Seasonal Adjustment with the X-11 Method

1 Brief History of Seasonal Adjustment.- 2 Outline of the X-11 Method.- 2.1 Components and Decomposition Models.- 2.2 Moving Averages.- 2.3 A Simple Seasonal Adjustment Algorithm.- 2.4 The Basic Algorithm of the X-11 Method.- 2.5 Extreme Observations and Calendar Effects.- 2.6 The Iterative Principle of X-11.- 2.6.1 Part A: Pre-Adjustments.- 2.6.2 Part B: First Automatic Correction of the Series.- 2.6.3 Part C: Second Automatic Correction of the Series.- 2.6.4 Part D: Seasonal Adjustment.- 2.6.5 Parts E, F and G: Statistics and Charts.- 2.7 From Census X-11 to X-11-ARIMA and X-12-ARIMA.- 3 Moving Averages.- 3.1 Some Definitions and a Little Theory.- 3.1.1 Definitions and Example.- 3.1.2 Gain and Phase Shift Functions.- 3.1.3 Trend Preservation.- 3.1.4 Elimination of Seasonality.- 3.1.5 Reduction of the Irregular Component.- 3.1.6 An Example of Construction of a Moving Average.- 3.2 The Symmetric Moving Averages Used in X-11.- 3.2.1 Composite Simple Moving Average.- 3.2.2 Henderson Moving Averages.- 3.3 Musgrave Asymmetric Moving Averages.- 3.3.1 Musgrave Asymmetric Moving Averages Associated with Henderson Symmetric Moving Averages.- 3.3.2 Comment About Musgrave Moving Averages.- 3.3.3 Asymmetric Moving Averages Associated With Composite Moving Averages.- 3.4 The X-11 Moving Average Filter.- 4 The Various Tables.- 4.1 B: Preliminary Estimation of Extreme Values and Calendar Effects.- 4.1.1 B1: Raw Series Adjusted a priori.- 4.1.2 B2: Trend-Cycle.- 4.1.3 B3: Unmodified Seasonal-Irregular.- 4.1.4 B4: Replacement Values for Extreme SI Values.- 4.1.5 B5: Seasonal Component.- 4.1.6 B6: Seasonally Adjusted Series.- 4.1.7 B7: Trend-Cycle.- 4.1.8 B8: Unmodified SI Component.- 4.1.9 B9: Replacement Values for Extreme SI Values.- 4.1.10 B10: Seasonal Component.- 4.1.11 B11 : Seasonlly Adjusted Series.- 4.1.12 B13: Irregular Component.- 4.1.13 The Trading-Day Component.- 4.1.14 B14: Irregular Values Excluded from the TD Regression.- 4.1.15 B15: Preliminary TD Regression.- 4.1.16 B16: Regression-D erived TD Adjustment Factors.- 4.1.17 B17: Preliminary Weights for the Irregular.- 4.1.18 B18: Combined TD Factors.- 4.1.19 B19: Raw Series Corrected for TD Effects.- 4.1.20 B20: Adjustment Values for Extreme Irregulars.- 4.2 C: Final Estimation of Extreme Values and Calendar Effects.- 4.2.1 C1: Modified Raw Series.- 4.2.2 C2: Trend-Cycle.- 4.2.3 C4: Modified SI.- 4.2.4 C5: Seasonal Component.- 4.2.5 C6: Seasonally Adjusted Series.- 4.2.6 C7: Trend-Cycle.- 4.2.7 C9: SI Component.- 4.2.8 C10: Seasonal Component.- 4.2.9 Cll: Seasonally Adjusted Series.- 4.2.10 C13: Irregular Component.- 4.2.11 C14: Irregulars Excluded from the TD Regression.- 4.2.12 C15: Final TD Regression.- 4.2.13 C16: Regression-Derived TD Adjustment Factors.- 4.2.14 C17: Final Weights for the Irregular.- 4.2.15 C18: Combined TD Factorstt.- 4.2.16 C19: Raw Series Corrected for TD Effects.- 4.2.17 C20: Adjustment Values for Extreme Irregulars.- 4.3 D: Final Estimation of the Different Componentst.- 4.3.1 D1: Modi fied Raw Series.- 4.3.2 D2: Trend-Cycle.- 4.3.3 D4: Modified SI.- 4.3.4 D5: Seasonal Componentt.- 4.3.5 D6: Seasonally Adjusted Seriestt.- 4.3.6 D7: Trend-Cycle.- 4.3.7 D8: Unmodified SI Component.- 4.3.8 D9: Replacement Values for Extreme SI Values.- 4.3.9 D9A: Moving Seasonality Ratios.- 4.3.10 Dl0: Final Seasonal Factors.- 4.3.11 D11 : Final Seasonally Adjusted Series 150.- 4.3.12 D11A: Final Seasonally Adjusted Series with Revised Annual Totals.- 4.3.13 D12: Final Trend-Cycle.- 4.3.14 D13: Final Irregular Component.- 4.3.15 D16: Seasonal and Calendar Effects.- 4.3.16 D18: Combined Calendar Effects Factors.- 4.4 E: Components Modified for Large Extreme Values.- 4.4.1 E1: Raw Series Modified for Large Extreme Values.- 4.4.2 E2: SA Series Modified for Large Extreme Values.- 4.4.3 E3: Final Irregular Component Adjusted for Large Extreme Values.- 4.4.4 E4: Comparing the Annual Totals of Raw and SA Series.- 4.4.5 E5: Changes in the Raw Series.- 4.4.6 E6: Changes in the Final SA Series.- 4.4.7 E7: Changes in the Final Trend-Cycle.- 4.4.8 E11: Robust Estimation of the Final SA Series.- 4.5 F: Seasonal Adjustment Quality Measures.- 4.5.1 F1: Smoothing the SA Series Using an MCD MA.- 4.5.2 F2A: Changes, in Absolute Value, of the Principal Components.- 4.5.3 F2B: Relative Contribution of Components to Changes in the Raw Series.- 4.5.4 F2C: Averages and Standard Deviations of Changes as a Function of the Time Lag.- 4.5.5 F2D: Average Duration of Run.- 4.5.6 F2E: Calculation of the MCD Ratio.- 4.5.7 F2F: Relative Contribution of Components to the Variance of the Stationary Part of the Original Series.- 4.5.8 F2G: Autocorrelations of the Irregular Component.- 4.5.9 F2H: % MathType!MTEF!2!1!+-
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$$ Ratios.- 4.5.10 F2I: Tests for the Presence of Seasonality.- 4.5.11 F3: Monitoring and Quality Assessment Statistics.- 5 Modelling of the Easter Effect.- 5.1 The Easter Holiday.- 5.1.1 A Brief History.- 5.1.2 Calculation of the Dates of Easter.- 5.1.3 Easter and Seasonal Adjustment.- 5.2 The X-11-ARIMA Models.- 5.2.1 The Immediate Impact Model.- 5.2.2 The Corrected Immediate Impact Model.- 5.2.3 The Gradual Impact Model.- 5.3 The X-12-ARIMA Models.- 5.3.1 The Bateman-Mayes Model.- 5.3.2 The Sceaster Model.- 5.3.3 The Easter Model.- References.