Published by Canadian Center of Science and Education

## Modelling Food Price Volatility and Testing Heat Waves and/or Meteor Showers Effects: Evidence for Asia and Pacific

Fardous Alom^{1}, Bert D. Ward^{1} & Baiding Hu^{1 }

1 Department of Accounting, Economics and Finance, Lincoln Universality, New Zealand

Correspondence: Fardous Alom, Department of Accounting, Economics and Finance, PO Box 84, Lincoln Universality, New Zealand. Tel: 64-3-321-8184. E-mail: [email protected];

Received: May 28, 2012 Accepted: June 15, 2012 Online Published: September 20, 2012
doi:10.5539/ass.v8n12p1 URL: http://dx.doi.org/10.5539/ass.v8n12p1** **

**Abstract **

This paper assesses the volatility and cross country mean and volatility spillover effects of food prices within and across global and selected Asian and Pacific countries namely Australia, New Zealand, South Korea, Singapore, Hong Kong, Taiwan, India and Thailand. The principal method of analysis comprises the development of a set of component GARCH-type models of conditional variance. Volatility characteristics and spillover effects of food prices are examined across a full (1995-2010) and two subsamples (1995-2001 and 2002-2010) with daily food price indices. Main findings of the study are as follows: (1) like other asset prices, food price volatility can be modelled by CGARCH variant of GARCH-family models for world as well as country specific levels, (2) increased risk does not necessarily lead to increased returns for world and specified countries except few instances, (3) mixed evidence of cross country mean and volatility spillover effects are reported. No exact direction of spillover effects from exporter to importer or importer to exporter countries can be drawn rather mixed evidence of spillover from exporter to importer, exporter to exporter, importer to exporter and geographical proximity can be documented. The ‘meteor shower’ hypothesis that the conditional variance of the change in one market depends on the past information of other markets dominates ‘heat wave’ hypothesis that the conditional variance depends on the past information of that market while for shorter time period ‘heat wave’

effects dominate ‘meteor shower’ effects.

**Keywords:** food price, volatility, asymmetry, persistence, spillover effects, heat wave, meteor showers
**1. Introduction **

Commodity price fluctuation or volatility has attracted increasing attention in recent economic and financial literature and has been recognised as one of the more important economic phenomena (R.F. Engle, 1982). The importance of understanding commodity price movement is now well documented. For example, Pindyck(2004) pointed out that changes in commodity prices can influence the total cost of production as well as the opportunity cost of producing commodities currently rather than later. It has also been argued that price volatility reduces welfare and competition by increasing consumer search costs (Zheng, Kinnucan, & Thompson, 2008). In the same line, Apergis and Rezitis(2003b) noted down that price volatility leads both producers and consumers to uncertainty and risk and thus volatility of commodity prices has been studied to some extent.

Commodity prices in general are volatile and in particular agricultural commodity prices are renowned for their continuously volatile nature (Newbery, 1989) and also deserve much attention from policy makers. Kroner et al.

(1999) reported that commodity prices are one of the most volatile of all international prices. It has been emphasized that continuous volatility causes concern for governments, traders, producers and consumers. Large fluctuations in prices can have a destabilizing effect on the real exchange rates of countries and a prolonged volatile environment makes it difficult to extract exact price signals from the market which leads to inefficient allocation of resources and also volatility can attract speculative activities (FAO, 2007).

Historic food prices show significant ups and down as can be seen in Figures 1 and 2. A large body of studies exist to document the causes and consequences of food price booms. The recent food price spike was explained from different angles such as supply shock (ESCAP, 2008; Hossain, 2007), demand shock (OECD, 2008), oil and metal price hike (Headey & Fan, 2008; Radetzki, 2006), chronic depreciation of US dollars against major currencies (Abott, Hurt, & Tyner, 2009; Headey & Fan, 2008) and increased demand for bio-fuel (Headey & Fan,

2008; Mitchell, 2008; Rosegrant, Zhu, Msangi, & Sulser, 2008). Along with these mainstream macroeconomic factors, the index based agricultural futures market attracted much attention for being one of the factors of the food price boom (Gilbert, 2010; Robles, Torero, & von Braun, 2009). Gilbert (2010) pin-pointed that the agricultural futures market is one of the major channels through which macroeconomic and monetary factors created the 2007-08 food price rises. Food commodity price futures are also gaining popularity like other financial funds. From 2005 to 2006, the average monthly volumes of futures for wheat and maize grew by more than 60 percent and those for rice by 40 percent(Robles et al., 2009). However, till date low attention has been paid for studying food price returns in the fashion of financial assets. Therefore, it is worthwhile to investigate the financial properties of food prices under the framework of generalized autoregressive conditional heteroscedasticity (GARCH) family models.

Volatility modelling is popular in financial economics. Financial variables such as stock price, interest rate and exchange rates are being modelled frequently by using financial econometrics models especially ARCH classes of models (Blair, 2001; Dewachter, 1996; Maneschiold, 2004; Wei, 2009). Recently energy prices have also been studied using the technique of Financial Econometrics, for example, Regnier(2007) has shown that the common view regarding energy price volatility is true. That is, testing a long span of data, he has shown that energy prices are more volatile than other commodity prices. Narayan and Narayan (2007) have documented mixed evidence concerning oil price shocks’ volatility. However, only a few studies are available in the field commodity price volatility in general and food price volatility modelling in particular. Valadkhani and Mitchell (2002) studied Australia’s export price volatility by using ARCH-GARCH models and provided evidence that Australia’s export prices vary with world prices significantly. Apergis and Rezitis(2003a) examined volatility spillover effects from macroeconomic fundamentals to relative food price volatility in Greece by using GARCH models. They reported that the volatility of relative food prices shows a positive and significant impact on its own volatility in the case of Greece. In another paper (2003b) using similar GARCH models, they pointed out that agricultural input and retail food prices exert positive and significant effects on the volatility of agricultural output prices and also output prices have significant positive effects on its own volatility in Greece. Price volatility spillover effects in US catfish markets have been studied by Buguk et al. (2003). They used univariate EGARCH models to check volatility spillover and provided evidence of volatility spillovers in agricultural markets. Zheng et al. (2008) studied time varying volatility of US food consumer prices using Exponential GARCH models and news impact curves.

However, as stated before, food price volatility using daily food price indices in the fashion of financial assets is still an area in which little empirical attention has been paid. Since food prices are getting popular positions in the portfolio of fund managers of food futures and options, it appears worthwhile to devote effort to modelling food prices with extended GARCH models particularly Component GARCH (CGARCH) models in the context of world and some countries of Asia and Pacific as well. Hence, the objectives of this paper are to model and examine cross country mean and volatility spillover effects of food price returns using Component GARCH models expecting to add to the scarce literature of food price volatility study.

The next section of the paper provides an overview of food export and import scenarios of countries covered by the study; section 2 discusses the data used for our analysis; the methodology used to carry out the analysis along with empirical findings have been presented in section 3 and section 4 of the paper summarises the main results of the study and draws relevant conclusions.

*1.1 Food Export Import Scenario *

We selected 8 different countries of Asia and Pacific based on food import and export criteria. Australia, New Zealand, Thailand and India are major food exporters while South Korea, Singapore, Hong Kong and Taiwan are net food importers and there exists considerable economic integration among them. As of 2008-09, top four food export items of Australia include meat, grains, dairy products and wine. Korea, Taiwan, Singapore and Hong Kong ranked third, fifth, sixth and seventh export destination of Australia respectively for meat export. Major food exporter countries also possesses on the top list except India. New Zealand and Thailand ranked as eighteenth and twenty seventh. As cereal export destination of Australia except Hong Kong all other countries are among top twenty five countries. For dairy and poultry products also these countries are among the top export destinations of Australia. Meat, fish and dairy products are on the top of New Zealand food export items for 2009. For all these products Australia, Korea, Singapore, Taiwan, Hong Kong are among the major trade partners including Thailand and India among minor partners. Hong Kong, Singapore, Australia and Taiwan are among the major rice export partners of Thailand. Korea, Singapore, Hong Kong and Taiwan are among the top fish export partners of Thailand. India also has considerable trade relationship with these countries regarding export of food items such as dairy products, fruits, vegetables and cereals. Export import statistics of these

countries support that there is strong trade relationship of agricultural products among these countries.

Furthermore, countries considered here are also member of some regional and trade associations.

ASEAN-Australia-New Zealand free trade agreement (FTA) went into operation from 1 January 2010. An FTA between Australia and Thailand went into force in January 2005, FTA between Australia and Singapore has already been signed. A negotiation of Australia-India FTA is going on. Singapore-New Zealand and Thailand-New Zealand FTAs went into force in 2001 and 2005 respectively. An FTA between India and Thailand has been signed in 2004 (Park, 2009).

**2. Data and Their Statistical Properties **

The study uses 4000 daily observations of food producers’ price indices for world aggregate and for Australia, New Zealand, South Korea, Singapore, Hong Kong, Taiwan, India and Thailand provided by DataStream Advance for the period 2 January 1995 to 30 April 2010. Returns of food prices for every variable are computed by using standard continuously computed logarithm technique as follows where Pt is the daily price of current time t:

1

ln( ^{t} )

*t*
*t*

*R* *P*
*P*_{}

(1) Table 1 displays summary statistics for each series. Large unconditional standard deviations of each series indicate high volatility of food prices, although the unconditional standard deviations for each return series show that net food importing countries returns are more volatile than those for net food exporting countries which asserts that net food importing countries are more affected by food price changes (von Braun, 2008). For the price series, only New Zealand data show negative skewness implying the distribution has a long left tail, whereas all other series have positive skewness implying long right tails. On the other hand, the world, Australia and Korean series show negative skewness meaning long left tails while other returns series show long right tails.

The values of excess Kurtosis for all series are high (close to 3 or higher) except the price series of New Zealand, Korea and Singapore, implying that distributions are relatively peaked rather than normal. The Jarque-Bera tests reject the null hypothesis of normality at 1 and 5 percent levels of significance. In support of J-B test, we also plot theoretical Quantile-Quantile as shown in Figures 3 and 4. None of the plots exhibit good fit of the distribution of observations. The graphs show that both positive and negative large shocks create non-normal distribution of the series for both price and returns. Hence, the samples appropriately contain financial characteristics such as volatility clustering, long tails and leptokurtosis.

In addition to the above, unit root tests results are also presented in Table 1. In levels, all the food price series appear non-stationary, however, they appear stationary in first differences, implying all series are integrated of order 1, denoted I (1). This suggests using the returns for estimating the GARCH models for examining conditional volatility over the time period selected. Figures 1 and 2 show the plots of food prices and their returns. In the returns graphs, it is clearly visible that there is evidence of volatility clustering for the return series of world and for all individual countries. Figure 1 shows that since 2002 there was a sharp rises in food prices (Mitchell, 2008) of each country and therefore we divide total time period into two subsamples ranging from 1995 to 2001 and 2002 to 2010 for the purpose of estimation. By dividing into two subsamples we can distinguish whether there is any significant difference between high rise and non-high rise period of food prices.

Table 1. Statistical properties of data

**Prices **

WFP AUSFP NZFP KORFP SINFP HKFP TWNFP INFP THFP Mean 1687.3 976.713 451.26 385.757 474.174 168.941 284.359 1078.30 550.57 Median 1447.5 895.335 483.450 333.6900 418.9700 116.6500 234.6900 899.3050 561.640 Maximum 3086.8 1905.49 744.57 871.13 1007.11 625.34 695.64 2989.23 1190.86 Minimum 939.8 477.210 206.460 124.310 117.190 33.390 116.250 254.140 176.560 Std. Dev. 542.4 363.048 129.657 180.137 218.316 132.946 135.559 630.132 171.329 Skewness 0.9645 0.63647 -0.24493 0.59562 0.52627 1.46040 0.86664 0.83363 0.37046 Kurtosis 2.9207 2.31378 1.86426 2.09315 1.98832 4.45968 2.67396 2.95978 3.35085 J-B 621.29 348.547 254.978 373.571 355.224 1776.97 518.426 463.562 112.012 Prob. 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 ADFL (prob) 0.9075 0.5574 0.4467 0.5817 0.8510 0.9998 0.5963 0.9843 0.9667 ADFFD(prob) 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001

Obs. 4000 4000 4000 4000 4000 4000 4000 4000 4000

**Returns **

WFP AUSFP NZFP KORFP SINFP HKFP TWNFP INFP THFP Mean 0.00025 0.00015 -6.78E-0 0.000261 0.00012 0.00045 0.00021 0.00045 0.00017 Median 0.00063 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 Maximum 0.06805 0.10508 0.21383 0.12514 0.15767 0.15568 0.15838 0.13291 0.16875 Minimum -0.0568 -0.1138 -0.1967 -0.14811 -0.13523 -0.15054 -0.08981 -0.08622 -0.15808 Std. Dev. 0.00773 0.01230 0.01603 0.02322 0.01932 0.02093 0.02257 0.01565 0.01861 Skewness -0.424 -0.045 0.078 -0.069 0.254 0.113 0.111 0.393 0.023 Kurtosis 10.860 11.0713 23.4145 7.71010 9.48634 9.26574 5.00237 8.14859 11.8719 J-B 10415.2 10856.4 69445.3 3699.7 7053.6 6550.1 676.3 4520.2 13115.6 Prob. 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 ADFL (prob) 0.0000 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001

Obs. 3999 3999 3999 3999 3999 3999 3999 3999 3999

800 1,200 1,600 2,000 2,400 2,800 3,200

1996 1998 2000 2002 2004 2006 2008 WFOOD prices

400 800 1,200 1,600 2,000

1996 1998 2000 2002 2004 2006 2008 AUSFOOD prices

200 300 400 500 600 700 800

1996 1998 2000 2002 2004 2006 2008 NZFOOD2 prices

0 200 400 600 800 1,000

1996 1998 2000 2002 2004 2006 2008 KORFOOD prices

0 200 400 600 800 1,000 1,200

1996 1998 2000 2002 2004 2006 2008 SINFOOD prices

0 200 400 600 800

1996 1998 2000 2002 2004 2006 2008 HKFOOD prices

0 200 400 600 800

1996 1998 2000 2002 2004 2006 2008 TWNFOOD prices

0 500 1,000 1,500 2,000 2,500 3,000 3,500

1996 1998 2000 2002 2004 2006 2008 INFOOD prices

0 200 400 600 800 1,000 1,200

1996 1998 2000 2002 2004 2006 2008 THFOOD prices

Figure 1. Daily food price indices 2 January 1995 to 30 April 2010

-.08 -.04 .00 .04 .08

1996 1998 2000 2002 2004 2006 2008 Returns WFOOD prices

-.12 -.08 -.04 .00 .04 .08 .12

1996 1998 2000 2002 2004 2006 2008 Returns AUSFOOD prices

-.3 -.2 -.1 .0 .1 .2 .3

1996 1998 2000 2002 2004 2006 2008 Returns NZFOOD prices

-.20 -.15 -.10 -.05 .00 .05 .10 .15

1996 1998 2000 2002 2004 2006 2008 Returns KORFOOD prices

-.2 -.1 .0 .1 .2

1996 1998 2000 2002 2004 2006 2008 Returns SINFOOD prices

-.2 -.1 .0 .1 .2

1996 1998 2000 2002 2004 2006 2008 Returns HKFOOD prices

-.10 -.05 .00 .05 .10 .15 .20

1996 1998 2000 2002 2004 2006 2008 Returns TWNFOOD prices

-.10 -.05 .00 .05 .10 .15

1996 1998 2000 2002 2004 2006 2008 Returns INFOOD prices

-.2 -.1 .0 .1 .2

1996 1998 2000 2002 2004 2006 2008 Returns THFOOD prices

Figure 2. Daily food price returns 2 January 1995 to 30 April 2010

-1,000 0 1,000 2,000 3,000 4,000

800 1,200 1,600 2,000 2,400 2,800 3,200 Quantiles of WFOOD prices

Quantiles of Normal

WFOOD prices

-400 0 400 800 1,200 1,600 2,000 2,400

400 800 1,200 1,600 2,000 Quantiles of AUSFOOD prices

Quantiles of Normal

AUSFOOD prices

0 200 400 600 800 1,000

200 300 400 500 600 700 800 Quantiles of NZFOOD prices

Quantiles of Normal

NZFOOD prices

-400 0 400 800 1,200

0 200 400 600 800 1,000 Quantiles of KORFOOD prices

Quantiles of Normal

KORFOOD prices

-400 0 400 800 1,200 1,600

0 200 400 600 800 1,000 1,200 Quantiles of SINFOOD prices

Quantiles of Normal

SINFOOD prices

-400 -200 0 200 400 600 800

0 200 400 600 800

Quantiles of HKFOOD prices

Quantiles of Normal

HKFOOD prices

-200 0 200 400 600 800

0 200 400 600 800

Quantiles of TWNFOOD prices

Quantiles of Normal

TWNFOOD prices

-2,000 -1,000 0 1,000 2,000 3,000 4,000

0 1,000 2,000 3,000 4,000 Quantiles of INFOOD prices

Quantiles of Normal

INFOOD prices

-400 0 400 800 1,200

0 200 400 600 800 1,000 1,200 Quantiles of THFOOD prices

Quantiles of Normal

THFOOD prices

Figure 3. Theoretical quantile-quantile plot for food prices

-.03 -.02 -.01 .00 .01 .02 .03

-.08 -.04 .00 .04 .08

Quantiles of RWFOOD

Quantiles of Normal

Returns WFOOD prices

-.06 -.04 -.02 .00 .02 .04 .06

-.12 -.08 -.04 .00 .04 .08 .12 Quantiles of RAUSFOOD

Quantiles of Normal

Returns AUSFOOD prices

-.06 -.04 -.02 .00 .02 .04 .06

-.3 -.2 -.1 .0 .1 .2 .3 Quantiles of RNZFOOD

Quantiles of Normal

Returns NZFOOD prices

-.10 -.05 .00 .05 .10

-.2 -.1 .0 .1 .2

Quantiles of RKORFOOD

Quantiles of Normal

Returns KORFOOD prices

-.08 -.04 .00 .04 .08

-.2 -.1 .0 .1 .2

Quantiles of RSINFOOD

Quantiles of Normal

Returns SINFOOD prices

-.08 -.04 .00 .04 .08

-.2 -.1 .0 .1 .2

Quantiles of RHKFOOD

Quantiles of Normal

Returns HKFOOD prices

-.10 -.05 .00 .05 .10

-.10 -.05 .00 .05 .10 .15 .20 Quantiles of RTWNFOOD

Quantiles of Normal

Returns TWNFOOD prices

-.06 -.04 -.02 .00 .02 .04 .06

-.10 -.05 .00 .05 .10 .15 Quantiles of RINFOOD

Quantiles of Normal

Returns INFOOD prices

-.08 -.04 .00 .04 .08

-.2 -.1 .0 .1 .2

Quantiles of RTHFOOD

Quantiles of Normal

Returns THFOOD prices

Figure 4. Theoretical quantile-quantile plot for food price returns
**3. Methods and Empirical Results **

*3.1 Methods *

3.1.1 CGARCH Models

For modelling financial characteristics of time series data, first scholarly efforts were put forward by Engle (1982). As an aid, he developed the Autoregressive Conditional Heteroskedasticity (ARCH) model which was later generalised by Bollerslev(1986) as GARCH models. Since then ARCH/GARCH models got momentum to grow in different dimensions not only for magnitudes but also on the directions to better capture the financial characteristics of assets (Robert F. Engle, 2001). One of these extended versions of GARCH family models is the Component GARCH (CGARCH) model developed by Ding et al. (1993). We use this variant of GARCH model in this study due to its superior performance in different aspects. According to Black and McMillan (2004), the CGARCH model decomposes conditional variances into a long-run time varying trend component and a short-run transitory component, which reverts to the trend following a shock. This model has superiority in terms of capturing both long and short-run properties of time series. Christoffersen et al. (2008) mention “The component model’s superior performance is partly due to its improved ability to model the smirk and the path of spot volatility, but its most distinctive feature is its ability to model the volatility term structure.”

In component GARCH (CGARCH) models, the constant conditional variance condition of GARCH (1, 1) model is replaced with a time varying component ‘q’ to capture long-run volatility. In general the ARMA (1, 1)-CGARCH (1, 1) model may be written in the following form:

Mean equation:

1 2 1 3 1

*t* *t* *t* *t*

*R* *R*_{} *e*_{} (2)
)

, 0 (

~ _{t}

*t* *iid* *h*

Variance equations:

2

0 1 1 0 2 1 1

2

3 1 1 4 1 1

( ) ( )

( ) ( )

*t* *t* *t* *t*

*t* *t* *t* *t* *t* *t*

*q* *q* *e* *h*

*h* *q* *e* *q* *h* *q*

(3) Where

*q*

_{t}is the

*permanent*component, (

*e*

_{t}

^{2}

_{}

_{1}

### *h*

_{t}

_{}

_{1}) serves as the driving force for the time dependent movement of the

*permanent*component and (

*h*

_{t}

_{}

_{1}

### *q*

_{t}

_{}

_{1}) represents the

*transitory*component of the conditional variance. The sum of parameters

###

_{3}and

###

_{4}measures the

*transitory*shock persistence and

###

_{1}measures the long-run persistence derived from the shock to a permanent component given by

###

_{2}.

We use CGARCH models to analyse data throughout the study. In the first stage, in order to estimate food price volatility of world and country specific data we use CGARCH-M (1, 1) models in asymmetric form to assess whether volatility in mean equations becomes a factor of risk or not and to see whether shocks to volatility are asymmetric or not. To this end, the ARMA (1, 1)-CGARCH (1, 1)-in mean models to be estimated may be written in the following general form:

Mean Equation:

, 1 2 , 1 3 1 4 , ,

*i t* *i t* *t* *i t* *i t*

*R* *R* _{} *e*_{} *h* (4)
)

, 0 (

~ _{t}

*t* *iid* *h*

Variance Equation:

2

, 0 1 , 1 0 2 , 1 , 1

2 2

, 3 , 1 , 1 4 , 1 , 1 1 5 , 1 , 1

( ) ( )

( ) ( ) ( )

*i t* *i t* *i t* *i t*

*i t* *t* *i t* *i t* *i t* *i t* *t* *i t* *i t*

*q* *q* *e* *h*

*h* *q* *e* *q* *e* *q* *d* *h* *q*

(5)

Where i refers to variables from 1 to 9 representing the world and 8 individual countries,

###

_{2}and

###

_{3}measure autoregressive and moving average coefficients,

###

_{4}is the coefficient for volatility in the mean equation (measuring risk in mean return) and

###

_{4}provides a measure of asymmetry. The lag order of ARMA is set by Box-Jenkins (1976) methodology and hence the lag orders selected may differ across the series depending on the nature of data.

3.1.2 CGARCH Models for Mean and Volatility Spillover Effects

One of the objectives of this study is to examine whether past information regarding the mean return in one food market affects other markets’ current mean return or not, and similarly past information of volatility in one market affects other markets’ current volatility or not. The second portion reveals information regarding the ‘heat waves’ or ‘meteor shower’ effects of Engle et al. (1990). If the current volatility of one food market, for example Australian food market, is not influenced by past volatilities of other markets, for example New Zealand, South Korea, Singapore, Hong Kong, Taiwan, India and Thailand, we can say that volatility in Australian food market takes an independent path and this is termed as ‘heat wave’ effects. On the other hand, if current volatility of one market is influenced by any past volatility of other markets we say that volatility is interdependent or spills over from one market to another and this notion is termed ‘meteor shower’ effects. To evaluate ‘heat wave’ and

‘meteor shower’ effects following methods are followed.

In fact, as stated earlier, the models are estimated in two steps. For the first step, we model each food price return series through an ARMA-CGARCH-M model with equations 4 and 5. In the second step of estimation, in order to check mean and volatility spillover we compute standard deviation and conditional variance series from step 1 and incorporate them into appropriate mean and variance equations. More specifically, in line with the ideas of Engle et al. (1990), Baillie et al. (1993), Liu and Pan (1997), Lin and Tamvakis(2001), and Hammoudeh et al.

(2003) we include conditional standard deviations derived for each variable from the first step into the mean equations of appropriate series to check mean spill over effects and insert conditional variances into the variance equations to assess volatility spillover effects form one food market to another. In particular, the following equations for checking mean spillover effects are estimated:

Mean Equation:

, 1 2 , 1 3 , 1 4ˆ, ,

*i t* *i t* *i t* *j t* *i t*

*R* *R* _{} *e* _{} *h* (6)
)

, 0 (

~ _{t}

*t* *iid* *h*

Variance Equation:

2 2

, 0 1 , 1 0 2 , 1 , 1

2 2 2

, 3 , 1 , 1 4 , 1 , 1

( ) ( )

( ) ( )

*i t* *i t* *i t* *i t*

*i t* *t* *i t* *i t* *i t* *i t*

*q* *q* *e* *h*

*h* *q* *e* *q* *h* *q*

(7) wherei represents series 1 to 8 for 8 individual countries. In order to examine long-run volatility spillover effects we put estimated conditional variances in the permanent component of the variance equations and hence we estimate the following ARMA-CGARCH (1, 1) model:

Mean Equation:

, 1 2 , 1 3 , 1 ,

*i t* *i t* *i t* *i t*

*R* *R* _{} *e* _{} (8)
)

, 0 (

~ _{t}

*t* *iid* *h*

Variance Equation:

2 2 2

, 0 1 , 1 0 2 , 1 , 1 , 1

2 2 2

, , 3 , 1 , 1 4 , , 1

( ) ( ) ˆ

( ) ( )

*i t* *i t* *i t* *i t* *j j t*

*i t* *i t* *i t* *i t* *i t* *i t*

*q* *q* *e* *h* *h*

*h* *q* *e* *q* *h* *q*

(9) wherei represents number of return series of 8 countries, j stands for the number of computed conditional variance series for 7 countries except the one under estimation. Appropriate lag orders for ARMA were set by Box-Jenkins (1976) methods in each case and models are selected based on the lowest AIC, highest R squared and maximum log likelihood values. The parameters of each model are estimated via maximum likelihood methods. To avoid possible violations of normally distributed error term assumption, all models are estimated assuming generalised error distributions (GED).

Following Engle et al. (1990) and Baillie et al. (1993) we compute robust Wald tests from each ARMA-CGARCH model to examine mean and volatility spill over effects across different countries covered by the study.

*3.2 Empirical Results *

3.2.1 CGARCH Models of Food Price Volatility

Table 2 displays empirical results of CGARCH estimates for food price returns of world aggregate and other
countries for the full sample period starting from 1995 to 2010. Asymmetric ARMA-CGARCH-in mean models
for each series are estimated. Almost all parameters in the mean equations are statistically significant at least at
5% level of significance; GARCH in mean parameters are not statistically significant except for the New
Zealand (_{} and Korean series (_{} implying risk does not necessarily lead to increased food price returns for
many of the countries with the exceptions of New Zealand and Korea.

In Table 2, the variance equations show that almost all the parameters (_{}_{}and _{} under permanent
components are statistically significant at 1% level of significance. That means that the initial effects of a shock
to the permanent component measured by _{}are highly statistically significant in all cases. Long-run persistence
parameters (_{}) are close to unity in all cases, implying long-run persistence of shock. The half lives of shock to
decay range from 53 days to 1322 days in all cases except New Zealand where the average decaying time for a
random shock is around 9 days. It implies that the effects of shocks to volatility are highly persistent in all
countries except New Zealand. Parameters measuring asymmetry (_{} are statistically significant for all the
series except the Singapore return series, and the positive signs of coefficients in every case imply that positive
shocks reduce volatility more than negative shocks. Only in the Singapore case, food price shocks show
symmetric effects on volatility. The measures of short-run persistence parameters are significant in all cases with
few exceptions. The sum of short-run persistence parameters (_{}and _{}are less than long-run persistence
parameters in all cases, implying slower mean reversion in the long-run.

Table 2 also shows that GED parameters in all cases are less than 1 and statistically significant at the 1% level of

significance, implying possible violation of normality assumptions. However, no other indication of serious misspecification of the models as specified is suggested by Ljung-Box Q statistics (both at level and squared) and ARCH (LM) tests with 10 lags.

Table 2. Asymmetric ARMA-CGARCH (1, 1)-M estimates for full sample period (1995-2010)

Paramet ers

RWFOOD AR(1)-CGAR CH(1,1)-M

RAUSFOOD ARMA(2,1)-C GARCH(1,1)- M

RNZFOOD ARMA(2,2)-C GARCH(1,1)- M

RKORFOOD ARMA(1,1)-C GARCH(1,1)- M

RSINFOOD ARMA(1,1)-C GARCH(1,1)- M

RHKFOOD ARMA(1,1)-C GARCH(1,1)- M

RTWNFOOD ARMA(1,1)-C GARCH(1,1)- M

RINFOOD AR(1)-CGAR CH(1,1)-M

RTHFOOD ARMA(2,2)-C GARCH(1,1)- M

0.0004
(0.000140)^{a }

0.000306 (0.000195)

-3.39E-06
(1.93E-10)^{a }

-0.000215 (0.000156)

0.000103 (0.000267)

1.50E-05 (1.93E-05)

-0.000261 (0.000496)

-1.06E-05 (0.000223)

2.37E-06 (0.000146)

0.1210
(0.016270)^{a }

0.9108
(0.012593)^{a }

-1.81E-06
(1.13E-08)^{a }

-0.279152
(0.070179)^{a }

0.103598 (0.586492)

-0.296881
(0.001289)^{a }

0.712563
(0.115140)^{a }

0.020015 (0.013815)

0.726090
(0.319522)^{b }

2.9329 (3.158709)

0.032734
(0.009869)^{a }

0.000172
(5.67E-06)^{a }

0.309243
(0.069130)^{a }

-0.101459 (0.586629)

0.297995
(0.012227)^{a }

-0.731517
(0.111493)^{a }

-0.070385 (1.119215)

-0.647129
(0.109094)^{a }

-0.947582

(0.005436)^{a }

0.832407
(0.389605)^{b }

-0.130736 (0.944110)

-0.025130 (0.485223)

0.939209 (1.071056)

-0.725815
(0.319826)^{b }

0.449158

(1.424413)

0.646695
(0.108975)^{a }

-0.010076

(0.516007)

0.000052
(1.35E-05)^{a }

0.000113
(1.69E-05)^{a }

0.018069
(0.000596)^{a }

0.000615
(0.000219)^{a }

0.000569 (0.000553)

0.000460
(7.61E-05)^{a }

0.000623
(0.000137)^{a }

0.000962 (0.003040)

0.000529
(0.000216)^{b }

0.993080
(0.002866)^{a }

0.993328
(0.002212)^{a }

0.920279
(0.000132)^{a }

0.990450
(0.004689)^{a }

0.998059
(0.002287)^{a }

0.994216
(0.007069)^{a }

0.986992
(0.005053)^{a }

0.999476
(0.001838)^{a }

0.988324
(0.006066)^{a }

0.050413
(0.010649)^{a }

0.027109
(0.004485)^{a }

-0.049617
(0.000100)^{a }

0.0733937
(0.013463)^{a }

0.040307
(0.009830)^{a }

0.038030
(0.014249)^{a }

0.0555664
(0.005046)^{a }

0.031106
(0.008235)^{a }

0.060941
(0.018036)^{a }

9.62E-06 (0.02433)

0.009489 (0.026282)

0.167576
(0.000144)^{a }

0.032286 (0.028457)

0.104826
(0.029123)^{a }

0.097507
(0.031558)^{a }

0.059532
(0.007943)^{a }

0.114966
(0.029116)^{a }

0.102653
(0.039210)^{a }

0.091371
(0.026196)^{a }

0.071431
(0.035415)^{b }

0.005083
(0.000240)^{a }

0.087685
(0.040688)^{b }

-0.023629 (0.032079)

0.064319
(0.038793)^{c }

0.112666
(0.019259)^{a }

0.086922
(0.036983)^{b }

0.077961
(0.046429)^{c }

0.800633
(0.060632)^{a }

-0.244412 (0.238757)

0.511558
(0.000254)^{a }

0.684564
(0.100281)^{a }

0.762846
(0.061275)^{a }

0.660190
(0.065184)^{a }

0.524760
(0.102282)^{a }

0.651681
(0.060614)^{a }

0.598373
(0.097800)^{a }
GED 1.538

(0.044377)^{a }
1.296
(0.024543)^{a }

0.132
(0.000685)^{a }

1.176
(0.031004)^{a }

1.120
(0.026189)^{a }

0.949
(0.022551)^{a }

1.100
(0.032544)^{a }

1.012
(0.025969)^{a }

0.816
(0.021391)^{a }
L-BQ(1

0)
L-BQ^{2}(1
0)
ARCH-
LM(10)

13.542

4.1526

0.5862

21.992^{a }

4.114

0.4519

11.496

38.654^{a }

0.6427

14.115^{c }

3.772

0.6411

20.293^{a }

2.576

0.6738

12.132

2.381

0.4836

12.706

8.661

0.1938

14.828^{c }

9.797

0.023^{b }

24.549^{a }

3.747

0.9094

Note: Values in parentheses including L-BQ are standard errors, ^{a}, ^{b }and ^{c} indicate significance at 1%, 5% and
10% level respectively; Last row shows probabilities of ARCH-LM(10) tests

Table 3 reports Asymmetric ARMA-CGARCH-in mean model estimates for the sub-sample period ranging from 1995 to 2001. Coefficients of interests in the mean equations are GARCH in mean parameters, which are not all statistically significant at any level of significance except for Australia, New Zealand and Korea although for

Australia statistical significance is indicated only at 10% level.

Table 3 also reveals that for the variance equations the long-run persistence parameters for world and for all other countries are statistically significant at 1% level of significance. The average half-life of the effects of shocks on volatility is at least more than 21 days in every case, while only the New Zealand series shows very low persistence of the effect of shocks. The effect of shocks dies out rapidly (only three days) in New Zealand.

Parameters measuring asymmetry are not statistically significant for Korea, Singapore and Hong Kong indicating that price shocks have symmetric effects on volatility for the 1995-2001 period data sets. In all other cases, there is evidence of positive asymmetric effects of shocks on price volatility meaning positive shocks reduce volatility more than negative shocks. The sums of the short-run persistence parameters are smaller than the long-run persistence parameters implying slower mean reversion in the long-run for all countrys as well as for world food prices.

In each equation the GED parameters are less than 2 and statistically significant at 1% level of significance, reinforcing the possible violation of normality assumptions. However, the results for the Ljung-Box Q statistics and the ARCH-LM test statistics do not suggest any other serious misspecification of the models.

Table 3. Asymmetric CGARCH (1, 1)-M estimates for sub-sample period (1995-2001)

Parame ters

RWFOOD AR(1)-CG ARCH(1,1) -M

RAUSFOOD ARMA(1,2)-C GARCH(1,1)- M

RNZFOOD ARMA(4,4)-C GARCH(1,1)- M

RKORFOOD AR(1)-CGAR CH(1,1)-M

RSINFOOD ARMA(2,2) -CGARCH(

1,1)-M

RHKFOOD ARMA(1,1)-C GARCH(1,1)- M

RTWNFOOD ARMA(1,1)-C GARCH(1,1)- M

RINFOOD ARMA(3,3)-C GARCH(1,1)- M

RTHFOOD AR(1)-CG ARCH(1,1) -M

0.000230 (0.000205)

0.000101
(9.05E-06)^{a }

-2.90E-05
(1.22E-08)^{a }

-0.000743
(0.000197)^{a }

-0.000324 (0.000547)

9.45E-05 (0.000192)

-0.000439 (0.000850)

-0.000566
(0.000102)^{a }

-3.91E-05
(9.12E-05)^{a }

0.172637
(0.024070)^{a }

-0.844670
(0.065378)^{a }

-0.359957
(2.82E-05)^{a }

0.074794
(0.021995)^{a }

-1.037680
(0.154595)^{a }

-0.582428
(0.131847)^{a }

0.725021
(0.128326)^{a }

0.444157
(0.011352)^{a }

0.000187 (0.003031)

5.570798 (5.652416)

0.836347
(0.068688)^{a }

0.581100
(0.000229)^{a }

0.923485
(0.089571)^{a }

-0.701380
(0.122787)^{a }

0.581908
(0.131967)^{a }

-0.726391
(0.128112)^{a }

0.551049
(0.005548)^{a }

0.113783 (0.087438)

-0.044835

(0.023583)^{c }

0.433879
(0.000348)^{a }

1.035440
(0.154503)^{a }

-0.192516
(0.371536)** **

1.154287 (1.957191)

-0.243788
(0.114033)^{b }

3.908729

(2.109195)^{c }

-0.433694
(1.93E-06)^{a }

0.703599
(0.122226)^{a }

-0.360958
(0.014051)^{a }

0.359928

(2.80E-05)^{a }

0.532263 (1.424729)

-0.582800
(0.004153)^{a }

-0.581121

(0.000229)^{a }

0.184092

(0.116612)

-0.433866

(0.000348)^{a }

2.604754

(0.406640)

0.433717

(2.02E-06)^{a }

0.008615

(5.29E-06)^{a }

4.87E-05
(2.25E-05)^{b }

9.10E-05
(7.03E-06)^{a }

0.008433
(2.27E-06)^{a }

0.001475 (0.001655)

0.000573
(0.000195)^{a }

0.001313
(0.000394)^{a }

0.001072
(0.000602)^{c }

0.000444 (0.000670)

0.016057 (0.013186)

0.994497
(0.003993)^{a }

0.967077
(0.013725)^{a }

0.791722
(0.000452)^{a }

0.994431
(0.007161)^{a }

0.991238
(0.006160)^{a }

0.897906
(0.042694)^{a }

0.999396
(0.000562)^{a }

0.999055
(0.002654)^{a }

0.999692
(0.000305)^{a }

0.049005
(0.014562)^{a }

0.026263
(0.010040)^{a }

0.243943
(0.000593)^{b }

0.081277
(0.021818)^{a }

0.051512
(0.009267)^{a }

0.273424
(0.055364)^{a }

0.005159 (0.004937)

0.018910
(0.008004)^{b }

0.042864
(0.020114)^{b }