# Presentation: 919580

## Seamless 	Timber Mart-South 		Time Series

- SOFEW -- April 18-20 1999 -- Biloxi MS

- Jeffrey P. Prestemon & John Pye
- Southern Research Station
- USDA-Forest Service, SRS
- Research Triangle Park, NC

**Notes:**
Jeffrey P. Prestemon is a Research Forester and John Pye is an Ecologist with the USDA-Forest Service’s Forestry Sciences Laboratory, Research Triangle Park, NC 27709.

## Introduction

- Seamless time-series of timber prices are essential for understanding market behavior
- Timber Mart-South has published stumpage and log prices since 1976, but the spatial and temporal scales have changed twice
- We devised and tested a way of accounting for the spatial changes

**Notes:**
Timber Mart-South’s time series of timber and delivered log prices have changed twice in its 22-year history of price reports.  We have developed a method of accounting for one of these changes, the spatial reconfiguration that occurred in 1992.

## Presentation Overview

- Description of TMS reporting changes
- Outline an aggregation technique
- Define a test for seamlessness
- Report the results of tests

**Notes:**
Our presentation begins with an overview of Timber Mart-South’s reporting changes.  We then describe the aggregation technique used to make the reported series spatially consistent over time and describe the method used to evaluate the effectiveness of the aggregation technique.  We complete this presentation by describing how well our technique held up to rigorous testing.

## Scope of Evaluation

- Stumpage and delivered prices
- Softwood and hardwood
- Sawtimber and pulpwood
- 21 new TMS regions

**Notes:**
Our evaluation covered 21 of Timber Mart-South’s current list of 26 price reporting zones--i.e., excluding Oklahoma, Kentucky, and Arkansas’ region 2, where consistency of reporting was spotty and harvest volumes low.  Series covered include pine and mixed hardwood pulpwood and pine sawtimber and both delivered and standing timber (stumpage) prices.

## TMS Frequency Change

- Monthly reporting 1976:12-1988:03
- Quarterly reporting 1988:I-1998:IV

**Notes:**
Timber Mart-South began its price reporting in December, 1976.  Until March of 1988, prices were reported monthly. Since the first quarter of 1988 prices have been reported quarterly.

There are several techniques for converting monthly series into quarterly series.  Some researchers average the three months of a quarter to create a quarterly price series.  Others take samples from the opening month, middle month, or closing month of each quarter.  

In our research we have preferred taking middle-month samples from the monthly data (i.e., February’s price is the price for the first quarter, May is the price for the second quarter, etc.) when creating the quarterly series from the monthly reporting from 1976:12-1987:12.

## Reporting Frequency Change

- 1988

- 1978

- 1999

- Texas pine sawtimber in nominal dollars

- monthly

- quarterly

**Notes:**
Many kinds of time-series analyses require more observations than the available quarterly series. If the monthly series from the earlier period are converted to quarterly series through regular sampling or averaging across the three months of a quarter, a longer quarterly series can be constructed--one that extends eighty-eight quarters to date.

## TMS Spatial Change

- Three (or two) regions per state 1976:12-1991:IV
- Two regions per state 1992:I-1998:IV
- Not all boundaries shifted

**Notes:**
The spatial changes in Timber Mart-South reporting may be viewed as a greater challenge than its temporal inconsistencies. From 1976-1991 most states had three reporting regions. In the Atlantic coast states, these three regions generally corresponded to the coastal plain (region 3), Piedmont (region 2), and mountains (region 1).  Along the Gulf of Mexico different schemes for division were used. Regardless, in 1992 Timber Mart-South reconfigured each state into two regions, a spatial configuration that continues to today. The exceptions to this three-to-two change were Texas, which began with two regions and thus underwent no change, and Florida, which began with three regions but which lost its southern-most region. Kentucky was a third exception but was not included in this study.

## Old Reporting Areas

**Notes:**
This map shows the original configuration of price reporting regions (omitting Kentucky). Timber Mart-South’s price data are generated by compiling price quotes based on timber sales and delivered wood costs within each region.  Due to low wood harvesting activities and few mills, some of these regions had very spotty reporting, making statistics generation difficult.  This spotty reporting was a major reason for the consolidation of regions in 1992.

## Lost Reporting Areas

**Notes:**
This diagram highlights the old reporting regions that were split up and merged into other regions to create the new regions. Other boundary changes were made as well, including dropping of South Florida’s price report and more minor boundary changes elsewhere. Merged regions with the most spotty reporting were those along the Mississippi Delta in Louisiana, Mississippi, and Arkansas. 

## Weighting Procedure Example

- relative harvest amounts dictate importance of old area prices
- weights in each new area sum to 100%

- example weights for AR hardwood poletimber

**Notes:**
We used a weighted average approach to reconstruct for the two new regions of each state quarterly prices for the pre-1992 period when prices were reported from three regions. Separate weights were calculated for each of the different product types (e.g.. softwood pulpwood, softwood sawtimber, etc.). The weights are based on average annual removals of the product whose price series is being reconstructed. The slide above illustrates the process for Arkansas. The black line separates Arkansas’ new regions one and two, the colored areas represent the original three regions. Numbers indicate the weights derived from removals in that area, here for hardwood poletimber. Note that weights for each new region total 100%.

## Weighting Procedure Equation

- (added for online version)

**Notes:**
Each TMS Area contains several counties and portions of counties.  The weight for product r that corresponds to the old TMS region (i=1,..I) and new TMS region region (j=1,2), wijr, is calculated based on the proportion of each county’s (k=1,...,K) removals of product r corresponding to the old and new areas.  The proportion is based on area, and removals are based on volume in cubic feet (pulpwood) or board-feet (sawtimber and sawlogs).  Two proportions are used--Pijk, the area of county k found in old region i and new region j, and Pjk, the area of county k found in new region j.

## Aggregation Technique

- New region prices are county removals-weighted averages of old region prices
- Weights are specific to product (r), old region (i=1,2,3) and new region (j =1,2)
- Form:  Prj,t = i  wijrPri,t
- Ex: P1=(0.14*$27) + (0.53*$25) + (0.33*$33) = $27.9

**Notes:**
Spatially-consistent series of prices can be constructed from the old prices by employing the weights as shown above.  For example, if the 1980 first quarter prices for delivered pine pulpwood ($/cord) in Alabama regions were as follows:

Alabama Region 1:  $27
Alabama Region 2:  $25
Alabama Region 3:  $33

and the weights for constructing the new Region 1 series were

w11 = 0.14
w21 = 0.53
w31 = 0.33

Then the new Region 1 series price would have been:

P1 = (0.14*27) + (0.53*25) + (0.33*33) = $27.9/cord

## Tests of Seamlessness

- Estimated ARIMA models of each series, using logarithmic, nominal, mid-month sampled quarterly prices, 1977-1998
- Included a dummy for the region shift, tested for its significance--an intervention analysis technique

**Notes:**
Autoregressive-integrated-moving average models of each series, which incorporated the weighting scheme just described for the pre-1992 portion of each new TMS series, were estimated.  Prices were expressed in nominal terms and transformed into natural logarithms.  The transformed nominal price series were all nonstationary.  Nonstationarity was tested by running augmented Dickey-Fuller tests for unit roots for the undifferenced series. The ADF test specification included an intercept.  The number of difference terms to include in each series’ test was determined by the minimum of the Akaike information criterion, choosing from among nine specifications (0 to 8 lagged difference terms).  

ARMA(p,q) models of each series were then estimated, including a dummy corresponding to the first quarter of 1992, when the new regions first took effect, and testing for whether the dummy coefficient was statistically different from zero at five percent significance.  Again, the specification of each series’ ARMA(p,q) was determined by the minimum of the Akaike information criterion.

## Significant Change in 1992 Qtr1

- PINE-PULP

- HARD-PULP

- PINE-SAW

- S*

- S

- S

- D

- D

- D

- D-delivered

- *S-stumpage

**Notes:**
This figure shows those series (highlighted in red) which had coefficients on the region dummy that were statistically different from zero at 5%.  The left side of the figure identifies the product and the top row identifies the new Timber Mart-South region.  The Timber Mart-South regions that had no boundary changes are darkened (FL1, LA2, MS2, SC1, TX1, TX2, VA1).
The region with the most series with significant dummies was South Carolina Region 1, which saw no change in its borders.  Indeed, it seems that the likelihood of a significant shift is unrelated to whether or not a boundary change occurred. Six significances out of the 42 series in the seven regions that were not reconfigured is roughly the same percentage as the eleven out of 84 significances in the regions that were reconfigured.
Further, there appears to be some spatial correlation in the series which had statistically significant dummy coefficients.  Almost all dummy coefficient estimates in these series were positive.  Many of the series were in regions surrounding the southern Appalachians and other interior portions of the South.  This spatial pattern and similar direction of shift could point to some weather-related or economic phenomenon common to those regions with significant shifts. 
Finally, we compared the shift seen in the TMS Mississippi pine sawtimber series with that from a similar but independently-collected price series from the State of Mississippi and found the shifts to be identical, arguing that the shift is more than a methodological artifact.

## Results of Test

- Most series were seamless
- Spatial clustering of regions with significant dummy coefficients
- No apparent relationship between degree of change and significance
- 1992:I shift found in non-TMS data

**Notes:**
We found that most TMS series created using our weighting scheme were seamless--109 out of the 126 series tested.

We found seventeen series where there was a statistically significant shift in the series (mostly positive), and there appeared to be some spatial clustering of those regions. Further, there appeared to be no relationship between reconfiguration and the finding of an improbable shock.  Finally, one comparison with an independent series revealed an identical shock as the comparison TMS series.

## Possible Explanations for Shifts

- Economic shifts--housing starts, GDP
- Weather factors affecting harvesting
- Reporting changes independent of region shifts

**Notes:**
What were the causes of the statistically large price shocks in the seventeen  series? We believe that the changes experienced by the price series can be at  be partially explained by three alternative factors. First, demand for timber  might have spiked because of the large jumps in U.S. GDP and housing starts at the beginning of 1992. Second, supply of timber might have become restricted due to particularly bad weather for harvesting in the first quarter of 1992, relative to the last quarter of 1991.

Third, there might have been some reporting changes at Timber Mart-South that were independent of the region shifts. If this last factor is responsible for  the significant dummy coefficients, then there is reason to be cautious when  applying the weighting factors that we have developed in constructing new TMS series from the old series prices. In that case, we would recommend avoiding using the weighting scheme for those seventeen series with identified statistically significant coefficient dummies.

## Conclusions

- TMS reporting changes are important to economic analyses
- Our technique produced reasonably seamless series for most series
- Weights are available for download from our website at www.rtp.srs.fs.fed.us/econ
-  	     		_[click here](http://www.rtp.srs.fs.fed.us/econ/)_