This paper investigates the dynamic relationship between the commodity price and the exchange rate in Australia and New Zealand. We focus on Australia and New Zealand . Not only do their primary commodities account for significant shares of their exports, but also their currencies share some distinctive characteristics that are unique from other commodity currencies. Using country-specific commodity price indices, we examine the relationship between the departure of currency value from its fair value and fundamental macroeconomic variables. Evidence of a strong and robust relationship between the exchange rate and the commodity price has been found. Results indicate that the commodity price can be used to improve the forecast ability of the future exchange rate. Our commodity-price-augmented exchange rate forecasting model consistently outperforms the random-walk model, for both in-sample and out-of-sample forecasting. These results shed some extra lights on policymaking for countries that rely on primary commodity production, and attempt to move towards floating exchange rate regimes as part of their global market liberalization process.
In past few decades, many attempts to investigate the relation between fundamental macroeconomic variables and exchange rates have been proven to be failure, not to mention numerous unsuccessful endeavours that economists have made on building various types of exchange rate forecasting models. In early 1970s, after the post-war Bretton Woods system of fixed exchange rates collapsed, a large number of industrialized economies shifted to floating exchange rate regimes. Thus, lots of interests have been put on foreign exchange markets studies. Majority of these work focused on the development of macroeconomic variables based empirical models when forecasting future exchange rates. Meese and Rogoff [
Recent literatures on exchange rate determination and forecasting are in line with the propositions found decades ago. Many empirical results conclude that the exchange rate follows a random walk process, and changes in exchange rate are unpredictable, and currencies for high-inflation countries tend to depreciate in long term with the magnitude being approximately the inflation differential. Movements of the actual exchange rate appear to be sometimes overshot and then followed by a smooth adjustment to the equilibrium [
There has been a strand of research investigating countries with differing exchange rate regimes and economic structures. In particular, countries with “Commodity Currencies” have been given more attentions, and evidences have been found that there exists a long-run relationship between the real exchange rate and the real commodity price for commodity-exporting countries1 [
Australia and New Zealand are two open economies in the OECD regime. They both share a number of distinctive features in economic structures and policy settings. These special features have made the two nation’s currencies demonstrate a remarkable strong “commodity currency phenomenon” and to stand out among other commodity currencies3. Australia is an export-oriented economy, whose exports in primary commodity products take a significant portion of their gross domestic production. Characterized by mainly mineral (or “hard”) commodity exporting, the primary commodity products exported by Australia include iron ore, metallurgical coal, thermal coal, gold and various other metal products. These non-energy products, along with other commodities account for more than 60% of Australian total exports. New Zealand, in contrast, its exports are heavily dependent on agricultural products such as dairy products, wools, meats and other “soft” commodities. Commodity products exporting contribute about 67% of its total exports in the late 80s. Primary commodity products still take about 50% of New Zealand’s total exports today. Moreover, New Zealand is a well-known key player of its commodity products in the global market, in spite of its relatively small economy. It supplies nearly 50% of the total world exports of lamb and mutton where only a fraction of less than 20% of its meat production is consumed domestically. Given both countries are heavily dependent on commodity products to gain export earnings, the price movement in world commodity market would then have an impact on the relative demand for the corresponding currency. Neither of the two countries is big enough to influence the world market, they both also have adopted a sufficiently long period of a floating exchange rate regime under the inflation targeting system4, central banks normally have very limited controls and interventions over exchange rate movements. Commodity price fluctuations can then essentially represent a source of exogenous shocks to their terms-of-trade, which eventually channel up and trigger the exchange rate responses. Therefore, the introduction of the country-specific commodity prices indices in Australia and New Zealand’s commodity exporting in early 1980s, has offered an opportunity to identify and measure exchange rate fluctuations using these indices.
Motivated by Chen and Rogff [
Australian and New Zealand commodity price index and their corresponding quoted exchange rate against US dollar from 1986 to 2010, respectively. The commodity index is the monthly time series and its base value is set at 100 as of 1st January 1986.
In
Previous studies have found that some economics models, i.e. PPP, UIP, can only provide valid information when forecasting exchange rates in the long run. Results from these models usually are not better than a simple random walk
model. Since the term “Commodity Currency” has been introduced and brought to the attention of international finance, researchers have found some promising evidences that commodity price may play some roles in determining and forecasting exchange rates7. A recent study by Luo and Plantier [
If a random walk is what the exchange rate movement follows, then effects of innovations on the exchange rate are highly persistent and the time series can fluctuate without bounds [
In
high as 0.7 around 1992 to as low as 0.95 in 1995 and 2005. In addition, the fair value appears to be relatively constant overtime and failed to pick up any major ‘break’ of actual exchange rate movements. The lacking correlation between the nominal exchange rate and its underlying long-term equilibrium value from existing literatures may be due to the fact that many attempted to model movements of nominal exchange rates using long-term equilibrium value as the explanatory variable. Therefore, in our model, we propose to use the “departure from currency’s long-term equilibrium value” (the difference between the nominal exchange rate and its long-term equilibrium value) rather than the long-term equilibrium value itself. This makes our methodology superior to previous studies.
The exchange rate and the commodity price index are monthly time series for the period from 1986 to 2010. Data are obtained from three sources: Federal Reserve of the U.S., DataStream database and the Reserve Bank of Australia. The Australian and New Zealand direct exchange rates against the US dollar are monthly mid-rate and obtained from the Federal Reserve Bank of the United States. The cross exchange rates between AUD and NZD are fixed at 4:00 p.m. (6:00 GMT) and loaded at approximately 4:30 p.m. (6:30 GMT) for daily records. The monthly series is the mid-point determined by the Reserve Bank of Australia on the basis of quotations in the Australian Foreign Exchange market (Source: Reserve Bank of Australia).
The commodity price indices used in this study are the country-specific indices of commodity export prices. These indices are constructed in a way to reflect the specific characteristics of the respective country’s commodity trading with the rest of the world. The CBA NZ Commodity Price Index and The RBA Commodity Index SDR are the two commodity price indices for New Zealand and Australia. They were developed by the Commonwealth Bank of Australia (CBA) and The Reserve Bank of Australia (RBA) in 1980s. For the US, we use
S & P GSCI Non-Energy Spot Price Index9. There are other indices potentially can be used as well. These include, the price of individual primary commodities, terms of trade indices and aggregate (non-country-specific) indices of commodity-price. The country-specific commodity exports price index is used due to the following reasons. Firstly, neither New Zealand nor Australia has the export price of a single commodity can well mirror the movements of overall commodity-export prices. Secondly, terms-of-trade indices could be affected not only by the composition of the country’s exports but also the composition of the country’s GDP. This is because terms-of-trade indices are typically calculated using exports and unit values. Thirdly, prices of individual commodities do not tend to move together on global-commodity-markets; the movements in aggregate commodity-price indices are likely to be a poor proxy of movements compared to the country-specific commodity export prices [
Purchasing Power Parity (PPP) states a relationship between the nominal exchange rate and the inflation (price level) differences between two countries. Such a relationship can be expressed in a basic form as the following:
S t = P t countryA − P t countryB + ε t (1)
where St is the nominal exchange rate; Pt is the price level, both in logarithm forms. Equation (1) simply defines that the change of the exchange rate can be approximated by the difference of the price levels between two counties and the purchasing power parity holds to a certain degree of error.
The Uncovered Interest Parity (UIP) condition gives an approximation that:
E t ( S t + 1 ) = S t + ( i t countryA − i t countryB ) (2)
where i is the nominal interest rate; E t represents the expected spot exchange rate at time t. Notes this setting is only valid under the risk-neutral assumption. If we relax this assumption and we get Equation (3):
E t ( S t + 1 ) = S t + i t countryA − i t countryB + R P t (3)
where RP is the risk premium on country A’s interest bearing assets over country B’s assets. As expectations are not necessarily rational, we therefore rearrange Equation (3) as following:
S t = E t ( S t + 1 ) + ( i t countryB − i t countryA − R P t ) (4)
Equation (4) differs from Equation (2) as it takes into consideration of the risk premium that the investor seeks in order to be willing to hold foreign assets. Equation (4) can be carried forward for the infinite future and can then be presented as: the current exchange rate equals the current interest rate differentials subtracted from the current risk premium and plus the future expected exchange rate. For example, the term St can be further expressed as following:
S t + 1 = ( i t + 1 countryB − i t + 1 countryA − R P t + 1 ) + E t + 1 ( S t + 2 ) (5)
S t + 2 then can be further expressed as:
S t + 2 = ( i t + 2 countryB − i t + 2 countryA − R P t + 2 ) + E t + 2 ( S t + 3 ) (6)
We therefore derive the following equation:
S t = i t countryB − i t countryA − R P t + ∑ K = 1 ∞ E t + k ( i t + k countryB − i t + k countryA − R P t + k ) + E t ( S ∞ ) (7)
The term S ∞ above can be represented by the PPP condition as Equation (1) and prevail in the infinite future under the assumption that there was no interest rate differential between two counties. In this case S ∞ can be expressed as:
S ∞ = P ∞ countryA − P ∞ countryB + ε ∞ (8)
Furthermore, we can then express the expected future PPP exchange rate as the sum of the current (today’s at time t) PPP exchange rate plus the sum of future expected inflation rate differentials and any expected changes of ε ∞ :
S ∞ = P t countryA − P t countryB + ε t + ∑ K = 1 ∞ E t + k ( Δ P t + k countryB − Δ P t + k countryA + Δ ε t + k ) (9)
If we substitute Equation (9) into Equation (7) and rearrange the equation, we can then derive the current exchange rate S t :
S t = ( i t countryB − i t countryA ) + ( P t countryA − P t countryB ) − ( R P t + ε t ) + ∑ K = 1 ∞ E t + k ( i t + k countryB − i t + k countryA − R P t + k ) + ∑ K = 1 ∞ E t + k ( Δ P t + k countryA − Δ P t + k countryB + Δ ε t + k ) (10)
Equation (10) above represents a dynamic relationship between two countries’ exchange rates, interest rates and price levels (inflation). The spot exchange rate is dependent on a number of observable factors as well as various unobservable factors. We define observable factors (interest rates and price levels in Equation (10)) as the “Fair Value” described in Equation (11) below:
FairValue = ( i t countryB − i t countryA ) + ( P t countryA − P t countryB ) − ( R P ¯ + ε ¯ ) (11)
All data are monthly and in logarithm forms except the average risk premium. i t is the monthly average one-year interbank swap rates10 from Jan 1986 to Mar 2010. P t is the logarithm form of monthly CPI over the same period, R P ¯ is the average risk premium between the two countries, in this case, the difference in the interest rates. The term ε ¯ is serving as a normalization factor.
We calculate the term “Departure from Fair Value” by subtracting Equation (11) from Equation (10) and arrives at the following reduced form:
DeparturefromFairValue = ( R P ¯ + ε ) − ( R P t + ε ) ∑ K = 1 ∞ E t + k ( i t + k countryB − i t + k countryA − R P t + k ) + ∑ K = 1 ∞ E t + k ( Δ P t + k c o u n t r y A − Δ P t + k c o u n t r y B + Δ ε t + k ) (12)
Define “Error” as the departure of the actual exchange rate from its long term fair value at time t, derive from Equation (12), we then use the following regression specification to examine the relationship between ‘Error’ and the following independent variables:
E r r o r t = α t + β 1 ( E r r o r t − 1 ) + β 2 Δ ( E r r o r t − 1 ) + β 3 Δ ( R a l . G D P t − 3 ) + β 4 Δ ( C o m m . P r t − 1 countryA ) + β 5 Δ ( C o m m . P r t − 1 countryB ) + ε t (13)
Data in Equation (13) are monthly data and in logarithm forms except the relative GDP which is the logarithm difference between two underlying countries’ GDP growth rates and the data is quarterly. α t is the constant term. β ( E r r o r t − 1 ) is the momentum term, where if the exchange rate appreciates in one month, it is more likely to continues the appreciation in the subsequent month, β Δ ( E r r o r t − 1 ) represents the reversion-to-fair-value term, where it captures the tendency of currency value reverse back towards its long term fair value over time11. β Δ ( R a l . G D P t − 3 ) captures the effects of the difference in relative GDP growth rates between two underlying countries. Notes it is lagged 3 months as the GDP data is quarterly other than monthly. β Δ ( C o m m . P r t − 1 ) captures the change of commodity prices.
In order to estimate significant shocks that cause the “Error” (the “departure” from the fair value), we take a reduced-form approach by adopting a general-to-specific search among potential variables that may have an impact on the currency value. We investigate a few macroeconomic variables that are relevant and significant both economically and statistically in determining the nominal value of NZD/AUD cross exchange rate. The specification for approximating NZD/AUD cross exchange rate is marginally different from the specification for NZD/USD and AUD/USD exchange rates estimations. This is due to differences in economic structures, policy marking and government regulations between Australia, New Zealand and the U.S. Therefore, impacts from shocks on underlying exchange rates may differ substantially. Specifically, we examine how do fluctuations in country-specific commodity prices translate into movements in the exchange rate? We give special emphasis on the determination of NZD/AUD cross-exchange-rate and the importance of its corresponding commodity prices. To illustrate this, we modify equation 13 as follows:
E r r o r t = α t + β 1 ( E r r o r t − 1 ) + β 2 Δ ( E r r o r t − 1 ) + β 3 Δ ( R a l . G D P t − 3 N Z & A U ) + β 4 ( N Z . C o m P r t − 1 ) + β 5 ( A U . C o m P r t − 1 ) + β 6 ( M i g r a t i o n t − 1 N Z ) + ε t (14)
The above specification follows an error-correction framework; it is conducted in a way that ensures the consistency of the robustness relationship of dependent variables with the exchange rate. The equation, therefore, established to estimate coefficients that are not sensitive to minor variations for the chosen sample period.
In
Variables | NZD/AUD | AUD/USD | NZD/USD | ||||
---|---|---|---|---|---|---|---|
Momentum | 0.9429*** | 0.9521*** | 0.9867*** | 0.9849** | 0.9822*** | 0.9789*** | |
(−55.809) | (−56.805) | −70.463 | (−72.490) | (−73.800) | (−74.520) | ||
Mean Reversion | −0.1521** | −0.1301** | −0.0751 | −0.0579 | |||
(−2.437) | (−2.077) | (−0.957) | (−0.794) | ||||
Ral.GDP.NZ&AU | 0.1876** | 0.1890** | |||||
(−2.187) | (−2.178) | ||||||
Ral.GDP.AU&US | 0.3733* | 0.3749** | |||||
(−1.955) | (−1.976) | ||||||
Ral.GDP.NZ&US | 0.1205 | ||||||
(−1.304) | |||||||
NZ Commodity Prices | −0.1977*** | −0.2099*** | −0.2192*** | −0.2131*** | |||
(−3.560) | (−3.748) | (−3.923) | (-4.583) | ||||
AU Commodity Prices | 0.1906*** | 0.1798*** | −0.3326*** | −0.2994*** | −− | ||
(−3.771) | (−3.526) | (−5.323) | (−5.995) | ||||
US Commodity Prices | 0.0423 | 0.0030 | |||||
(−0.9828) | (−0.078) | ||||||
NZ Migration | 0.0000*** | ||||||
(−2.727) | |||||||
Adj. R-squared | 0.9293 | 0.9276 | 0.9485 | 0.9486 | 0.9543 | 0.9515 | |
Sample period | 1986M1-2010M1 | 1986M1-2010M1 | 1986M1-2010M1 | 1986M1-2010M1 | 1986M1-2010M1 | 1986M1-2010M1 | |
No. obs. | 291 | 291 | 291 | 291 | 291 | 291 | |
Durbin-Watson | 2.0057 | 1.9823 | 1.9336 | 1.9903 | 1.9181 | 2.0135 |
The coefficients for mean reversion and the relative GDP growth in
We now turn to examine possible structural breaks during our sample period. Two possible structural breaks are chosen to reflect two most recent major financial crises; early 2001 and late 2007. We simply give the time-dependent dummy variable a value of “one” for the period before the break date and a value of “zero” for the period after the break date. Results in
In this section, the following regression equation is going to be used to perform the in-sample forecasting for NZD/AUD cross rate:
E r r o r t + k = α + β 1 ( E r r o r t + k − 1 ) + β 2 Δ ( E r r o r t + k − 1 ) + β 3 Δ ( R a l . G D P t + k − 3 N Z & A U ) + β 4 ( N Z . C o m P r t + k − 1 ) + β 5 ( A U . C o m P r t + k − 1 ) + ε t + k (15)
However, despite the superiority of our NZD/AUD cross rate in-sample forecasting model, it is necessary for us to use contemporaneous data when conducting such estimates. Therefore, an out-of-sample forecast performance test is to be conducted. For out-of-sample forecasting, we first adopt standard quantitative procedures involved in forecasting the departure from the fair value from Equation (12), where the forecasting errors are defined as: F E t + k = S t + k − S t + k ^ , where k ≥ 1 and S t + k represents the k-step-ahead forecast.
We measure forecasting errors for four time intervals, 1-month-ahead,
NZD/AUD | NZD/USD | AUD/USD | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Coefficient | Std. Error | t-Statistic | Coefficient | Std. Error | t-Statistic | Coefficient | Std. Error | t-Statistic | ||
Momentum | 0.9521*** | 0.0168 | 56.8054 | 0.9823*** | 0.0133 | 73.7959 | 0.9867*** | 0.0140 | 70.4635 | |
D*Momentum | −0.0325 | 0.0391 | −0.8293 | 0.0088 | 0.0321 | 0.2750 | 0.0413 | 0.0322 | 1.2839 | |
Mean Reversion | −0.1301** | 0.0626 | −2.0769 | −0.0578 | 0.0728 | −0.7944 | −0.0751 | 0.0784 | −0.9574 | |
D*Mean Reversion | 0.1199 | 0.1258 | 0.9526 | 0.0585 | 0.1577 | 0.3710 | 0.1583 | 0.1597 | 0.9912 | |
Ral.GDP.NZ&AU | 0.1890** | 0.0868 | 2.1770 | |||||||
D*Ral.GDP.NZ&AU | −0.3875** | 0.1729 | −2.2413 | |||||||
Ral.GDP.AU&US | 0.3733** | 0.1909 | 1.9555 | |||||||
D*Ral.GDP.AU&US | −0.1217 | 0.3837 | −0.3172 | |||||||
Ral.GDP.NZ&US | 0.1205 | 0.0924 | 1.3043 | |||||||
D*Ral.GDP.NZ&US | −0.1904 | 0.1973 | −0.9650 | |||||||
NZ Commodity Prices | −0.2099*** | 0.0560 | −3.7483 | −0.2192*** | 0.0559 | −3.9230 | ||||
D*NZ Commodity Prices | −0.1672 | 0.1131 | −1.4776 | −0.0269 | 0.1175 | −0.2293 | ||||
AU Commodity Prices | 0.1798*** | 0.0510 | 3.5259 | −0.3326*** | 0.0625 | −5.3230 | ||||
D*AU Commodity Prices | −0.0300 | 0.1152 | −0.2607 | −0.1171 | 0.1380 | −0.8490 | ||||
US Commodity Prices | 0.0030 | 0.0386 | 0.0782 | 0.0423 | 0.0431 | 0.9828 | ||||
D*US Commodity Prices | 0.0031 | 0.0817 | 0.0377 | −0.1003 | 0.0885 | −1.1329 | ||||
Adj. R Square | 0.9290 | 0.9540 | 0.9490 | |||||||
No. obs. | 170 | 170 | 170 | |||||||
NZD/AUD | NZD/USD | AUD/USD | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Coefficient | Std. Error | t-Statistic | Coefficient | Std. Error | t-Statistic | Coefficient | Std. Error | t-Statistic | ||
Momentum | 0.9521*** | 0.0168 | 56.8054 | 0.9823*** | 0.0133 | 73.7959 | 0.9867*** | 0.0140 | 70.4635 | |
D*Momentum | −0.4251*** | 0.1116 | −3.8083 | −0.0700 | 0.0364 | −1.9246 | 0.0576 | 0.0420 | 1.3695 | |
Mean Reversion | 0.1310** | 0.0626 | −2.0769 | −0.0578 | 0.0728 | −0.7944 | −0.0751 | 0.0784 | −0.9574 | |
D*Mean Reversion | 0.1204 | 0.1553 | 0.7753 | 0.4246** | 0.1928 | 2.2030 | 0.6048*** | 0.1936 | 3.1237 | |
Ral.GDP.NZ&AU | 0.1890** | 0.0868 | 2.1770 | |||||||
D*Ral.GDP.NZ&AU | −0.3100 | 0.3235 | −0.9583 | |||||||
Ral.GDP.AU&US | 0.3733** | 0.1909 | 1.9555 | |||||||
D*Ral.GDP.AU&US | 0.4663 | 0.6114 | 0.7627 | |||||||
Ral.GDP.NZ&US | 0.1205 | 0.0924 | 1.3043 | |||||||
D*Ral.GDP.NZ&US | −0.4470 | 0.4800 | −0.9312 | |||||||
NZ Commodity Prices | −0.2099*** | 0.0560 | −3.7483 | −0.2192*** | 0.0559 | −3.9230 | ||||
D*NZ Commodity Prices | −0.2205 | 0.1430 | −1.5421 | 0.2731** | 0.1378 | 1.9824 | ||||
AU Commodity Prices | 0.1798*** | 0.0510 | 3.5259 | −0.3326*** | 0.0625 | −5.3230 | ||||
D*AU Commodity Prices | 0.0941 | 0.1055 | 0.8924 | −0.1637 | 0.1490 | −1.0990 | ||||
US Commodity Prices | 0.0030 | 0.0386 | 0.0782 | 0.0423 | 0.0431 | 0.9828 | ||||
D*US Commodity Prices | −0.1399 | 0.0992 | −1.4114 | −0.3772*** | 0.1066 | −3.5377 | ||||
Adj. R Square | 0.9310 | 0.9560 | 0.9520 | |||||||
No. obs. | 243 | 243 | 243 | |||||||
3-month-ahead, 6-month-ahead and 12-month-ahead. The estimation involves the prediction of the long term Fair Value (FV) of NZD/AUD cross rate, this FV is not constant over time. We first need to define the FV before the forecasting error can be derived. To ensure a theoretically sound process of approximating FVs, we apply four methods to predict FVs over the testing time horizon. Firstly, we assume the Fair Value (FV) is known for the out-of-sample period. Hence, FVs are directly taken from the in-sample forecasting models which have been done in the previous section15. Secondly, FVs are assumed to be unknown for the out-of-sample period, and are therefore predicted using an AR(1) model, an ARMA(1, 1) model and a random walk model, respectively. To evaluate the forecasting performance, four forecasting measures are applied: Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) and Theil Inequality Coefficient (THEIL).
These measurements offer a set of quantitative values, which specifically measure how far the forecasted fair values are away from the actual observed exchange rates. A lower value indicates a better fit, hence, higher accuracy of the forecasting model. The out-of-sample forecasting involves re-estimating the NZD/AUD cross rate for each historical period, using only data that would have been available to us at that time. Appendix B provides a detailed illustration for a 3-month-ahead out-of-sample forecasting.
The relationship between the exchange rate and fundamental macroeconomic variables has drawn lots of attentions to many researchers for many years, yet, no clear consensus has been emerged. In this paper, we focus on a set of selective currencies which are considered as the “Commodity Currencies”, namely the New Zealand and the Australian dollars. We incorporate commodity prices from these two countries into the exchange rate forecasting model. Results shed extra light on two main issues. Firstly, commodity currencies are not the same across countries. Some are more of “commodity currencies” than others, i.e. more pronounce in New Zealand and Australia than in the U.S. This is due to the fact that
Method of FV | Horizon | RMSE_RW | RMSE | MAE_RW | MAE | MAPE_RW | MAPE | THEIL_RW | THEIL |
---|---|---|---|---|---|---|---|---|---|
In-Sample | |||||||||
3 m | 0.0341 | 0.0289* | 0.0258 | 0.0221* | 19.7553 | 16.8073* | 0.1139 | 0.0970* | |
6 m | 0.0422 | 0.0359* | 0.0319 | 0.0267* | 24.3345 | 20.3970* | 0.1436 | 0.1228* | |
9 m | 0.0459 | 0.0406* | 0.0351 | 0.0309* | 27.1057 | 23.5763* | 0.1584 | 0.1412* | |
12 m | 0.0491 | 0.0445* | 0.0381 | 0.0345* | 29.5235 | 26.0723* | 0.1727 | 0.1574* | |
AR(1) | |||||||||
3 m | 0.0341 | 0.0309* | 0.0258 | 0.0234* | 19.7553 | 17.9228* | 0.1139 | 0.1036* | |
6 m | 0.0422 | 0.0385* | 0.0319 | 0.0285* | 24.3345 | 22.0458* | 0.1436 | 0.1315* | |
9 m | 0.0459 | 0.0435* | 0.0351 | 0.0331* | 27.1057 | 25.6278* | 0.1584 | 0.1508* | |
12 m | 0.0467 | 0.0469 | 0.0359 | 0.0360 | 26.6700 | 26.0377* | 0.1443 | 0.1483 | |
ARMA(1, 1) | |||||||||
3 m | 0.0341 | 0.0309* | 0.0258 | 0.0234* | 19.7553 | 17.9302* | 0.1139 | 0.1036* | |
6 m | 0.0422 | 0.0385* | 0.0319 | 0.0285* | 24.3345 | 22.0642* | 0.1436 | 0.1315* | |
9 m | 0.0459 | 0.0435* | 0.0351 | 0.0332* | 27.1057 | 25.6551* | 0.1584 | 0.1508* | |
12 m | 0.0491 | 0.0476* | 0.0381 | 0.0370* | 29.5235 | 28.4387* | 0.1727 | 0.1674* | |
RW | |||||||||
3 m | 0.0341 | 0.0309* | 0.0258 | 0.0233* | 19.7553 | 17.7198* | 0.1139 | 0.1038* | |
6 m | 0.0422 | 0.0385* | 0.0319 | 0.0282* | 24.3345 | 21.5511* | 0.1436 | 0.1321* | |
9 m | 0.0459 | 0.0435* | 0.0351 | 0.0328* | 27.1057 | 25.0227* | 0.1584 | 0.1519* | |
12 m | 0.0467 | 0.0467* | 0.0359 | 0.0357* | 26.6700 | 25.5167* | 0.1443 | 0.1490 |
Method of FV | Horizon | RMSE_RW | RMSE | MAE_RW | MAE | MAPE_RW | MAPE | THEIL_RW | THEIL |
---|---|---|---|---|---|---|---|---|---|
In-Sample | |||||||||
3 m | 0.0341 | 0.0297* | 0.0258 | 0.0232* | 19.7553 | 17.7513* | 0.1139 | 0.0986* | |
6 m | 0.0422 | 0.0371* | 0.0319 | 0.0282* | 24.3345 | 21.7370* | 0.1436 | 0.1249* | |
9 m | 0.0459 | 0.0417* | 0.0351 | 0.0325* | 27.1057 | 25.2778* | 0.1584 | 0.1422* | |
12 m | 0.0491 | 0.0458* | 0.0381 | 0.0360* | 29.5235 | 28.0641* | 0.1727 | 0.1583* | |
AR(1) | |||||||||
3 m | 0.0341 | 0.0314* | 0.0258 | 0.0243* | 19.7553 | 18.7275* | 0.1139 | 0.1031* | |
6 m | 0.0422 | 0.0396* | 0.0319 | 0.0300* | 24.3345 | 23.4934* | 0.1436 | 0.1327* | |
9 m | 0.0459 | 0.0444* | 0.0351 | 0.0344* | 27.1057 | 27.3163 | 0.1584 | 0.1504* | |
12 m | 0.0491 | 0.0458* | 0.0381 | 0.1583 | 29.5235 | 30.4585 | 0.1727 | 0.1666* | |
ARMA(1, 1) | |||||||||
3 m | 0.0341 | 0.0299* | 0.0258 | 0.0232* | 19.7553 | 16.7393* | 0.1139 | 0.0899* | |
6 m | 0.0422 | 0.0395* | 0.0319 | 0.0299* | 24.3345 | 23.3982* | 0.1436 | 0.1327* | |
9 m | 0.0459 | 0.0443* | 0.0351 | 0.0344* | 27.1057 | 27.2125 | 0.1584 | 0.1505* | |
12 m | 0.0491 | 0.0433* | 0.0381 | 0.1583 | 29.5235 | 30.4585 | 0.1727 | 0.1666* | |
RW | |||||||||
3 m | 0.0341 | 0.0316* | 0.0258 | 0.0316 | 19.7553 | 18.7100* | 0.1139 | 0.1051* | |
6 m | 0.0422 | 0.0395* | 0.0319 | 0.0296* | 24.3345 | 22.9353* | 0.1436 | 0.1333* | |
9 m | 0.0459 | 0.0443* | 0.0351 | 0.0341* | 27.1057 | 26.6482* | 0.1584 | 0.1515* | |
12 m | 0.0491 | 0.0486* | 0.0381 | 0.0380* | 29.5235 | 29.6799 | 0.1727 | 0.1686* |
Australia and New Zealand are commodity-export dependent countries. They also share some distinctive economic structures and policies comparing to other countries. In this regard, considerations should not be solely given to commodity export components, but various other factors as well. Results in our study confirmed that there is a strong and robust relationship between the exchange rate and commodity prices in Australia and New Zealand.
Secondly, evidences have indicated that the cross exchange rate between NZD and AUD can be better measured and forecasted than the direct quoted (against USD) exchange rate pairs. As illustrated in this paper, when including commodity prices as independent variables in our model, the NZD/AUD cross rate model not only outperforms other two models in almost every aspect, but also offers a remarkable forecasting ability. The commodity-price-augmented exchange model (NZD/AUD cross rate model) developed in this paper consistently outperforms a random walk at short horizons according to four evaluating methods. However, there are some evidences suggest that, in out-of-sample forecasts, the superiority of such a model does slightly deteriorate as the forecasting horizon increases.
The attributes behind our empirical results are likely to be the “Enhanced Commodity Currencies Phenomenon”, represented by the fact that both underlying currencies (NZD and AUD) are commodity currencies, and they are both subject to the “Commodity Currencies Phenomenon” discovered in recent literatures. In addition, there is a unique underlying economic relationship between these two OECD nations: close geographically, free from trade restrictions, high co-movement in financial markets, and being contributing to our findings.
Results in this paper have provided further understanding of exchange rate dynamics to commodity prices. In addition, the superior and potential exploitable forecast ability of commodity-price-augmented exchange rate forecasting model may provide important information for nations that heavily rely on primary commodity production, and wish to develop the capital market liberalization by moving towards floating exchange rate regimes. The model developed in this paper can also benefit portfolio managers in better modeling NZD/AUD cross rates, hence, making better strategic decisions on currency trading and portfolio rebalancing.
Zou, L.P., Zheng, B.L. and Li, X.M. (2017) The Commodity Price and Exchange Rate Dynamics. Theoretical Economics Letters, 7, 1770-1793. https://doi.org/10.4236/tel.2017.76120
CBA NZ Commodity Price Index (base at 01/01/1986 = 100)
The Commonwealth Bank New Zealand Commodity Price Index is based on 18 different commodities that make up over 60% of New Zealand’s total merchandise exports. The index includes: the major forestry products (logs, pulp, paper); dairy products (e.g. whole & skim milk powder, butter, cheese, and casein); other livestock products (e.g. wool, lamb, & beef, leather and skins); assorted commodities such as aluminium, fruit, fish, and crude petroleum products. The commodity weights are determined by the importance of each commodity in New Zealand’s trade, i.e. Dairy 35%, Forestry 20%, Livestock 30%, Fishery 8%, Aluminum 7%. For example, in 2010 the CBA NZ Commodity Price Index weights are based on contributions to merchandise exports in the previous year (2009). The weights for 2010 are: Wool 0.033; Beef 0.093; Lamb 0.150; Venison 0.013; Skins 0.019; Dairy 0.383; Apples 0.021; Kiwifruit 0.053; Logs 0.049; Sawn Timber 0.045; Wood Pulp 0.030; Seafood 0.065; Aluminium 0.046.
RBA Commodity Index SDR (Index of Commodity Prices)
The ICP is a Laspeyres index, which means that the index is a weighted average of recent changes in commodity prices. While the initial weight given to each commodity reflects its relative importance in total commodity export earnings in the base period, at any point in time thereafter the effective weight of each commodity in the index reflects the impact of subsequent changes in its price. However, since export values change as a result of movements in quantities exported as well as changes in prices, it is necessary to update periodically the base-period weights to reflect changes in export volumes. In addition, since the importance of individual commodities in Australia’s export values changes over time―with the weight of some commodities becoming very small while others rise in importance―it is necessary to periodically review the commodities that are included in the index. RBA staffs have recently completed such a review, with updating conducted in 2003. As a result, the following changes have been made:
・ the ICP will be re-based from 2001/02 to 2008/09;
・ crude oil will be reintroduced to the index and the whole history of the ICP back-cast accordingly; and
・ milk powder will be added and rice will be excluded from the index, back-cast to July 2008.
The updated index will include the prices of 20 of Australia’s key commodity exports, which currently account for around 85 per cent of primary commodity export earnings. The re-basing to 2008/09 and addition of crude oil have a noticeable effect on the weights of each sub-index and individual commodity; adding milk powder and excluding rice have only small effects on the ICP.
The following table shows the weights of each component in the RBA Commodity Index SDR.
USA S&P GSCI Non-Energy Spot―Price Index
The S&P GSCI is world-production weighted; the quantity of each commodity
Current index weights | Updated index weights | |||
---|---|---|---|---|
Initial 2001/02 | Effective 2008/09 | Initial 2008/09 | Effective Sep 2009 | |
Rural commodities | 29.1 | 17.1 | 10.3 | 12.5 |
Beef and veal | 7.9 | 4.1 | 3.2 | 4.1 |
Wheat | 8.3 | 5.3 | 3.2 | 2.9 |
Wool | 4.1 | 2.0 | 1.1 | 1.6 |
Milk powder | - | - | 0.8 | 1.0 |
Sugar | 2.5 | 1.6 | 0.7 | 1.5 |
Barley | 1.9 | 1.3 | 0.6 | 0.6 |
Canola | 1.0 | 0.7 | 0.4 | 0.5 |
Cotton | 2.8 | 1.5 | 0.3 | 0.4 |
Rice | 0.5 | 0.7 | - | - |
Base metals | 15.7 | 10.8 | 6.8 | 9.6 |
Aluminium | 8.1 | 3.9 | 3.4 | 4.1 |
Copper | 2.8 | 3.1 | 1.8 | 2.8 |
Lead | 0.7 | 0.8 | 0.6 | 1.2 |
Zinc | 1.5 | 0.9 | 0.6 | 1.0 |
Nickel | 2.6 | 2.0 | 0.4 | 0.6 |
Other resources | 55.3 | 72.1 | 82.9 | 77.9 |
Metallurgical coal | 14.7 | 28.1 | 23.3 | 15.9 |
Iron ore | 9.3 | 15.1 | 21.8 | 20.8 |
Thermal coal | 9.7 | 10.7 | 11.4 | 9.8 |
Gold | 9.4 | 10.0 | 10.8 | 15.1 |
LNG | 4.8 | 3.9 | 6.5 | 5.1 |
Crude oil | - | - | 5.3 | 7.3 |
Alumina | 7.4 | 4.3 | 3.8 | 3.8 |
in the index is determined by the average quantity of production in the last five years of available data. Such weighting provides the S&P GSCI with significant advantages, both as an economic indicator and as a measure of investment performance. Below is a table from Goldman Sachs shown the most recent S&P GSCI index components and weight. For more detail about this index, readers can refer to following web address: http://www2.goldmansachs.com/services/securities/products/sp-gsci-commodity-index/tables.html
S & P GSCI™ Components and Weights
Currently, 24 commodities meet the eligibility requirement for the S&P GSCI™. A list of these components and their dollar weights in the S&P GSCI™ organized by subsector, is presented in
Energy | 68.3 | Industrial | 8.57 | Precious | 3.56 | Agriculture | 15.18 | Livestock | 4.39 |
---|---|---|---|---|---|---|---|---|---|
Crude Oil | 35.65 | Metals | Metals | Wheat | 3.53 | Live Cattle | 2.57 | ||
Brent Crude Oil | 14.58 | Aluminium | 2.6 | Gold | 3.13 | Red Wheat | 0.73 | Cattle | 0.42 |
RBOB Gas | 4.3 | Copper | 3.88 | Silver | 0.42 | Corn | 3.8 | Lean Hogs | 1.4 |
Heating Oil | 4.66 | Lead | 0.49 | Soybeans | 2.29 | ||||
Gas Oil | 5.92 | Ni | 0.92 | Cotton | 1.4 | ||||
Natural Gas | 3.21 | Kel | Sugar | 2.29 | |||||
Zinc | 0.69 | Coffee | 0.85 | ||||||
Cocoa | 0.31 |
An out-of-sample forecasting example: 3-month-ahead forecast
First, as we mentioned in the in-sample forecasting section, our sample period of in-sample forecasting is the full data set from January 1986 to January 2010. However, due to the consideration of the exchange rate regime shift, we define out-of-sample forecasting period as from February 1990/March 1993 to January 2010. We set May 2002 as time “t”, we assume it is the last month of the “in-sample” period and it is 3-month before the “out-of-sample” forecasting period. Next, we derive NZD/AUD long term fair value by adopting either one of the four methods we mentioned in the paper. Here, for simplicity, we assume FVs are all known and same as the FV values estimated in the in-sample forecasting. Having the FVs, we can then generate a series of values termed “departures from NZD/AUD Fair Value” by subtract the actual NZD/AUD exchange rates from corresponding FVs. This will give us 148 observations (from February 1990 to May 2002). We then perform the following regression for the departure from NZD/AUD cross rate fair value on independent variables:
E r r o r t + k = α + β 1 ( E r r o r t + k − 1 ) + β 2 Δ ( E r r o r t + k − 1 ) + β 3 Δ ( R a l . G D P t + k − 4 N Z & A U ) + β 4 ( N Z . C o m P r t + k − 1 ) + β 5 ( ( A U . C o m P r t + k − 1 ) + ε t + k
We then use corresponding parameters from above regression model to forecast the departure value of 3 month-ahead. And the forecasted departure is added to the corresponding FV value to derive the “3 month-ahead-forecasted exchange rate”. Hence, the forecasting error at time t+3 is: F E t + 3 = S t + 3 − S t + 3 ^ , where S t + 3 represents the 3-month-ahead forecast. To do the out-of-sample forecast of further 3 month-ahead NZD/AUD exchange rate from time “t + 3”, the same process is repeated, but with 3 more set of observations added into the initial 148 observations as they become available at time “t + 3”.
Other out-of-sample forecasting in different time horizons and/or with different sample period are conducted in similar fashion with the same underlying rationales.
NZD/AUD | NZD/USD | AUD/USD | |||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
OLS Test | OLS + Break dummy | OLS Test | OLS + Break dummy | OLS Test | OLS + Break dummy | ||||||||||||||
Momentum | 0.952 | *** | 0.962 | *** | 0.965 | *** | 0.982 | *** | 0.996 | *** | 0.976 | *** | 0.987 | *** | 0.983 | *** | 0.957 | *** | |
(56.805) | (57.909) | (44.763) | (73.795) | (66.960) | (34.829) | 70.46345 | 65.06186 | 35.41659 | |||||||||||
Mean Reversion | −0.130 | ** | −0.127 | * | −0.204 | ** | −0.058 | −0.177 | ** | −0.113 | −0.075 | −0.190 | ** | −0.140 | |||||
(−2.077) | (−1.848) | (−2.364) | (−0.794) | (−2.043) | (−0.895) | −0.95738 | −2.16437 | −1.22082 | |||||||||||
Ral.GDP.NZ&AU | 0.189 | ** | 0.221 | ** | 0.365 | *** | |||||||||||||
(2.177) | (2.492) | (2.982) | |||||||||||||||||
Ral.GDP.AU&NZ | 0.373 | * | 0.303 | 0.449 | * | ||||||||||||||
(1.955) | (1.544) | (1.615) | |||||||||||||||||
Ral.GDP.NZ&US | 0.120 | 0.161 | * | 0.188 | * | ||||||||||||||
(1.304) | (1.722) | (1.615) | |||||||||||||||||
NZ Commodity Prices | −0.210 | *** | −0.208 | *** | −0.118 | −0.219 | *** | −0.289 | *** | −0.209 | ** | ||||||||
(−3.748) | (−3.312 | (−1.381) | (−3.922) | (−4.516) | (−2.257) | ||||||||||||||
AU Commodity Prices | 0.179824 | *** | −0.1846 | *** | 0.228426 | ** | −0.33262 | *** | −0.29504 | *** | −0.23721 | ** | |||||||
(3.526) | (2.782) | (2.341) | (−5.323) | (−3.879) | (−2.071) | ||||||||||||||
US Commodity Prices | 0.003 | 0.019 | 0.004 | 0.042 | 0.089 | * | 0.086 | ||||||||||||
(−0.078) | (0.416) | (0.059) | (0.982) | (1.816) | (1.288) | ||||||||||||||
Breakpoint | 2007M12 | 2000M1 | 2007M12 | 2000M1 | 2007M12 | 2000M1 | |||||||||||||
Adj.R^2 | 0.928 | 0.931 | 0.929 | 0.954 | 0.956 | 0.954 | 0.948 | 0.952 | 0.949 | ||||||||||
No. obs. | 268 | 243 | 170 | 268 | 243 | 170 | 268 | 243 | 170 | ||||||||||
Sample period | 1986M1-2010M1 |
This table reports the original OLS regression results as well as the OLS results after each breaking point is added into the regression models, where βt = 1 if t ≥ 1 Breakpoint and βt = 0 otherwise. Breakpoints are selected as the starting of the year 2000 and end of the year 2007 to reflex two of the most recent major global financial crisis. Corresponding t-statistics are reported in parentheses. No.obs is the number of observations. *, **, *** indicate 10%, 5%, 1% significant level.