The main aim of this seminar is to define, examine and present Smooth Transition Autoregressive Model (STAR) which is a model used to analyze nonlinear time-series economic data with regime-switching. In going forward, the overall structure of the seminar is designed to study the nonlinear features of production sector production index of Germany using data from January 1991 to April 2017. The author did first a Chow Test to evidence the existence of a data structural breakpoint. Then a model specification procedure given by Teräsvirta (1994) was followed. The author used, accordingly, three steps to specify the model. First, a linear AR model was developed using the data. Secondly, a linearity test against the STAR model was carried out. Once a test of the null hypothesis of linearity against non-linearity is rejected by the carried out Lagrange Multiplier (LM) test, the delay parameter d was determined. Afterwards, a choice between the LSTAR and the ESTAR model was made using a sequence of tests.
Finally, the estimation of the model is done. As the results from the set of tests indicate, the STAR model is found to be appropriate for modeling and analyzing the data.
Table of Contents
1 Introduction
2 Smooth Transition Autoregressive (STAR) Model
2.1 Introduction to STAR
2.2 Logistic and Exponential STAR models (LSTAR and ESTAR)
2.3 Specification of STAR model
2.3.1 Linear autoregressive model specification
2.3.2 Test for Non-linearity with Lagrange Multiplier (LM) type test
2.3.3 Choosing between LSTAR and ESTAR
3 Data Analysis
3.1 The Data
3.2 Autoregressive model construction and Structural change and break points
3.2.1 Linear Autoregressive Model
3.2.2 Testing structural change and break points
3.3 Testing for linearity
3.4 Choosing between LSTAR and ESTAR
3.5 Estimation of the model
4 Conclusion
Research Objectives and Key Topics
The primary objective of this seminar paper is to define, examine, and apply the Smooth Transition Autoregressive (STAR) model to analyze nonlinear time-series data, specifically focusing on the production sector index of Germany from 1991 to 2017.
- Theoretical foundation of STAR and its variants (LSTAR and ESTAR).
- Econometric testing for structural breaks and data stationarity.
- Specification of linear autoregressive models (AR) as a baseline.
- Application of Lagrange Multiplier (LM) tests to detect nonlinearity.
- Model estimation and determination of regime-switching parameters.
Excerpt from the Book
2.2 Logistic and Exponential STAR models (LSTAR and ESTAR)
The transition function F(Yt−d), as explained by different authors, is bounded by values of 0 and 1. Two interpretations are possible with respect to the transition function. 1) When the transition function takes extreme values of either 0 or 1 and where the transition between one value to the other is smooth, it can be interpreted as regime-switching model. 2) When the transition function is taking different values between 0 and 1, it can be interpreted as continuum of regimes.
The transition function consists of parameters γ, Yt−d and c. Van Dijk, Teräsvirta, and Franses (2002) stated that the parameter γ determines the smoothness of the change in the value of the transition function. On the other hand the parameter c is interpreted as the threshold between the two regimes.
The LSTAR and ESTAR functions mentioned in (2.3) and (2.4) are having different behaviors. In an attempt clarify this, graphical representations of both functions are usually used. In the following graphs, LSTAR and ESTAR transition functions would be depicted assuming that c = 0, Yt−d ranging from -7 to +7 and γ = 3 and 10.
Summary of Chapters
1 Introduction: Provides an overview of nonlinear economic time-series behavior and outlines the objective to apply the STAR model to German industrial production data.
2 Smooth Transition Autoregressive (STAR) Model: Defines the theoretical framework of STAR, including the transition functions and the specification procedures for LSTAR and ESTAR models.
3 Data Analysis: Presents the empirical application, including unit root testing, structural break analysis, linearity testing, and the final estimation of the STAR model.
4 Conclusion: Summarizes the findings, confirming that the STAR model provides a robust nonlinear fit for the analyzed production index data compared to linear alternatives.
Keywords
Smooth transition autoregression, regime switching, testing for non-linearity, Lagrange Multiplier (LM) test, time-series, LSTAR, ESTAR, production index, Germany, structural break, econometrics, stationarity, model specification, autoregressive model, transition function.
Frequently Asked Questions
What is the core focus of this research paper?
The paper focuses on the definition, specification, and practical application of the Smooth Transition Autoregressive (STAR) model to analyze nonlinear economic time-series data.
Which specific economic data is analyzed?
The study analyzes the monthly production sector index of Germany, covering the time frame from January 1991 to April 2017.
What is the primary objective of this work?
The goal is to determine if a nonlinear STAR model is more appropriate than a linear model for describing the dynamics of German industrial production, considering regime-switching behavior.
Which scientific methodology is employed?
The methodology follows Teräsvirta (1994), involving linear AR specification, structural break testing using Chow tests, and nonlinearity detection via Lagrange Multiplier (LM) tests.
What does the main body of the paper cover?
The main body covers the mathematical derivation of STAR models, the testing of stationarity, the identification of structural break points, and the final estimation of an LSTAR model.
Which keywords best characterize this study?
Key terms include Smooth transition autoregression, regime switching, nonlinearity, LM test, structural break, and econometrics.
Why was the LSTAR model chosen over the ESTAR model?
Based on a sequence of F-tests conducted on the auxiliary regression, the LSTAR model was determined to be a statistically better fit for the specific data set analyzed.
What role does the parameter gamma (γ) play in the model?
The parameter gamma determines the smoothness of the transition between the two regimes; a higher value indicates a faster, more abrupt switch.
What was the outcome of the structural break test?
The test for structural change revealed a significant break point, which was identified as occurring in April 2009.
How is the transition function interpreted?
The transition function acts as a mechanism to model the continuum of states between two extreme regimes of the business cycle, allowing for smooth rather than instantaneous changes.
- Arbeit zitieren
- Behailu Shiferaw Benti (Autor:in), 2017, Smooth Transition Autoregressive Model. A study of production index of production sector in Germany, München, GRIN Verlag, https://www.grin.com/document/490761
