Benchmarking, Temporal Distribution, and Reconciliation Methods for Time Series

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Springer Science & Business Media, Sep 23, 2006 - Business & Economics - 410 pages
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In modern economies, time series play a crucial role at all levels of activity. They are used by decision makers to plan for a better future, by governments to promote prosperity, by central banks to control inflation, by unions to bargain for higher wages, by hospital, school boards, manufacturers, builders, transportation companies, and by consumers in general.

A common misconception is that time series data originate from the direct and straightforward compilations of survey data, censuses, and administrative records. On the contrary, before publication time series are subject to statistical adjustments intended to facilitate analysis, increase efficiency, reduce bias, replace missing values, correct errors, and satisfy cross-sectional additivity constraints. Some of the most common adjustments are benchmarking, interpolation, temporal distribution, calendarization, and reconciliation.

This book discusses the statistical methods most often applied for such adjustments, ranging from ad hoc procedures to regression-based models. The latter are emphasized, because of their clarity, ease of application, and superior results. Each topic is illustrated with many real case examples. In order to facilitate understanding of their properties and limitations of the methods discussed, a real data example, the Canada Total Retail Trade Series, is followed throughout the book.

This book brings together the scattered literature on these topics and presents them using a consistent notation and a unifying view. The book will promote better procedures by large producers of time series, e.g. statistical agencies and central banks. Furthermore, knowing what adjustments are made to the data and what technique is used and how they affect the trend, the business cycles and seasonality of the series, will enable users to perform better modeling, prediction, analysis and planning.

This book will prove useful to graduate students and final year undergraduate students of time series and econometrics, as well as researchers and practitioners in government institutions and business.

From the reviews:

"It is an excellent reference book for people working in this area." B. Abraham for Short Book Reviews of the ISI, December 2006

 

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Contents

751 Trend Stationary Models
179
752 Difference Stationary Models
180
753 The Stram and Wei Approach
185
76 Combining SubAnnual and Annual Forecasts
187
Signal Extraction and Benchmarking
192
The Hillmer and Trabelsi Method
195
The Durbin and Quenneville Method
199
the Additive Model
202

The Components of Time Series
14
22 Time Series Decomposition Models
16
23 The Secular or LongTerm Trend
20
231 Deterministic Trend Models
21
232 Stochastic Trends
24
24 The Business Cycle
25
241 Deterministic and Stochastic Models for the Business Cycle
26
242 Limitations of SameMonth Comparisons
27
25 Seasonality
30
252 Models for Seasonality
33
26 The MovingHoliday Component
35
27 The TradingDay Component
39
272 Models for TradingDay Variations
42
273 Sunday Opening of Stores
43
28 The Irregular Component
45
281 Redistribution Outliers and Strikes
46
282 Models for the Irregular Component and Outliers
47
The CholetteDagum RegressionBased Benchmarking Method The Additive Model
51
32 Simple Benchmarking Methods
57
33 The Additive Benchmarking Model
60
34 A Conservative Specification of Deterministic Trends
65
35 Flow Stock and Index Series
68
36 Matrix Representation of the Model
69
37 Other Properties of the RegressionBased Benchmarking Method
75
38 Proportional Benchmarking with the RegressionBased Model
80
the Canadian Total Retail Trade Series
82
Covariance Matrices for Benchmarking and Reconciliation Methods
85
42 Minimization of an Objective Function
87
43 Weak versus Strong Movement Preservation
93
44 Weak versus Strong Proportional Movement Preservation
103
45 Minimizing the Size of the Corrections
104
46 Other ARMA Error Models and Movement Preservation
105
47 Guidelines on the Selection of SubAnnual Error Models
110
48 The Covariance Matrix of the Benchmarks
111
The CholetteDagum RegressionBased Benchmarking Method The Multiplicative Model
113
52 The Multiplicative Benchmarking Model
114
53 Matrix Representation
117
54 NonLinear Estimation of the Multiplicative Model
118
55 Other Properties of the RegressionBased Multiplicative Benchmarking Model
122
The Canadian Total Retail Trade Series
128
The Denton Method and its Variants
135
62 The Original and Modified Additive First Difference Variants of the Denton Method
136
621 Preserving Continuity with Previous Benchmarked Values
141
622 Approximation of the Original and Modified Denton Variants by the Additive RegressionBased Model
143
623 Preferred Variant of Movement Preservation
145
63 The Proportional First Difference Variants of the Denton Method
146
631 Approximation of the Original and Modified Proportional Variants by the Additive RegressionBased Model
149
632 Preferred Variant of Proportional Movement Preservation
150
64 Other Variants of the Denton Method
153
641 The Additive Second Difference Variants
154
642 The Proportional Second Different Variants
157
Temporal Distribution Interpolation and Extrapolation
159
72 Ad Hoc Interpolation and Distribution Methods
162
73 Interpolation and Temporal Distribution Based on Regression Methods
165
74 The ChowLin RegressionBased Method and Dynamic Extensions
174
75 ARIMA Interpolation Temporal Distribution and Extrapolation
178
Additive Model
203
The Chen Cholette and Dagum Method
206
Calendarization
209
92 The Assignment Calendarization Procedure
211
93 The Fractional Calendarization Method and its Variants
217
94 ModelBased Calendarization Methods
219
942 RegressionBased Method
223
95 Calendarizing MultiWeekly Data Covering 4 or 5 Weeks
228
96 Calendarizing Payroll Deductions
234
A Unified RegressionBased Framework for Signal Extraction Benchmarking and Interpolation
235
103 Signal Extraction
239
104 Benchmarking With and Without Signal Extraction
241
105 Interpolation Temporal Distribution and Extrapolation
243
106 Multiplicative Models for Signal Extraction and Benchmarking
246
the Canadian Total Retail Trade Series
250
Benchmarking with Signal Extraction Interpolation and Extrapolation
256
Reconciliation and Balancing Systems of Time Series
263
112 General RegressionBased Reconciliation Method
269
113 Choosing the Covariance Matrices
272
114 Data Problems
277
115 Strategies for Reconciliation
280
Reconciling OneWay Classified Systems of Time Series
285
122 The Reconciliation Model for OneWay Classified Systems of Series
286
123 Implementation of the Analytical Solution
290
124 Redundant Constraints in the OneWay Reconciliation Model
293
125 An Example of OneWay Reconciliation
294
OneWay Reconciliation Model of The Seasonally Adjusted Canadian Retail Trade Series
303
Reconciling the Marginal Totals of TwoWay Classified Systems of Series
308
132 The Marginal TwoWay Reconciliation Model
311
1321 Deriving an Analytical Solution in Terms of the Main Partitions
313
1322 Deriving an Analytical Solution for Each Series
314
1323 General Analytical Solution of the Marginal TwoWay Reconciliation Model
317
133 Implementation of the Analytical Solution
319
134 Redundant Constraints
322
the Seasonally Adjusted Canadian Retail Trade Series
324
1351 The Indirect Seasonal Adjustment
326
1352 The Direct Seasonal Adjustment
330
Reconciling TwoWay Classifed Systems of Series
337
142 The Reconciliation Model for TwoWay Classified Systems of Time Series
338
1421 Deriving an Analytical Solution in Terms of the Main Partitions
341
1422 Deriving an Analytical Solution for Each Series
342
1423 Analytical Solution of the TwoWay Reconciliation Model
346
143 Particular Cases of the TwoWay Reconciliation Model
347
1433 The TwoWay Model Without the Grand Total
348
144 InputOutput Models
350
145 Implementation of the TwoWay Reconciliation Model
353
146 Redundant Constraints in the TwoWay Reconciliation Model
358
147 A Real Data Example of a Large TwoWay System of Series
359
Extended GaussMarkov Theorem 1
363
An Alternative Solution for the CholetteDagum Model for Binding Benchmarks
369
Formulae for Some Recurring Matrix Products
373
Seasonal Regressors
377
TradingDay Regressors
387
References
393
Index
403
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