Modified Two-Stage Sampling Around the Mean of the First Order Autoregressive Model

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Sajjadipanah S.; MAHMOUDI E.; ZAMANI M.

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Paper Information

Journal: JOURNAL OF STATISTICAL SCIENCES Year:2022 | Volume:16 | Issue:1 Page(s): 127-148

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Information Journal Paper

Title

Modified Two-Stage Sampling Around the Mean of the First Order Autoregressive Model

Author(s)

Sajjadipanah S. | MAHMOUDI E. | ZAMANI M. | Issue Writer Certificate

Keywords

Modified two-stage procedure

Autoregressive model

least-squares estimator

Monte Carlo simulation

Abstract

Introduction Due to its simplicity, the autoregressive process is widely used in practice. In some cases, we face restrictions in estimating the parameter for predicting the expected value of the time series models and cannot use an optimal fixed sample size procedure. One appropriate approach to tackle this problem is to use sequential methods. Sequential procedures are distinguished by the definition of the stopping rule and are stopped by a pre-defined stopping rule as soon as asymptotic properties of the procedure are observed. Many authors have researched sequential sampling procedures, namely purely sequential and two-stage procedures. We are also interested in investigating the performance of the modified twostage procedure because of the most important and widely used sequential methods and the operational savings of these procedures. The modified twostage approach proposes a situation where we can provide a strategy for determining the initial sample size in the two-stage process that, in many cases, prevents overestimation of the final sample size. The advantages of the modified two-stage include the simplicity of implementation and reduced weakness of the two-stage procedure in estimating. The point estimation is studied based on the least-squares estimator as the reciprocal of the cost per observation tends to infinity and interval estimation when the width of the confidence interval goes to zero. We presented the performance of the procedure under the theorems that demonstrate the asymptotic properties of the procedures, including asymptotic risk efficiency, asymptotic efficiency, and asymptotic consistency. Material and Methods We conduct Monte Carlo simulation studies to investigate the performance of procedures based on least-squares estimators. The performance of estimators and confidence intervals are evaluated utilizing a simulation study. We report the results in terms of the stopping variables, the ratio of the average stopping variable to the optimal fixed sample size, the root of mean square error (RMSE) of the estimators, and the proportion of risk efficiency functions. Furthermore, real-time series data is considered to illustrate the applicability of the Modified two-stage procedure. Results and Discussion The simulation results confirm the theoretical results and show the procedure’, s effectiveness compared to the optimal fixed sample size. Also, the actual data results show the excellent performance of this procedure in practice. Conclusion The Modified two-stage procedure and operational savings are more accessible to implement than the most commonly used purely sequential procedure. It is also more accurate than the two-stage procedure. Also, the procedure performs well and is an excellent candidate for analyzing time series models.

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APA: Copy

Sajjadipanah, S., MAHMOUDI, E., & ZAMANI, M.. (2022). Modified Two-Stage Sampling Around the Mean of the First Order Autoregressive Model. JOURNAL OF STATISTICAL SCIENCES, 16(1 ), 127-148. SID. https://sid.ir/paper/1021474/en

Vancouver: Copy

Sajjadipanah S., MAHMOUDI E., ZAMANI M.. Modified Two-Stage Sampling Around the Mean of the First Order Autoregressive Model. JOURNAL OF STATISTICAL SCIENCES[Internet]. 2022;16(1 ):127-148. Available from: https://sid.ir/paper/1021474/en

IEEE: Copy

S. Sajjadipanah, E. MAHMOUDI, and M. ZAMANI, “Modified Two-Stage Sampling Around the Mean of the First Order Autoregressive Model,” JOURNAL OF STATISTICAL SCIENCES, vol. 16, no. 1 , pp. 127–148, 2022, [Online]. Available: https://sid.ir/paper/1021474/en

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