Dealing with Seasonal Products in Price Indexes By E. Diewert, P. Armknecht and A. Nakamura 2008 World Congress on NAEP Measures for Nations

May 15, World Congress on NAEP Measrues2 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, World Congress on NAEP Measrues3 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, World Congress on NAEP Measrues4 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, World Congress on NAEP Measrues5 Rolling Year Annual Indices

May 15, World Congress on NAEP Measrues6 Rolling Year Annual Indices Practically the same results obtained using approximate (base year weights only) year over year indices

May 15, World Congress on NAEP Measrues7 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, World Congress on NAEP Measrues8 Rolling Year Annual Indices

May 15, World Congress on NAEP Measrues9 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

May 15, World Congress on NAEP Measrues10 Rolling Year Annual Indices

May 15, World Congress on NAEP Measrues11 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

May 15, World Congress on NAEP Measrues12 Lowe and Rothwell Indices

May 15, World Congress on NAEP Measrues13 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

May 15, World Congress on NAEP Measrues14 Forecasting Rolling Year Indices

May 15, World Congress on NAEP Measrues15 Forecasting Rolling Year Indices

May 15, World Congress on NAEP Measrues16 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