Commodity prices and the AUD-Yen exchange rate: a real-time forecasting analysis

ABSTRACT

I study the impact of the GSCI commodity price indices on the Australian dollar-Japanese yen nominal exchange rate using a modified version of the classic monetary approach of exchange rate determination. I use a broad range of model-selection and model-averaging criteria. I find some evidence for a short-lived relationship as far as inclusions in the optimal forecasting models are concerned. In general, though, results of the Diebold-Mariano and Clark-West test show that results are not stable over the whole sample.

KEYWORDS:

• Exchange rates
• forecasting
• commodity prices

JEL CLASSIFICATION:

• E17
• F31
• Q02

Acknowledgments

I would like to thank two anonymous reviewers and especially Christian Pierdzioch for helpful suggestions. Furthermore, I would like to thank the German Research Foundation for financial support.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ For a comparison of the performance of local approaches like the nearest neighbour approach and global approaches like genetic programming see, for example, Alvarez-Diaz (2008).

² For an overview of recent literature dealing with exchange rate predictability see, for example, Rossi (2013).

³ In contrast to Kohlscheen, Avalos, and Schrimpf (2017) I use a real-time forecasting approach to control for model uncertainty and model instability. They use a panel regression to analyse the influence of commodity prices on different nominal exchange rate pairs.

⁴ According to the Australian Department of Foreign Affairs and Trade, in 2011/12 a total of $16.8\mathrm{\%}$ of Australian exports went to Japan. This ranked Japan second place of the most important purchasers of Australian goods and services after China. In 2015 (the last year of the sample), Japan’s share of Australian exports still was $13.4\mathrm{\%}$, which also ranked them second place. See http://dfat.gov.au/pages/default.aspx for further information.

⁵ For robustness checks, I analyse a fourth sample; please see Section 4.5 for further details.

⁶ Due to data availability, I use nominal interest rate differentials in contrast to Frankel (1979), who uses real interest rate differentials.

⁷ Since the five subindices are included in the GSCI, it does not make sense to estimate a specification that includes the GSCI as well as the five subindices.

⁸ In total, I estimate more than 800,000 different models. All computations were coded up using the free R programming environment (R Development Core Team 2016).

⁹ For a more detailed description of the assumed hypotheses of the DM test see Section 4.4.

¹⁰ For the model-selection approach, this is not necessary per se since in every period a different combination of predictor variables is selected by each criterion. Although all predictor variables of the basic model are comprised in the advanced and extended model one does not have to control for nested models as long as not all predictor variables are included in the optimal predictor variable combination in every forecasting period.

¹¹ The choice of data frequency is governed by the fact that Australian income (GDP as well as industrial production) is only available on a quarterly basis.

¹² To use the last quarter of 2015 for the forecasts I choose the last observation from December the 4th as the end-of-quarter value for 2015Q4. This is reasonable because in real time, it is the last observation that is available to a forecaster.

¹³ Using government bond rates instead of three-months interest rates is governed by the fact that the latter is only available for Japan from 2002 onwards.

¹⁴ I am aware of the fact that macroeconomic data is probably subject to data revisions, therefore it is difficult to still classify the forecasting analysis as ‘real-time’ forecasting. Though, as for example Döpke, Hartmann, and Pierdzioch (2008) show, data revisions on macroeconomic data do not have a significant impact on the results created by the real-time forecasting approach.

¹⁵ All the data are taken from the FRED board of the Fed of St. Louis (see https://research.stlouisfed.org/fred2/) except the GSCI data and the Japanese GDP data which are taken from Datastream. The corresponding datastream source codes for the GSCI data are: GSCI main index: CGSYSPT; GSCI energy index: GSENSPT; GSCI precious metals index: GSPMSPT; GSCI agriculture index: GSAGSPT; GSCI livestock index: GSLVSPT; GSCI industrial metals index: GSINSPT. The corresponding source code for the Japanese GDP is: JPGDP…B.

¹⁶ The skewness of the series is 0.52.

¹⁷ Precious metals returns and livestock returns only seem volatile compared to the other indices due to different axis labelling.

¹⁸ Later, for robustness checks, I shall change the length of the training period as well as the rolling window length to 15 years.

¹⁹ The first-order autocorrelation coefficient is 0.004.

²⁰ The figures for the basic and advanced model are not reported, but are available from the author upon request.

²¹ For example, for the first quarter of 2000, I replace the end-of-March 2000 observation by the end-of-February 2000 observation.

²² It should be noted that these insights only result from a graphical analysis. When the forecasts and actual returns are tested for independently distributed series using the Pesaran-Timmermann (1992) test for directive accuracy, the null hypothesis of independently distributed series cannot be rejected for any of the, in total, 12 criteria at a $5\mathrm{\%}$-level. These results are applied for all three model specifications.

²³ The results for the Pesaran and Timmermann (1992) test of directive accuracy equal the results for the forecasts created by the recursive window approach. For all three model specifications for all of the 12 criteria, the null hypothesis of independently distributed series cannot be rejected at a $5\mathrm{\%}$-level. 

²⁴ The corresponding forecasting errors for a naive random walk are 982.49 (MSFE) and 31.34 (RMSFE).

²⁵ Results for the other criteria look similar and are available upon request.

²⁶ It should be noted that due to the time-varying nature of the search-and-updating technique, the real-time forecasting approach somehow already controls for nonlinearity.

²⁷ Since the Diebold-Mariano test is a symmetric test, the p-value for the other alternative hypothesis, that model 1 is more accurate than model 2, is $1-p$. In this case, the hypothesis are $H_0:e_1\ge e_2$ and $H_1:e_1<e_2$.

²⁸ See also Section 4.6.

²⁹ See Section 4.5 for further details.

³⁰ For simplicity, I will further refer to the alternative hypothesis, that model 3 (extended model) has a higher forecasting accuracy (which means that the forecasting errors created by model 3 are significantly smaller) than model 2 (advanced) and model 1 (basic) as alternative hypothesis 1. For ‘the other way round’, that model 1 has a higher forecasting accuracy than model 2 and model 3 I will further refer to as alternative hypothesis 2. The p-values given in the tables always refer to alternative hypothesis 1, but, as mentioned before, since the Diebold-Mariano test is a symmetric test, the p-values corresponding to alternative hypothesis 2 are derived from calculating one minus the p-values given in the tables.

³¹ When instead of the Diebold-Mariano test the Giacomini-White test (Giacomini and White 2006; Giacomini and Rossi 2013) is applied, the results hardly change. (Results are not reported but are available upon request.) When the advanced model is tested against the benchmark, only for the DCC criterion for the recursive approach the null hypothesis of equal forecasting errors can be declined at the 10%-level. When the extended model is tested against the benchmark, the null hypothesis can only be declined for the following criteria: DCC recursive (10%-level), AIC rolling (5%-level), FIC rolling (5%-level), MAV recursive (5%-level) and TAV rolling (10%-level). It should be noted that the recursive window approach is not consistent with the assumption of nonvanishing estimation errors required by the Giacomini-White test (Manzan 2015). Therefore, results for the recursive window approach should be considered as approximations.

³² For, the p-values for the four criteria are: 0,89 (SAV), 0.84 (MAV), 0.89 (AAV) and 0.84 (TAV).

³³ I will further refer to this specification as ‘middle month model’.

³⁴ Otherwise, the inclusion of the GSCI data would be $0\mathrm{\%}$ for all criteria.

³⁵ For the model-averaging criteria, all models are considered.

³⁶ Figures for all the other criteria are available upon request.

Additional information

Funding

This work was supported by the German Research Foundation [Project Macroeconomic Forecasting in Great Crises; Grant No. FR 2677/4-1].