Dealing with Seasonal
Products in Price Indexes
By
E. Diewert, P. Armknecht and
A. Nakamura
2008 World Congress on NAEP
Measures for Nations
Dealing with Seasonal Products

The Problem of Seasonal Products



Seasonal fluctuations and unavailability
Index compilation is difficult for products
available only part of the year
A Seasonal Product Data Set



Test data set developed by Turvey
Four years of price and quantities with
several products missing part year
Used to test alternative index methods
May 15, 2007
2008 World Congress on NAEP Measrues
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Year over Year Annual Indices
Use 12-month changes with monthly
weights to calculate Laspeyres,
Paasche, and Fisher indices
 Use monthly weights to derive annual
average 12-month change as a
weighted average of the individual
monthly indices
 Approximate indices (using base year
weights only) are close to actual
annual indices

May 15, 2007
2008 World Congress on NAEP Measrues
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Rolling Year Annual Indices
12-month indices not helpful in
analyzing month-to-month inflation
rates
 Calculate 12-month rolling (moving)
averages centered on month 6
 Provides estimate of monthly trend

May 15, 2007
2008 World Congress on NAEP Measrues
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Rolling Year Annual Indices
Figure 22.1 Rolling Year Fixed Base and Chained Laspeyres,
Paasche, and Fisher Indices
1.4
PL (fixed)
PP (fixed)
Index
1.3
PF (fixed)
1.2
PL (chain)
1.1
PP (chain)
PF (chain)
1.0
1
3
5
7
9
11 13
15 17
19 21 23
25 27 29
31 33 35
37
Months
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2008 World Congress on NAEP Measrues
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Rolling Year Annual Indices

Practically the same results obtained
using approximate (base year weights
only) year over year indices
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2008 World Congress on NAEP Measrues
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Rolling Year Annual Indices

Predicting a rolling year index using a
current period year over year monthly
index


Estimate a seasonal factor by comparing
monthly 12-month index to the rolling
year index
These factors can be used to seasonally
adjust the monthly indices
May 15, 2007
2008 World Congress on NAEP Measrues
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Rolling Year Annual Indices
Figure 22.3 Rolling Year Fixed Base Laspeyres and Seasonally
Adjusted Approximate Rolling Year Price Indices
1.5
1.4
1.3
Index
Plry
1.2
Psaary
1.1
Pary
SAF
1
0.9
0.8
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Months
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2008 World Congress on NAEP Measrues
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Chapter 22. The Treatment of Seasonal
Products

Annual basket indices with imputation
of unavailable prices


Use first year annual weights and
December price reference period (similar
to practice of many countries)
Impute missing seasonal prices by
average change in prices for available
products
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2008 World Congress on NAEP Measrues
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Rolling Year Annual Indices
Figure 22.5 Lowe, Young, Geometric Laspeyres, and Centered Rolling
Year Indices with Imputed Prices
1.9
1.8
Index
1.7
1.6
Ploi
1.5
Pyi
1.4
Pgli
Pcry
1.3
1.2
1.1
1
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
Months
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2008 World Congress on NAEP Measrues
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Bean and Stine Type C
or Rothwell Indices
Use seasonal weights for each
product in each month
 Requires monthly weights from the
weight reference period

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2008 World Congress on NAEP Measrues
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Lowe and Rothwell Indices
Figure 22.6 Lowe and Normalized Rothwell Indices
1.9
1.8
1.7
Index
1.6
1.5
Plo
1.4
Pnr
1.3
1.2
1.1
1
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37
Months
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2008 World Congress on NAEP Measrues
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Forecasting Rolling Year Indices

Forecasting using month to month
annual basket indices



Seasonally adjust series by using base
year seasonal factors
Seasonal factors computed using monthly
index compared to rolling average index
in base year
Seasonal factors could also be computed
using standard software like X-11
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2008 World Congress on NAEP Measrues
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Forecasting Rolling Year Indices
Figure 22.8a Se asonally Adjuste d Lowe , Young, and Ge ome tric
Laspe yre s Indice s with Impute d Price s, Se asonally Adjuste d Rothwe ll
and Ce nte re d Rolling Ye ar Indice s
1.5
1.4
Plosa
1.3
Index
Pysa
Pglsa
1.2
Pcry
Prothsa
1.1
1
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
Months
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2008 World Congress on NAEP Measrues
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Forecasting Rolling Year Indices
Figure 22.8b Seasonally Adjusted (X-11) Lowe, Young, and Geometric
Laspeyres Indices with Imputed Prices, and Centered Rolling Year
Indices
1.5
1.4
Plox11
Index
1.3
Pyx11
Pglx11
1.2
Pcry
1.1
1
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
Months
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2008 World Congress on NAEP Measrues
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Conclusions



Year over year indices should be calculated
as a supplemental series along with rolling
year indices
Seasonally adjusted indices should also be
produced to assist in analysis of monthly
inflation measures
Annual basket indices appear to provide
adequate measures when imputation
techniques are used
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2008 World Congress on NAEP Measrues
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