Forecasting, time series, and regression : an applied approach

Abstract

Part I: INTRODUCTION AND REVIEW OF BASIC STATISTICS. 1. An Introduction to Forecasting. Forecasting and Data. Forecasting Methods. Errors in Forecasting. Choosing a Forescasting Technique. An Overview of Quantitative Forecasting Techniques. 2. Basic Statistical Concepts. Populations. Probability. Random Samples and Sample Statistics. Continuous Probability Distributions. The Normal Probability Distribution. The t-Distribution, the F-Distribution, the Chi-Square Distribution. Confidence Intervals for a Population Mean. Hypothesis Testing for a Population Mean. Exercises. Part II: REGRESSION ANALYSIS. 3. Simple Linear Regression. The Simple Linear Regression Model. The Least Squares Point Estimates. Point Estimates and Point Predictions. Model Assumptions and the Standard Error. Testing the Significance of the Slope and y Intercept. Confidence and Prediction Intervals. Simple Coefficients of Determination and Correlation. An F Test for the Model. Exercises. 4. Multiple Linear Regression. The Linear Regression Model. The Least Squares Estimates, and Point Estimation and Prediction. The Mean Square Error and the Standard Error. Model Utility: R2, Adjusted R2, and the Overall F Test. Testing the Significance of an Independent Variable. Confidence and Prediction Intervals. The Quadratic Regression Model. Interaction. Using Dummy Variables to Model Qualitative Independent Variables. The Partial F Test: Testing the Significance of a Portion of a Regression Model. Exercises. 5. Model Building and Residual Analysis. Model Building and the Effects of Multicollinearity. Residual Analysis in Simple Regression. Residual Analysis in Multiple Regression. Diagnostics for Detecting Outlying and Influential Observations. Exercises. Part III: TIME SERIES REGRESSION, DECOMPOSITION METHODS, AND EXPONENTIAL SMOOTHING. 6. Time Series Regression. Modeling Trend by Using Polynomial Functions. Detecting Autocorrelation. Types of Seasonal Variation. Modeling Seasonal Variation by Using Dummy Variables and Trigonometric Functions. Growth Curves. Handling First-Order Autocorrelation. Exercises. 7. Decomposition Methods. Multiplicative Decomposition. Additive Decomposition. The X-12-ARIMA Seasonal Adjustment Method. Exercises. 8. Exponential Smoothing. Simple Exponential Smoothing. Tracking Signals. Holts Trend Corrected Exponential Smoothing. Holt-Winters Methods. Damped Trends and Other Exponential Smoothing Methods. Models for Exponential Smoothing and Prediction Intervals. Exercises. Part IV: THE BOX-JENKINS METHODOLOGY. 9. Nonseasonal Box-Jenkins Modeling and Their Tentative Identification. Stationary and Nonstationary Time Series. The Sample Autocorrelation and Partial Autocorrelation Functions: The SAC and SPAC. An Introduction to Nonseasonal Modeling and Forecasting. Tentative Identification of Nonseasonal Box-Jenkins Models. Exercises. 10. Estimation, Diagnostic Checking, and Forecasting for Nonseasonal Box-Jenkins Models. Estimation. Diagnostic Checking. Forecasting. A Case Study. Box-Jenkins Implementation of Exponential Smoothing. Exercises. 11. Box-Jenkins Seasonal Modeling. Transforming a Seasonal Time Series into a Stationary Time Series. Three Examples of Seasonal Modeling and Forecasting. Box-Jenkins Error Term Models in Time Series Regression. Exercises. 12. Advanced Box-Jenkins Modeling. The General Seasonal Model and Guidelines for Tentative Identificatino. Intervention Models. A Procedure for Building a Transfer Function Model. Exercises. Appendix A: Statistical Tables Appendix B: Matrix Algebra for Regression Calculations. Matrices and Vectors. The Transpose of a Matrix. Sums and Differences of Matrices. Matrix Multiplication. The Identity Matrix. Linear Dependence and Linear Independence. The Inverse of a Matrix. The Least Squares Point Esimates. The Unexplained Variation and Explained Variation. The Standard Error of the Estimate b. The Distance Value. Using Squared Terms. Using Interaction Terms. Using Dummy Variable. The Standard Error of the Estimate of a Linear Combination of Regression Parameters. Exercises. Appendix C: References.

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