Seasonal Adjustment with the X-11 Method

Transcription

1 Dominique Ladiray Benoit Quenneville Seasonal Adjustment with the X-11 Method Springer

2 Preface vii Introduction 1 1 Brief History of Seasonal Adjustment 5 2 Outline of the X-11 Method Components and Decomposition Models Moving Averages A Simple Seasonal Adjustment Algorithm... \ The Basic Algorithm of the X-11 Method... \ Extreme Observations and Calendar Effects The Iterative Principle of X Part A: Pre-Adjustments Part B: First Automatic Correction of the Series Part C: Second Automatic Correction of the'series Part D: Seasonal Adjustment Parts E, F and G: Statistics and Charts From Census X-11 to X-11-ARTMA and X-l 2-ARIMA Moving Averages Some Definitions and a Little Theory Definitions and Example Gain and Phase Shift Functions 26

3 3.1.3 Trend Preservation Elimination of Seasonality Reduction of the Irregular Component An Example of Construction of a Moving Average The Symmetric Moving Averages Used in X Composite Simple Moving Average Henderson Moving Averages Musgrave Asymmetric Moving Averages Musgrave Asymmetric Moving Averages Associated with Henderson Symmetric Moving Averages Comment About Musgrave Moving Averages Asymmetric Moving Averages Associated With Composite Moving Averages The X-11 Moving Average Filter 41 The Various Tables B: Preliminary Estimation of Extreme Values and Calendar Effects B.1: Raw Series Adjusted a priori B2: Trend-Cycle B3: Unmodified Seasonal-Irregular B4: Replacement Values for Extreme ST Values B5: Seasonal Component B6: Seasonally Adjusted Series B7: Trend-Cycle B8: Unmodified SI Component B9: Replacement Values for Extreme SI Values B10: Seasonal Component '.. 83 " BIT: Seasonally Adjusted Series B13: Irregular Component The Trading-Day Component. I B14: Irregular Values Excluded from the TD Regression B1.5: Preliminary TD Regression B16: Regression-Derived TD Adjustment Factors Bl 7: Preliminary Weights for the Irregular B18: Combined TD Factors Bl 9: Raw Series Corrected for TD Effects../ B20: Adjustment Values for Extreme Irregulars C: Final Estimation of Extreme Values and Calendar Effects Cl: Modified Raw Series C2: Trend-Cycle C4: Modified ST C5: Seasonal Component C6: Seasonally Adjusted Series C7: Trend-Cycle 109

4 xiii C9: SI Component C10: Seasonal Component C1.1: Seasonally Adjusted Series C13: Irregular Component C14: Irregulars Excluded from the TD Regression C15: Final TD Regression C16: Regression-Derived TD Adjustment Factors Cl 7: Final Weights for the Irregular C18: Combined TD Factors C1.9: Raw Series Corrected for TD Effects C20: Adjustment Values for Extreme Irregulars D: Final Estimation of the Different Components Dl: Modified Raw Series D2: Trend-Cycle D4: Modified SI D5: Seasonal Component D6: Seasonally Adjusted Series D7: Trend-Cycle D8: Unmodified SI Component D9: Replacement Values for Extreme SI Values D9A: Moving Seasonally Ratios D10: Final Seasonal Factors D11: Final Seasonally Adjusted Series Dl 1 A: Final Seasonally Adjusted Series with Revised Annual Totals D12: Final Trend-Cycle 157, D13: Finarirregular Component.'"." D16: Seasonal and Calendar Effects D18: Combined Calendar Effects Factors E: Components Modified for Large Extreme Values. ; El: Raw Series Modified for Large Extreme Values E2: SA Series Modified for Large Extreme Values E3: Final Irregular Component Adjusted for Large Extreme Values E4: Comparing the Annual Totals of Raw and SA Series E5: Changes in the Raw Series E6: Changes in the Final SA Series E7: Changes in the Final Trend-Cycle E11: Robust Estimation of the Final SA Series F: Seasonal Adjustment Quality Measures FT: Smoothing the SA Series Using an MCD MA F2A: Changes, in Absolute Value, of the Principal Components 169

5 4.5.3 F2B: Relative Contribution of Components to Changes in the Raw Series F2C: Averages and Standard Deviations of Changes as a Function of the Time Lag F2D: Average Duration of Run F2E: Calculation of the MCD Ratio F2F: Relative Contribution of Components to the Variance of the Stationary Part of the Original Series F2G: Autocorrelations of the Irregular Component F2H: I/C and I/S Ratios F2T: Tests for the Presence of Seasonality F3: Monitoring and Quality Assessment Statistics. 176 Modelling of the Easter Effect The Easter Holiday A Brief History Calculation of the Dates of Easter Easter and Seasonal Adjustment TheX-11-ARlMA Models The Immediate Impact Model The Corrected Immediate Impact Model The Gradual Impact Model The X-12-AR IMA Models The Bateman-Mayes Model The Sceaster Model The Easter Model 210 References 215 Index 221