1. 1 Pulp Price Analysis Prepared by Professor Martin L. Puterman for BABS 502 Sauder School of Business March 24, 2004

2. 2 Pulp Prices and Exchange Rates Quarterly 1983-2003

3. 3 Study Objectives Determine whether there is any relationship between US$/CDN$ Exchange rates and pulp prices. Systematically investigate the suitability of using models to forecast pulp prices. Produce two year ahead quarterly pulp price forecasts.

4. 4 Autocorrelations of Differences

5. 5 Regression Analysis Pulp Price on US/CDN$ Exchange Rate Nominal Values IndependentRegressionStandard T-Value P-value VariableCoefficientError Intercept80.80165.98 0.480.62 US_Exchange666.2195220.90 3.010.003 R-Squared0.10 Durbin-Watson 0.22 Results are spurious because of significant autocorrelation in residuals (See Durbin-Watson Statistic) Suggests that data be differenced before further analysis

6. 6 2003 Nobel Prize in Economics Background Paper It was not well understood (prior to the work of Granger and Newbold) that testing hypotheses about the coefficients in a simple linear regression … might lead to spurious results. Granger and Newbold, 1974 pointed out that tests of such a regression may often suggest a statistically significant result when none exists. The problem was that the residuals of the estimated equation display extremely strong positive autocorrelation. A simple approach to address this problem is to base tests for causality on differences of variables.

7. 7 Regression Analysis Pulp Price on US/CDN$ Exchange Rate Differences IndependentRegressionStandard T-Value P-value VariableCoefficientError Intercept2.047.196 0.280.78 diff_rate670.7493.786 1.360.18 R-Squared0.02 Durbin Watson 1.37 Analysis suggests that changes in pulp price are not predictable by changes in exchange rates

8. 8 Forecasting Pulp Prices Directly Models Considered –Exponential Smoothing –ARIMA models –Trend Models

9. 9 ARIMA Models ARIMA(1,1,0) and ARIMA(0,1,1) fit the data similarly well in sample. –In both cases residuals appear to be white noise and the coefficients are statistically significant. –The RMSE of each is about 62 ARIMA(0,1,1) ARIMA(1,1,0)

10. 10 Exponential Smoothing Simple Exponential Smoothing Exponential Smoothing with Trend

11. 11 Regression with trends quadratic linear

12. 12 Out of Sample Forecasts Hold Out 8 Quarters of Data In general the fit of all models are quite poor. None pick up on the upswing in prices in the last 3 quarters. Three models; simple exponential smoothing, ARIMA(0,1,1) and ARIMA(2,1,0) have MAPE of 7.8% but the absolute percentage errors of the ARIMA(2,1,0) model are less variable. There does not seem to be any benefit in pooling models here. Using regression on exchange rate is problematic because it requires an exchange rate forecast.

13. 13 Forecasts Out of sample analysis suggests that forecasts based on the ARIMA(2,1,0) model are best. Recalibrating the model on the entire data set gives the forecasts for 2004- 2005 in the graph.

14. 14 Concluding Remarks Using past information; it appears the best two year ahead forecast is a constant value close to the present value. Results should be accurate to roughly +/- 16%.