay was slightly more biased for the tobit estimator than for the ordinary least squares estimator, even with a large number of zero percents in the data set. Possible explanations for the Monte Carlo simulation results and recommendations for fitting percent decay equations are given in the paper.

Generalized Forecast Averaging in Autoregressions with a Near Unit Root

2020 ◽  
Author(s):  
Mohitosh Kejriwal ◽  
Xuewen Yu
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Mean Squared Error ◽  
Model Averaging ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Finite Sample ◽  
Deterministic Components ◽  
Asymptotic Mean Squared Error ◽  
Near Unit Root

Summary This paper develops a new approach to forecasting a highly persistent time series that employs feasible generalized least squares (FGLS) estimation of the deterministic components in conjunction with Mallows model averaging. Within a local-to-unity asymptotic framework, we derive analytical expressions for the asymptotic mean squared error and one-step-ahead mean squared forecast risk of the proposed estimator and show that the optimal FGLS weights are different from their ordinary least squares (OLS) counterparts. We also provide theoretical justification for a generalized Mallows averaging estimator that incorporates lag order uncertainty in the construction of the forecast. Monte Carlo simulations demonstrate that the proposed procedure yields a considerably lower finite-sample forecast risk relative to OLS averaging. An application to U.S. macroeconomic time series illustrates the efficacy of the advocated method in practice and finds that both persistence and lag order uncertainty have important implications for the accuracy of forecasts.

Estimation of Models with Variable Coefficients

1991 ◽  
Vol 3 ◽  
pp. 27-49 ◽  
Author(s):  
John E. Jackson
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Least Squares ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Variable Coefficients ◽  
Coefficient Estimates ◽  
Explanatory Variables ◽  
Varying Coefficients

The ordinary least squares (OLS) estimator gives biased coefficient estimates if coefficients are not constant for all cases but vary systematically with the explanatory variables. This article discusses several different ways to estimate models with systematically and randomly varying coefficients using estimated generalized least squares and maximum likelihood procedures. A Monte Carlo simulation of the different methods is presented to illustrate their use and to contrast their results to the biased results obtained with ordinary least squares. Several applications of the methods are discussed and one is presented in detail. The conclusion is that, in situations with variables coefficients, these methods offer relatively easy means for overcoming the problems.

Nuisance vs. Substance: Specifying and Estimating Time-Series-Cross-Section Models

1996 ◽  
Vol 6 ◽  
pp. 1-36 ◽  
Author(s):  
Nathaniel Beck ◽  
Jonathan N. Katz
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Cross Section ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Correlated Errors ◽  
Section Data ◽  
Variable Approach ◽  
Parameter Heterogeneity ◽  
Lagged Dependent Variable

In a previous article we showed that ordinary least squares with panel corrected standard errors is superior to the Parks generalized least squares approach to the estimation of time-series-cross-section models. In this article we compare our proposed method with another leading technique, Kmenta's “cross-sectionally heteroskedastic and timewise autocorrelated” model. This estimator uses generalized least squares to correct for both panel heteroskedasticity and temporally correlated errors. We argue that it is best to model dynamics via a lagged dependent variable rather than via serially correlated errors. The lagged dependent variable approach makes it easier for researchers to examine dynamics and allows for natural generalizations in a manner that the serially correlated errors approach does not. We also show that the generalized least squares correction for panel heteroskedasticity is, in general, no improvement over ordinary least squares and is, in the presence of parameter heterogeneity, inferior to it. In the conclusion we present a unified method for analyzing time-series-cross-section data.

scholarly journals EXPLOITING INFINITE VARIANCE THROUGH DUMMY VARIABLES IN NONSTATIONARY AUTOREGRESSIONS

2013 ◽  
Vol 29 (6) ◽  
pp. 1162-1195 ◽  
Author(s):  
Giuseppe Cavaliere ◽  
Iliyan Georgiev
Keyword(s):  
Unit Root ◽  
Asymptotic Properties ◽  
Ordinary Least Squares ◽  
Infinite Variance ◽  
Local Power ◽  
Test Statistic ◽  
Asymptotically Normal ◽  
Normal Test ◽  
Order Of Magnitude ◽  
Near Unit Root

We consider estimation and testing in finite-order autoregressive models with a (near) unit root and infinite-variance innovations. We study the asymptotic properties of estimators obtained by dummying out “large” innovations, i.e., those exceeding a given threshold. These estimators reflect the common practice of dealing with large residuals by including impulse dummies in the estimated regression. Iterative versions of the dummy-variable estimator are also discussed. We provide conditions on the preliminary parameter estimator and on the threshold that ensure that (i) the dummy-based estimator is consistent at higher rates than the ordinary least squares estimator, (ii) an asymptotically normal test statistic for the unit root hypothesis can be derived, and (iii) order of magnitude gains of local power are obtained.

An Investigation of the Time Series Behaviour of International Tourist Arrivals

1997 ◽  
Vol 3 (2) ◽  
pp. 185-199 ◽  
Author(s):  
Kevin KF. Wong
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Preliminary Investigation ◽  
Model Misspecification ◽  
Theoretical Implication ◽  
Ordinary Least Squares ◽  
Initial State ◽  
International Tourist ◽  
Stationary Type ◽  
Parameter Estimators

Most tourism econometric models are based on conventional least squares estimation, which assumes stationarity in their data generating mechanism. However, they fail to recognize the implications of the integrated properties of the historical time series of tourism data. Such time series properties may have important consequences with regard to the theoretical implication and interpretation of these tourism models. In this paper, historical data on international tourist arrivals from six major regions and seventeen individual countries are analysed to determine whether the series is better characterized by a stationary or non-stationary type process. Based on unit root tests, the results in most cases indicate that international tourist arrivals exhibit a non-stationary stochastic process that has the tendency to fluctuate away from a given initial state as time passes. These findings imply that studies which conveniently draw standard inferences from ordinary least squares estimated tourism models based on the levels of international tourist arrivals can be very misleading since non-stationarity in the data will produce inconsistent parameter estimators and unreliable test statistics. Furthermore, model misspecification that arises from unrelated integrated series can seriously bias conventional significance tests towards the acceptance of an apparently significant relationship. In this preliminary investigation, we conclude that econometric tourism models that focus on the levels of international tourist arrivals may not be reliable since the series is non-stationary and is integrated of order one, I(1).

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