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## Über dieses Buch

The authors, Dominique Ladiray and Benoit Quenneville, provide a unique and comprehensive r~view of the X-11 Method of seasonal adjustment. They review the original X-11 Method developed at the US Bureau of the Census in the mid-1960's, the X-ll core of the X-ll-ARTMA Method developed at Statistics Canada in the 1970's, and the X-11 module in the X- 12-ARTMA Method developed more recently at the Bureau of the Census. The review will prove extremely useful to anyone working in the field of seasonal adjustment who wants to understand the X-11 Method and how it fits into the broader picture of seasonal adjustment. What the authors designate as the X-11 Method was originally desig­ nated the X-11 Variant of the Census Method IT Seasonal Adjustment Program. It was the culmination of the pioneering work undertaken at the Bureau of the Census by Julius Shiskin in the 1950's. Shiskin introduced the Census Method T Seasonal Adjustment Program in 1954 and soon followed it with the introduction of Method TT in 1957.

## Inhaltsverzeichnis

### Introduction

Abstract
When it comes to seasonal adjustment, the most widely used statistical method is without a doubt that implemented in the Census X-l 1 software. Developed at the US Bureau of the Census in the 1950’s and 1960’s, this computer program has undergone numerous modifications and improvements, leading especially to the X-11-AR1MA software packages in 1975 and 1988 (Dagum [19, 20]) and X-12-ARIMA (the first beta version of which is dated 1998, Findley et al. [23]). While these software packages integrate, to varying degrees, parametric methods, and especially the AR IMA models popularized by Box and Jenkins [9], they remain in essence very close to the initial X-11 method, and it is this “core” that will interest us here.
Dominique Ladiray, Benoit Quenneville

### 1. Brief History of Seasonal Adjustment

Abstract
It is common today to decompose an observed time series X t into several components, themselves unobserved, according to a model such as:
$$X_t = T_t + C_t + S_t + I_t ,$$
where T t ,C t ,S t and I t designate, respectively, the trend, the cycle, the seasonality and the irregular components. This is an old idea, and it is doubtless to astronomy that one should turn to find its origin1.
Dominique Ladiray, Benoît Quenneville

### 2. Outline of the X-11 Method

Abstract
The X-11 method is based on an iterative principle of estimation of the different components, this estimation being done at each step using appropriate moving averages. The method is designed for the decomposition and seasonal adjustment of monthly and quarterly series.
Dominique Ladiray, Benoît Quenneville

### 3. Moving Averages

Abstract
The X-l1 method of seasonal adjustment uses moving averages to estimate the main components of the series: trend-cycle and seasonality. These filters, which do not involve a priori the use of sophisticated concepts or model, are very simple in principle and especially flexible in their application: it is possible to construct a moving average that has good properties in terms of trend preservation, elimination of seasonality, noise reduction, and so on.
Dominique Ladiray, Benoît Quenneville

### 4. The Various Tables

Abstract
This chapter presents a complete and detailed example of seasonal adjustment with the X-11 method. The series that is used in this example is a monthly series; it is in such cases that the softwares’ options are most numerous and complex. The series studied X t is the monthly index of industrial production in France between October 1985 and March 19951. The series is represented in the top panel of Figure 4.1, which gives a decomposition plot. The seasonal factors S t (Table D10) are graphed in the third panel, and, in the case at hand, the trading-day factors D t (Table C18) are provided in the fourth panel. These two sets of factors are used to compute the seasonally adjusted series A t (Table D11), which is shown with the original series in the top panel, and with the trend-cycle C t (Table D12) in the second panel. Finally, the irregular component I t (Table D13) is graphed in the bottom panel. It is obtained by removing the trend-cycle from the seasonally adjusted series.
Dominique Ladiray, Benoît Quenneville

### 5. Modelling of the Easter Effect

Abstract
X-11-ARIMA and X-12-ARIMA propose different models for correcting the Easter effect based on an estimate of the irregular component. The proposed models and the methods used are sometimes quite different in the two softwares, which is why we have not integrated them directly into the seasonal adjustment example of Chapter 4.
Dominique Ladiray, Benoît Quenneville

### Backmatter

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