TAILIEUCHUNG - Lecture Applied econometric time series (4e) - Chapter 4: Models with trend

This chapter’s objectives are to: Formalize simple models of variables with a time-dependent mean, compare models with deterministic versus stochastic trends, show that the so-called unit root problem arises in standard regression and in timesseries models,. | Chapter 4 Applied Econometric Time Series 4th ed. Walter Enders 1 2 The Random Walk Model yt = yt–1 + et (or Dyt = et). Given the first t realizations of the {et} process, the conditional mean of yt+1 is Etyt+1 = Et(yt + et+1) = yt Similarly, the conditional mean of yt+s (for any s > 0) can be obtained from Hence var(yt) = var(et + et–1 + . + e1) = ts2 var(yt–s) = var(et–s + et–s–1 + . + e1) = (t – s)s 3 Random Walk Plus Drift yt = yt–1 + a0 + et Given the initial condition y0, the general solution for yt is Etyt+s = yt + a0s. E[(yt – y0)(yt–s – y0)] = E[(et + et–1+.+ e1)(et–s+ et–s–1 +.+e1)] = E[(et–s)2+(et–s–1)2+.+(e1)2] = (t – s)s2 The autocorrelation coefficient = [(t – s)/t] Hence, in using sample data, the autocorrelation function for a random walk process will show a slight tendency to decay. 5 6 7 Table : Selected Autocorrelations From Nelson and Plosser 8 Worksheet Consider the two random walk plus drift processes yt = + yt 1 + yt zt = + zt 1 + zt Here {yt} and {zt} series are unit-root processes with uncorrelated error terms so that the regression is spurious. Although it is the deterministic drift terms that cause the sustained increase in yt and the overall decline in zt, it appears that the two series are inversely related to each other. The residuals from the regression yt = are nonstationary. Scatter Plot of yt Against zt Regression Residuals Worksheet 3. UNIT ROOTS AND REGRESSION RESIDUALS yt = a0 + a1zt + et Assumptions of the classical model: both the {yt} and {zt} sequences be stationary the errors have a zero mean and a finite variance. In the presence of nonstationary variables, there might be what Granger and Newbold (1974) call a spurious regression A spurious regression has a high R2 and t-statistics that appear to be significant, but the results are without any economic meaning. The regression output “looks good” because the least-squares estimates are not consistent and the customary tests

• Kinh tế học
• Econometric time series
• Applied econometric time series
• Stochastic trends
• Chuỗi thời gian
• Kinh tế lượng
• Models with trend
• Lecture Applied econometric time series
• Stationary time series models
• Intervention analysis
• Multiequation time series models
• Cobweb model
• Modeling volatility
• Error correction models
• Nonlinear models
• Time series
• Spatial market integration
• Groundnut markets
• Econometric analysis on groundnut markets
• Overview of groundnut market
• Polynomial models
• Trend in area
• Production and productivity
• Productivity of cotton crop
• Important cash crops
• Auto correlation function
• Hydrologic models
• Savitri basin
• Climatic parameters of Savitri basin
• Temporal trend analysis
• Linear growth rate
• Compound growth rate
• Statistical models
• Trend analysis of wheat crop
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• Time Series Forecasting
• Components of Time Series
• Evaluation Methods of Forecast
• Smoothing Methods of Time Series
• Time series models
• Components of a time series
• Trend component
• Technologies
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• Conservation of mass
• Multiphase flow models
• Multiphase flow notation
• distribution functions
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• Parametric regression
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• Apple (Malus domestica)
• Productivity and area trends
• Linear time trend
• Eigen value
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