XploRe® - Application Guide

I Regression Models.- 1 Quantile Regression.- 1.1 Introduction.- 1.2 Quantile Regression.- 1.2.1 Definitions.- 1.2.2 Computation.- 1.3 Essential Properties.- 1.3.1 Equivariance.- 1.3.2 Invariance to Transformations.- 1.3.3 Robustness.- 1.4 Inference.- 1.4.1 Main Asymptotic Results.- 1.4.2 Wald Test.- 1.4.3 Rank Tests.- 1.5 Description of Quantlets.- 1.5.1 Quantlet rqfit.- 1.5.2 Quantlet rrstest.- 2 Least Trimmed Squares.- 2.1 Robust Regression.- 2.1.1 Introduction.- 2.1.2 High Breakdown point Estimators.- 2.2 Least Trimmed Squares.- 2.2.1 Definition.- 2.2.2 Computation.- 2.3 Supplementary Remarks.- 2.3.1 Choice of the Trimming Constant.- 2.3.2 LTS as a Diagnostic Tool.- 2.3.3 High Subsample Sensitivity.- 3 Errors-in-Variables Models.- 3.1 Linear EIV Models.- 3.1.1 A Single Explanatory Variable.- 3.1.2 Vector of Explanatory Variables.- 3.2 Nonlinear EIV Models.- 3.2.1 Regression Calibration.- 3.2.2 Simulation Extrapolation.- 3.3 Partially Linear EIV Models.- 3.3.1 The Variance of Error Known.- 3.3.2 The Variance of Error Unknown.- 3.3.3 XploRe Calculation and Practical Data.- 4 Simultaneuos-Equations Models.- 4.1 Introduction.- 4.2 Estimation.- 4.2.1 Identification.- 4.2.2 Some Notation.- 4.2.3 Two-Stage Least Squares.- 4.2.4 Three-Stage Least Squares.- 4.2.5 Computation.- 4.3 Application: Money-Demand.- 5 Hazard Regression.- 5.1 Data Structure.- 5.2 Kaplan-Meier Estimates.- 5.3 The Cox Proportional Hazards Model.- 5.3.1 Estimating the Regression Coefficients.- 5.3.2 Estimating the Hazard and Survival Functions.- 5.3.3 Hypothesis Testing.- 5.3.4 Example: Length of Stay in Nursing Homes.- 6 Generalized Partial Linear Models.- 6.1 Estimating GPLMs.- 6.1.1 Models.- 6.1.2 Semiparametric Likelihood.- 6.2 Data Preparation.- 6.2.1 General.- 6.2.2 Example.- 6.3 Computing GPLM Estimates.- 6.3.1 Estimation.- 6.3.2 Estimation in Expert Mode.- 6.4 Options.- 6.4.1 Setting Options.- 6.4.2 Grid and Starting Values.- 6.4.3 Weights and Offsets.- 6.4.4 Control Parameters.- 6.4.5 Model Parameters.- 6.4.6 Specification Test.- 6.4.7 Output Modification.- 6.5 Statistical Evaluation and Presentation.- 6.5.1 Statistical Characteristics.- 6.5.2 Output Display.- 6.5.3 Model selection.- 7 Generalized Additive Models.- 7.1 Brief Theory.- 7.1.1 Models.- 7.1.2 Marginal Integration.- 7.1.3 Backfitting.- 7.1.4 Orthogonal Series.- 7.2 Data Preparation.- 7.3 Noninteractive Quantlets for Estimation.- 7.3.1 Estimating an AM.- 7.3.2 Estimating an APLM.- 7.3.3 Estimating an AM and APLM.- 7.3.4 Estimating a GAM.- 7.3.5 Estimating a GAPLM.- 7.3.6 Estimating Bivariate Marginal Influence.- 7.3.7 Estimating an AM with Interaction Terms.- 7.3.8 Estimating an AM Using Marginal Integration.- 7.4 Interactive Quantlet GAMFIT.- 7.5 How to Append Optional Parameters.- 7.6 Noninteractive Quantlets for Testing.- 7.6.1 Component Analysis in APL Models.- 7.6.2 Testing for Interaction.- 7.6.3 Testing for Interaction.- 7.7 Odds and Ends.- 7.7.1 Special Properties of GAM Quantlib Quantlets.- 7.7.2 Estimation on Principal Component by PCAD.- 7.8 Application for Real Data.- II Data Exploration.- 8 Growth Regression and Counterfactual Income Dynamics.- 8.1 A Linear Convergence Equation.- 8.2 Counterfactual Income Dynamics.- 8.2.1 Sources of the Growth Differential With Respect to a Hypothetical Average Economy.- 8.2.2 Univariate Kernel Density Estimation and Bandwidth Selection.- 8.2.3 Multivariate Kernel Density Estimation.- 9 Cluster Analysis.- 9.1 Introduction.- 9.1.1 Distance Measures.- 9.1.2 Similarity of Objects.- 9.2 Hierarchical Clustering.- 9.2.1 Agglomerative Hierarchical Methods.- 9.2.2 Divisive Hierarchical Methods.- 9.3 Nonhierarchical Clustering.- 9.3.1 K-means Method.- 9.3.2 Adaptive K-means Method.- 9.3.3 Hard C-means Method.- 9.3.4 Fuzzy C-means Method.- 10 Classification and Regression Trees.- 10.1 Growing the Tree.- 10.2 Pruning the Tree.- 10.3 Selecting the Final Tree.- 10.4 Plotting the Result of CART.- 10.5 Examples.- 10.5.1 Simulated Example.- 10.5.2 Boston Housing Data.- 10.5.3 Density Estimation.- 11 DPLS: Partial Least Squares Program.- 11.1 Introduction.- 11.2 Theoretical Background.- 11.2.1 The Dynamic Path Model DPLS.- 11.2.2 PLS Estimation with Dynamic Inner Approximation.- 11.2.3 Prediction and Goodness of Fit.- 11.3 Estimating a DPLS-Model.- 11.3.1 The Computer Program DPLS.- 11.3.2 Creating design-matrices.- 11.3.3 Estimating with DPLS.- 11.3.4 Measuring the Forecasting Validity.- 11.4 Example: A Model for German Share Prices.- 11.4.1 The General Path Model.- 11.4.2 Manifest Variables and Sources of Data.- 11.4.3 Empirical Results.- 12 Uncovered Interest Parity.- 12.1 The Uncovered Interest Parity.- 12.2 The Data.- 12.3 A Fixed Effects Model.- 12.4 A Dynamic Panel Data Model.- 12.5 Unit Root Tests for Panel Data.- 12.6 Conclusions.- 12.7 Macro Data.- 13 Correspondence Analysis.- 13.1 Introduction.- 13.1.1 Singular Value Decomposition.- 13.1.2 Coordinates of Factors.- 13.2 XploRe Implementation.- 13.3 Example: Eye-Hair.- 13.3.1 Description of Data.- 13.3.2 Calling the Quantlet.- 13.3.3 Documentation of Results.- 13.3.4 Eigenvalues.- 13.3.5 Contributions.- 13.3.6 Biplots.- 13.3.7 Brief Remark.- 13.4 Example: Media.- 13.4.1 Description of the Data Set.- 13.4.2 Calling the Quantlet.- 13.4.3 Brief Interpretation.- III Dynamic Statistical Systems.- 14 Long-Memory Analysis.- 14.1 Introduction.- 14.2 Model Indepependent Tests for 1(0) against 1(d).- 14.2.1 Robust Rescaled Range Statistic.- 14.2.2 The KPSS Statistic.- 14.2.3 The Rescaled Variance V/S Statistic.- 14.2.4 Nonpaxametric Test for 1(0).- 14.3 Semiparametric Estimators in the Spectral Domain.- 14.3.1 Log-periodogram Regression.- 14.3.2 Semiparametric Gaussian Estimator.- 15 ExploRing Persistence in Financial Time Series.- 15.1 Introduction.- 15.2 Hurst and Fractional Integration.- 15.2.1 Hurst Constant.- 15.2.2 Fractional Integration.- 15.3 Tests for 1(0) against fractional alternatives.- 15.4 Semiparametric estimation of difference parameter d.- 15.5 Exploiting the Data.- 15.5.1 Typical Spectral Shape.- 15.5.2 Typical Distribution: Mean, Variance, Skewness and Kur-tosis.- 15.6 The Data.- 15.7 The Quantlets.- 15.8 The Results.- 15.8.1 Equities.- 15.8.2 Exchange.- 15.9 Practical Considerations.- 15.9.1 Risk and Volatility.- 15.9.2 Estimating and Forecasting of Asset Prices.- 15.9.3 Portfolio Allocation Strategy.- 15.9.4 Diversification and Fractional Cointegration.- 15.9.5 MMAR and FIGARCH.- 15.10Conclusion.- 16 Flexible Time Series Analysis.- 16.1 Nonlinear Autoregressive Models of Order One.- 16.1.1 Estimation of the Conditional Mean.- 16.1.2 Bandwidth Selection.- 16.1.3 Diagnostics.- 16.1.4 Confidence Intervals.- 16.1.5 Derivative Estimation.- 16.2 Nonlinear Autoregressive Models of Higher Order.- 16.2.1 Estimation of the Conditional Mean.- 16.2.2 Bandwidth and Lag Selection.- 16.2.3 Plotting and Diagnostics.- 16.2.4 Estimation of the Conditional Volatility.- 17 Multiple Time Series Analysis.- 17.1 Getting Started.- 17.1.1 Data Preparation.- 17.1.2 Starting multi.- 17.2 Preliminary Analysis.- 17.2.1 Plotting the Data.- 17.2.2 Data Transformation.- 17.3 Specifying a VAR Model.- 17.3.1 Process Order.- 17.3.2 Model Estimation.- 17.3.3 Model Validation.- 17.4 Structural Analysis.- 17.4.1 Impulse Response Analysis.- 17.4.2 Confidence Intervals for Impulse Responses.- 18 Robust Kalman Filtering.- 18.1 State-Space Models and Outliers.- 18.1.1 Outliers and Robustness Problems.- 18.1.2 Examples of AO’s and IO’s.- 18.1.3 Problem Setup.- 18.2 Classical Method: Kalman Filter.- 18.2.1 Features of the Classical Kalman Filter.- 18.2.2 Optimality of the Kalman Filter.- 18.3 The rLS filter.- 18.3.1 Derivation.- 18.3.2 Calibration.- 18.3.3 Examples.- 18.3.4 Possible Extensions.- 18.4 The rIC filter.- 18.4.1 Filtering = Regression.- 18.4.2 Robust Regression Estimates.- 18.4.3 Variants: Separate Clipping.- 18.4.4 Criterion for the Choice of b.- 18.4.5 Examples.- 18.4.6 Possible Extensions.- 18.5 Generating Influence Curves.- 18.5.1 Definition of IC.- 18.5.2 General Algorithm.- 18.5.3 Explicite Calculations.- 18.5.4 Integrating along the Directions.- 18.5.5 Auxiliary routines.