Estimating Discrete Parameters: An Application to Cointegration and Unit Roots

Robert M. Kunst

doi:10.17713/ajs.v25i2.554

Estimating Discrete Parameters: An Application to Cointegration and Unit Roots

Austrian Journal of Statistics ◽

10.17713/ajs.v25i2.554 ◽

2016 ◽

Vol 25 (2) ◽

Author(s):

Robert M. Kunst

Keyword(s):

Time Series ◽

Monte Carlo Simulation ◽

Time Series Data ◽

Decision Rules ◽

Unit Roots ◽

Series Data ◽

Bivariate Model ◽

Quarterly Data ◽

Testing Problem ◽

Optimum Decision

The problem of detecting unit roots in time series data is treated as a problem of multiple decisions instead of a testing problem, as is otherwise common in the econometric and statistical literature. The multiple decision design is based on a distinction between continuous primary and discrete secondary parameters. Four examples for such multiple decision designs are considered: first- and second-order integrated univariate processes; cointegration in a bivariate model; seasonal integration for semester data; seasonalintegration for quarterly data. In all cases, restricted optimum decision rules are established based on Monte Carlo simulation.

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Analysis of Time-Series Data by Merging Decision Rules

Journal of Advanced Computational Intelligence and Intelligent Informatics ◽

10.20965/jaciii.2017.p1026 ◽

2017 ◽

Vol 21 (6) ◽

pp. 1026-1033

Author(s):

Yoshiyuki Matsumoto ◽

Junzo Watada ◽

◽

Keyword(s):

Time Series ◽

Decision Rule ◽

Set Theory ◽

Rough Set ◽

Time Series Data ◽

Rough Set Theory ◽

Decision Rules ◽

Series Data ◽

Rule Set ◽

Analysis Of Time Series

Rough set theory was proposed by Z. Pawlak in 1982. This theory enables the mining of knowledge granules as decision rules from a database, the web, and other sources. This decision rule set can then be used for data analysis. We can apply the decision rule set to reason, estimate, evaluate, or forecast an unknown object. In this paper, rough set theory is used for the analysis of time-series data. We propose a method to acquire rules from time-series data using regression. The trend of the regression line can be used as a condition attribute. We predict the future slope of the time-series data as decision attributes. We also use merging rules to further analyze the time series data.

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Air passengers forecasting for Australian airline based on hybrid rough set approach

Journal of Applied Mathematics Statistics and Informatics ◽

10.2478/jamsi-2018-0001 ◽

2018 ◽

Vol 14 (1) ◽

pp. 5-18

Author(s):

H. Kumar Sharma ◽

K. Kumari ◽

S. Kar

Keyword(s):

Time Series ◽

Set Theory ◽

Rough Set ◽

Hybrid Method ◽

Time Series Data ◽

Rough Set Theory ◽

Decision Rules ◽

Series Data ◽

Long Term Forecasting ◽

Des Model

Abstract Accurate and reliable air passenger demand is very important for policy-making and planning by tourism management as well as by airline authorities. Therefore, this article proposed a novel hybrid method based on rough set theory (RST) to construct decision rules for long-term forecasting of air passengers. Level (mean) and trend components are first estimated from the air passengers time series data using DES model in the formulation of the proposed hybrid method. Then the rough set theory is employed to combine the output of DES model and generated decision rules is used to forecasting air passengers. We compare the proposed approach with other time series models using a corrected classified accuracy (CCA) criterion. For the empirical analysis, yearly air transport passenger from 1992 to 2004 is used. Empirical results show that the proposed method is highly accurate with the higher corrected classified accuracy. Also, forecasting accuracy of the proposed method is better than the other time series approaches.

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Modeling and Forecasting of Tourism Time Series Data using ANN-Fourier Series Model and Monte Carlo Simulation

2021 9th International Symposium on Digital Forensics and Security (ISDFS) ◽

10.1109/isdfs52919.2021.9486325 ◽

2021 ◽

Author(s):

Salim Jibrin Danbatta ◽

Asaf Varol

Keyword(s):

Time Series ◽

Monte Carlo Simulation ◽

Monte Carlo ◽

Fourier Series ◽

Time Series Data ◽

Series Data ◽

Modeling And Forecasting

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Knowledge Acquisition from Rough Sets Using Merged Decision Rules

Journal of Advanced Computational Intelligence and Intelligent Informatics ◽

10.20965/jaciii.2018.p0404 ◽

2018 ◽

Vol 22 (3) ◽

pp. 404-410

Author(s):

Yoshiyuki Matsumoto ◽

Junzo Watada ◽

◽

Keyword(s):

Time Series ◽

Knowledge Acquisition ◽

Decision Rule ◽

Rough Sets ◽

Time Series Data ◽

Rough Set Theory ◽

Decision Rules ◽

Series Data ◽

Economic Time Series ◽

Knowledge Based

Rough set theory was proposed by Z. Pawlak in 1982. This theory can mine knowledge based on a decision rule from a database, a web base, a set, and so on. The decision rule is used for data analysis as well as calculating an unknown object. We analyzed time-series data using rough sets. Economic time-series data was predicted using decision rules. However, there are cases where an excessive number of decision rules exist, from which, it is difficult to acquire knowledge. In this paper, we propose a method to reduce the number of decision rules by merging them. Similar to how it is difficult to acquire knowledge from multiple rules, it is also difficult to acquire knowledge from rules with a large number of condition attributes. We propose a method to reduce the number of condition attributes and thereby reduce the number of rules. We analyze time-series data using this proposed method and acquire knowledge for prediction using decision rules. We use TOPIX and the yen–dollar exchange rate as knowledge-acquisition data. We propose a method to facilitate knowledge acquisition by merging rules.

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Unit-roots test for time-series data with a linear time trend

Journal of Econometrics ◽

10.1016/0304-4076(91)90104-l ◽

1991 ◽

Vol 47 (2-3) ◽

pp. 285-303 ◽

Cited By ~ 9

Author(s):

Saïd E. Saïd

Keyword(s):

Time Series ◽

Time Trend ◽

Time Series Data ◽

Linear Time ◽

Unit Roots ◽

Series Data ◽

Linear Time Trend

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Time Series Regression with Mixtures of Integrated Processes

Econometric Theory ◽

10.1017/s0266466600009968 ◽

1995 ◽

Vol 11 (5) ◽

pp. 1033-1094 ◽

Cited By ~ 7

Author(s):

Yoosoon Chang ◽

Peter C.B. Phillips

Keyword(s):

Time Series ◽

Least Squares ◽

Time Series Data ◽

Unit Roots ◽

Ordinary Least Squares ◽

Series Data ◽

Vector Autoregressions ◽

Time Series Regression ◽

First Order ◽

Unknown Mixture

The paper develops a statistical theory for regressions with integrated regressors of unknown order and unknown cointegrating dimension. In practice, we are often unsure whether unit roots or cointegration is present in time series data, and we are also uncertain about the order of integration in some cases. This paper addresses issues of estimation and inference in cases of such uncertainty. Phillips (1995, Econometrica 63, 1023–1078) developed a theory for time series regressions with an unknown mixture of 1(0) and 1(1) variables and established that the method of fully modified ordinary least squares (FM-OLS) is applicable to models (including vector autoregressions) with some unit roots and unknown cointegrating rank. This paper extends these results to models that contain some I(0), I(1), and I(2) regressors. The theory and methods here are applicable to cointegrating regressions that include unknown numbers of I(0), I(1), and I(2) variables and an unknown degree of cointegration. Such models require a somewhat different approach than that of Phillips (1995). The paper proposes a residual-based fully modified ordinary least-squares (RBFMOLS) procedure, which employs residuals from a first-order autoregression of the first differences of the entire regressor set in the construction of the FMOLS estimator. The asymptotic theory for the RBFM-OLS estimator is developed and is shown to be normal for all the stationary coefficients and mixed normal for all the nonstationary coefficients. Under Gaussian assumptions, estimation of the cointegration space by RBFM-OLS is optimal even though the dimension of the space is unknown.

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UNDERSTANDING INDONESIA’S MACROECONOMIC DATA: WHAT DO WE KNOW AND WHAT ARE THE IMPLICATIONS?

Buletin Ekonomi Moneter dan Perbankan ◽

10.21098/bemp.v21i2.967 ◽

2018 ◽

Vol 21 (2) ◽

pp. 229-264 ◽

Cited By ~ 2

Author(s):

Susan Sunila Sharma

Keyword(s):

Time Series ◽

Unit Root ◽

Structural Breaks ◽

Time Series Data ◽

Unit Roots ◽

Series Data ◽

Econometric Modelling ◽

Shock Response ◽

Macroeconomic Time Series ◽

Root Properties

Unit root properties of macroeconomic data are important for both econometric modelling specifications and policy making. The form of variables (whether they are a unit root process) helps determine the correct econometric modelling. Equally, the form of variables helps explain how they react to shocks (both internal and external). Macroeconomic time-series data are often at the forefront of shock analysis and econometric modelling. There is a growing emphasis on research on Indonesia using time-series data; yet, there is limited understanding of data characteristics and shock response of these data. Using an extensive dataset comprising 33 macroeconomic time-series variables, we provide an informative empirical analysis of unit root properties of data. We find that regardless of data frequencies the empirical evidence of unit roots is mixed, some series respond quickly to shocks others do take time, and almost every macroeconomic data suffers from structural breaks. We draw implications of these findings.

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Graphical Exploratory Data Analysis for Categorical Longitudinal and Time Series Data

PsycEXTRA Dataset ◽

10.1037/e634372013-001 ◽

2013 ◽

Author(s):

Stephen J. Tueller ◽

Richard A. Van Dorn ◽

Georgiy Bobashev ◽

Barry Eggleston

Keyword(s):

Time Series ◽

Data Analysis ◽

Exploratory Data Analysis ◽

Time Series Data ◽

Series Data ◽

Exploratory Data

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Faktor-Faktor Yang Mempengaruhi Nilai Tukar Dollar Amerika Serikat Terhadap Rupiah Tahun 2000–2013

Jurnal Riset Manajemen Sekolah Tinggi Ilmu Ekonomi Widya Wiwaha Program Magister Manajemen ◽

10.32477/jrm.v1i2.72 ◽

2017 ◽

Vol 1 (2) ◽

pp. 177-191

Author(s):

Rizki Rahma Kusumadewi ◽

Wahyu Widayat

Keyword(s):

Time Series ◽

Exchange Rate ◽

Money Supply ◽

Time Series Data ◽

The United States ◽

Economic Conditions ◽

Series Data ◽

Arch Model ◽

United States Dollar ◽

The Exchange Rate

Exchange rate is one tool to measure a country’s economic conditions. The growth of a stable currency value indicates that the country has a relatively good economic conditions or stable. This study has the purpose to analyze the factors that affect the exchange rate of the Indonesian Rupiah against the United States Dollar in the period of 2000-2013. The data used in this study is a secondary data which are time series data, made up of exports, imports, inflation, the BI rate, Gross Domestic Product (GDP), and the money supply (M1) in the quarter base, from first quarter on 2000 to fourth quarter on 2013. Regression model time series data used the ARCH-GARCH with ARCH model selection indicates that the variables that significantly influence the exchange rate are exports, inflation, the central bank rate and the money supply (M1). Whereas import and GDP did not give any influence.

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