Food and Nutrition Sciences, 2013, 4, 252261 http://dx.doi.org/10.4236/fns.2013.43034 Published Online March 2013 (http://www.scirp.org/journal/fns) An Application of Wavelet Analysis to Meat Consumption Cycles Marija Banović1,2,3*, Luis Catela Nunes2, Vladan Arsenijevic4 1CIISA—Faculty of Veterinary Medicine, Technical University of Lisbon, Lisbon, Portugal; 2INOVA—Nova School of Business and Economics, Nova University of Lisbon, Lisbon, Portugal; 3MAPP—Aarhus School of Business, Aarhus University, Aarhus, Denmark; 4SIM—Faculty of Sciences, University of Lisbon, Lisbon, Portugal. Email: *admbanovic@fmv.utl.pt Received January 22nd, 2013; revised February 22nd, 2013; accepted March 4th, 2013 ABSTRACT The existence or nonexistence of changes in meat consumption cycles is critical to meat industry. If the change is exis tent, there is a need to understand what motivates the change to identify the most appropriate response. Wavelet analy sis is considered here as a promising technique that may lead to a better understanding of characteristic patterns and changes in the meat consumption cycles. Keywords: Meat Consumption Cycles; Wavelet Analysis 1. Introduction Changes in the meat consumption cycles have been the focus of much research over the last decades [14]. Even though considerable effort has been put through on stud ies examining the demand for meats the debate is still going around the factors causing these changes [58]. Whatever the explanation may be, the existence or nonexistence of changes in meat consumption cycles is of paramount importance for the meat industry in order to remain competitive in the market. If the change is ex istent, there is a need to understand what motivates this change in order to identify the most appropriate response. Accordingly, if the explanation behind the change is that consumer preferences have altered and white meat is preferred, industry needs to take action and allocate re sources to research, product development and advertising. If the change is nonexistent and changes in meat con sumption cycles can be explained by alterations in rela tive prices then the red meat industry should devote all efforts to produce alternatives that will be able to com pete with the white meats on price. Determining whether the changes in the meat consumption cycles have oc curred, what motivated them, their duration, and if they repeat over time, is critical for the future industry poli cies. Inability to detect their occurrence or nonoccurrence could come out costly for the meat industry. Wavelet analysis has already been successfully applied in a wide variety of disciplines, such as economics, fi nance, physics, and engineering [913]. This proficient approach has also been used in agriculture and food quality inspection where it can very well resolve issues of signal processing in various systems used for quality assessment of food products [14]. For example, wavelet analysis has been used to characterize the surface texture of fresh meat giving the predictive models of meat pal atability [15]. The typical approach in meat demand studies has been to employ different techniques using only timedomain, giving quite mixed results and complicating any defini tive conclusion about the existence or nonexistence of changes in the meat consumption cycles. However, im portant relations also exist in the frequency domain which cannot be adequately studied using the standard methods. For example, it is possible that consumers react to news about BSE outbreak in the shortrun, while in the long run, the consumption levels are essentially determined by their income. Or, it is possible that the effects of a certain policy may change and evolve over time, therefore af fecting the consumption cycles in different ways at dif ferent frequencies. The ability to explain the nature and detect dominant patterns in the meat consumption cycles may be one of the most important ways to understand changes in the meat sector, as it also affects other food sectors, both upstream and downstream. Understanding the patterns in the meat consumption cycles may also assist in designing policies affecting the industry and economies where meat production and processing are important economic activities. *Corresponding author. Copyright © 2013 SciRes. FNS
An Application of Wavelet Analysis to Meat Consumption Cycles 253 Using the wavelet analysis, this research provides a basis for the identification of characteristic patterns or structures in the meat consumption cycles, which are often masked in the traditional methods. Furthermore, it checks if these patterns exist in other factors (e.g., prices, income), often related to the changes in the meat con sumption cycles, and if such relations have evolved over time. For this purpose, several tools are utilized: the wavelet power spectrum, the crosswavelet spectrum, the wavelet coherence, and the wavelet phase. These tech niques show how the use of wavelet analysis may help to unravel timefrequency relationships that would other wise remain hidden. This study proceeds as follows. In Section 2, we de scribe and discuss the wavelet analysis, continuous wave let transform, wavelet tools, as well as the advantages of wavelet over Fourier transform. Section 3 presents the results of applying wavelet tools to meat consumption cycles and discuss its insights. Section 4 concludes. 2. Wavelet Analysis The wavelet transform is a powerful tool for analyzing economic timeseries data characterized by nonlinear dy namics. It allows for a variablesize view of the eco nomic timeseries data studying at the same time its time and frequency properties. Thus, the wavelet analysis en ables the researcher to separate out a timeseries into its constituent multiresolution components [9]. In this way very fine details are detected in a timeseries, as well as particular characteristics, patterns, changes, discontinui ties and selfsimilarity that are often some of the most interesting features of a timeseries. Furthermore, differ ent relationships between economic variables that can possibly be found at the disaggregate level rather than at an aggregate level may be analyzed. This section intends to provide some intuition and the necessary knowledge for the discussion of the empirical results. For more de tails about wavelet technique [13,1618]. 2.1. Continuous Wavelet Transform Wavelet analysis examines a timeseries by cutting it into small waves of different frequency which are localized in time. In particular, wavelets are obtained by shifting and scaling a specific function ψ(t), called the mother wavelet, and are defined as: , 1 s t t s (1) where the parameter τ determines the wavelet localiza tion in time, and the parameter s determines the scale or width of the wavelet. A low value of the scale parameter s results in a high frequency wavelet capable of capturing localized short cycles, and vice versa. The large scales (or in terms of frequencies, the low frequencies) corre spond to overall information of a timeseries, while small scales (high frequencies) correspond to a detailed view. Thus, high frequencies are used to isolate very fine de tails in a timeseries (i.e., changes that occur in a short run), while the low frequencies can identify coarse de tails (i.e., changes that occur in a longrun). The mother wavelet ψ(t) is simply an oscillating func tion of time that first grows and then decays and obeys two conditions. The first condition is that the function ψ(t) has a zero mean in the time domain: d0tt . (2) The second condition consists of a normalization re quirement: 2d1tt , (3) and is also known as the unit energy condition. The most commonly used mother wavelet function is the Mo rle t wavelet given by 2 0 1 M4 π, t it tee 2 , s (4) where i is the imaginary number and ω0 is the central frequency of the wavelet. In order to study timevarying frequency features, the Morlet wavelet with ω0 = 6 is an optimal choice, as it gives the best balance between time and frequency domains [11,17]. The choice of the mother wavelet will depend on the features of a timeseries that will be decomposed. Depending on the application, mother wavelet should be as similar as possible to a timeseries (or to its portion under analysis). In our case, and after series of tests with different bases, the Morlet wavelet is found to be the optimal option (choice). The continuous wavelet transform (CWT) of a timeseries x(t) with re spect to ψ(t) is given by the convolution: , ,d x Wsxt tt (5) where the asterisk * denotes the complex conjugate. As with the Fourier counterpart, it is possible to recover the original timeseries from the wavelets by using an in verse wavelet transform that integrates over all the time and frequency space. The CWT of a timeseries defined in discrete time 1, , t tN s , assuming a uniform unit time step, is obtained as: , 1 , N xt t Wsx t . (6) Computation of the CWT is usually undertaken over the whole time dimension τ and over a range of relevant scales s. In this manner a fairly good approximation of a given timeseries is obtained by using only a few dozen Copyright © 2013 SciRes. FNS
An Application of Wavelet Analysis to Meat Consumption Cycles 254 coefficients from the coarser scales which is a major ad vantage in comparison to Fourier transform. 2.2. Wavelet Tools 2.2.1. Wavelet Power Spectrum The wavelet power spectrum (WPS) is defined as 2 , x Ws , and provides a measure of local variance, as it measures the contribution of each scale, or frequency, to the timeseries variance, at each point in time. If the WPS is integrated over time, the global wavelet power spectrum (GWPS) is obtained: 2 ,d xx GWPS sWs, (7) which can be used for comparison with classical spectral methods that measure the overall contribution of each frequency to the overall timeseries variance. Thus, the wavelet power spectrum shows how the variance of a time series is changing over time. To study the relationships between two timeseries xt and yt in both frequency and time domain, one can use the crosswavelet power (XWT), the wavelet coherence (WCT), and the wavelet phase which generalize the basic univariate wavelet concepts. 2.2.2. CrossWavelet Spectrum The crosswavelet spectrum (XWT) of two timeseries xt and yt captures the covariance in the timefrequency space and is defined as * ,, xyx y WxWsWs , , where Wx and Wy are the wavelet transforms of xt and yt, respectively. The XWT gives a measure of common power between two timeseries. While the wavelet power spectrum depicts the variance of a timeseries, the cross wavelet transform of two timeseries demonstrates co variance between these timeseries in the timefrequency space. Thus, XWT shows quantified indication of the similarity of power between two timeseries. 2.2.3. Wavelet Coherence and Phase The wavelet coherence (WCT) is obtained from the cross spectrum and provides a measure of the local linear rela tion between two timeseries in the timefrequency plane. It is given by: 2 1 2 2 2 11 , , ,, xy xy SsW s Rs Ss WsSsWs , (8) where S is a smoothing operator in both time and scale. The WCT is always between 0 and 1 and may be also seen as an extension of the traditional R2 coefficient, as it gives a measure of the strength of the relationship be tween two timeseries in the timefrequency plane. It is equal to 1 when there is a perfect linear relationship be tween the two timeseries at the particular time and scale. The wavelet phase is a useful tool to characterize the phase relationship between two timeseries, i.e., their phase difference. The wavelet phase is defined as: 1 1 1 , ,tan %, xy xy SsW s s SsW s , (9) with ,π,π xy , and I and R denote the imaginary and real parts, respectively. The wavelet phase captures leadlag relationships between two timeseries in time and scale. A phase difference of zero suggests that two timeseries move together at the specified frequency, which corresponds to positive covariance. In this case, if , then two timeseries move inphase, but the timeseries y leads x; while if 0, π2 xy ,xy then x leads y. On the other hand, a phase difference of π (or −π) denotes an antiphase relationship, which corresponds to negative covariance; where if π2,0 ,π2,π xy then x is leading, and if ,π2, π xy then y is leading. 3. Wavelet Analysis and Meat Consumption Cycles Annual data for the US per capita consumption of beef, pork, poultry (including chicken and turkey consump tion), and fish, as well as beef and pork prices were ob tained from the online sources of the United States De partment of Agriculture (USDA) for the 19092008 pe riod for a total of N = 100 observations. Prices were de flated using the CPI index (base period 19821984 = 100) from the United States Bureau of Labor Statistics. For per capita GDP the online source of the Historical Sta tistics of the World Economy was used. These series are shown in Figure 1. The wavelet analysis is applied to the growth rates of these series in order to characterize their cycles. Figure 1 shows that the timeseries are more likely to exhibit different degrees of temporal stationarity (i.e., nonstationary behavior) which represents no prob lem for wavelet analysis equipped to deal with character istics of timeseries that more traditional approaches like Fourier analysis cannot handle [16]. Moreover, the length of the timeseries (N = 100 observations) is adequate to gather statistically reliable information about occurrence of long cycles. 3.1. Wavelet Power Spectrum: Identifying Patterns in the Meat Consumption Cycles Wavelet analysis allowed us to decompose each of the given timeseries as a function of frequency and time. Figure 2 shows the estimated wavelet power spectrum (WPS) for US beef, pork, poultry, and fish consumption, as well as for beef and pork prices and income per capita. The estimated WPS in Figure 2 characterize variance of the timeseries across the timefrequency plane. The black Copyright © 2013 SciRes. FNS
An Application of Wavelet Analysis to Meat Consumption Cycles Copyright © 2013 SciRes. FNS 255 Figure 1. Timeseries. contour designates the 5% significance level. The regions with high variance (or high power) are presented by red color, while the regions with low variance (or low power) are depicted by blue color. Figure 2 points to some characteristic patterns of the timeseries. The common characteristic of the analyzed timeseries is that they exhibit a greater volatility until the late 1950s, which is reflected by higher WPS (i.e., the variance of the timeseries). This is quite unlike the sec ond half of the century where volatility decreases, point ing to the beginning of the 1960s as a significant step in time when a structural change occurred. The analysis of the WPS further reveals two types of common cycles across meats: short ones with a periodic ity of 2  4 years, which characterize beef, pork, and poultry consumption; and longer cycles with a periodic ity of around 8 years for the beef and poultry consump tion. Especially interesting are the short cycles during the first half of the century when the timeseries are charac terized by greater volatility. On the other hand, the longer cycles of beef and poultry disappear after the 1950s. An important finding is that the pork consumption be haves in a rather unique manner when compared to the other meats. Pork consumption exhibits no evidence of long cycles, only short cycles with 2  4year periodicity during the 1970s. Two types of mechanism are responsi ble for this distinct behavior of pork consumption. First, the more stable and repetitive short cycles in pork con sumption point to the insensitivity of pork consumption to changes in own prices and incomes (see next two sub sections). Second, the fact that short cycles continue throughout the 1970s is particularly interesting, and this is probably influenced by changes in production practices in the US pork industry during the 1970s. In that decade the US pork industry improved breeding and husbandry practices and began trimming outside fat on retail cuts, which lowered the fat content of pork [8]. This might have led consumers to perceive pork as healthier (con taining less fat, calories and cholesterol) reflecting more stability in pork consumption. The estimated WPS of beef and pork prices differ. The pork prices display shorter cycles with 2  6 years perio dicity until the 1950s, while beef prices show rather long cycles with 2  10year periodicity around the 1940s. In come has a major peak close to the 8 year periodicity, coinciding with the long cycles and a minor peak at the 2  4year band corresponding to the shorter cycles in meat consumption found earlier. These cycles correspond to the business cycle frequencies reported in the literature (see e.g. [10]). As seen from Figures 2(e)(g) these cy cles appear only up to the mid 1950s, which is in line with the Great Moderation period found for the US economy after this time. 3.2. CrossWavelet Spectrum: Understanding Common Features in the Meat Consumption Cycles The crosswavelet power spectrum (XWT) estimate shows the common features of any two timeseries. Figure 3 demonstrates the pattern similarity in the timeseries. The black contour designates the 5% significance level. The power similarity between two timeseries is depicted by color system ranging from bluelow covariance to red high covariance. The relative phase relationship is shown as arrows with inphase (positive covariance) pointing right, and antiphase (negative covariance) pointing left. The results from Figure 3 confirm that there is a sig nificant covariance between the different timeseries at the shorter and longer cycles identified during the first half of the century. In particular, the XWT of beef and poultry consumption suggests a large interdependence between these two timeseries at 2  4year cycles from the early 1920s until the late 1950s, as well as in the 6  12year cycles from the early 1930s until the late 1950s. However, the XWT of pork and poultry consumption exhibits highly significant areas of interdependence from the 1920s to the late 1970s. Interestingly, poultry and fish consumption show a large area of common power but in
An Application of Wavelet Analysis to Meat Consumption Cycles 256 Figure 2. Estimated wavelet power spectra (WPS) of timeseries growth rates. The xaxis represents time in years, while the yaxis shows period in years. The black contour designates the 5% significance level. The regions with high variance (or high power) are presented by red color, while the regions with low variance (or low power) are depicted by blue color. the 2  16year band during the late 1920s until the 1960s. Pork and fish consumption exhibit quite a similar pattern. Figure 3(j) presents the relationship between income and different types of meat and fish consumption where the late 1950s and the beginning of 1960s has again been confirmed as a turningpoint in meat consumption time series, when significant changes occurred. The estimated XWT shows higher sensitivity of meat consumption to income changes until the late 1950s, shown by joint power both at low and high scales. A similar pattern has been observed for the relationship between beef con sumption and own prices. Nevertheless, the pork con sumption exhibits less sensitivity to own price, after the late 1950s. A similar pattern occurs in the association between income and fish consumption. Since the relationship be tween income and meat consumption, as well as income and fish consumption, is mainly in positive covariance across all scales, it can be confirmed increased sensitivity of meat and fish consumption to changes in income. This is also evident even outside the cone of influence, point ing to important links between income and meat con sumption even after the decade of 2000s. Since the XWT exposes regions with common features (high common power) between two timeseries, but does not explain their local crosscorrelation, i.e., their strength of relationship, we further analyze wavelet coherence and phase. 3.3. Wavelet Coherence and Phase: Unraveling Strength of Factors Influencing the Meat Consumption Cycles The crosswavelet coherence (WCT) checks for a sig nificant correlation between different timeseries. Figure 4 displays the WCT estimates of the crosscorrelation between the different timeseries as a function of cycle Copyright © 2013 SciRes. FNS
An Application of Wavelet Analysis to Meat Consumption Cycles 257 Figure 3. Estimated crosswavelet transforms (XWT) of the timeseries growth rates. The xaxis represents time in years, while the yaxis shows period in years. The black contour designates the 5% significance level. The power similarity between two timeseries is depicted by color system ranging from bluelow covariance to redhigh covariance. The relative phase rela tionship is shown as arrows with inphase (positive covariance) pointing right, and antiphase (negative covariance) pointing left. Copyright © 2013 SciRes. FNS
An Application of Wavelet Analysis to Meat Consumption Cycles 258 Figure 4. Estimated wavelet coherences (WCT) of timeseries growth rates. The xaxis represents time in years, while the yaxis shows period in years. The black contour designates the 5% significance level. The strength of relationship between two timeseries is explained by a color system ranging from bluelow coherency to redhigh coherency. The mutual interac tion of timeseries is shown by arrows. Arrows pointing to the right mean that the timeseries are inphase, while arrows pointing to the left mean that the timeseries are in antiphase. Copyright © 2013 SciRes. FNS
An Application of Wavelet Analysis to Meat Consumption Cycles Copyright © 2013 SciRes. FNS 259 periodicity and time, showing their relationship strength and mutual interaction. The black contour designates the 5% significance level. The strength of relationship be tween two timeseries is explained by a color system ranging from bluelow coherency to redhigh coherency. The mutual interaction (or locally phase locked behavior) among timeseries is shown by arrows. Arrows pointing to the right mean that the timeseries are inphase, while arrows pointing to the left mean that the timeseries are in antiphase. When two timeseries are inphase arrows pointing right and up mean that first timeseries lags be hind second timeseries, while to the right and down first one leads second one. On the other hand, when two timeseries are in antiphase arrows pointing left and up show that first timeseries leads second timeseries, and left and down indicate that first one lags behind second one. Figure 4 exposes several ranges of significant coher ence (dependence) between the different timeseries. The correlation between beef and poultry consumption is very strong and significant from the beginning of the century until the late 1950s in the 16  20year band, during the 1980s in the 8 year band and in the 1990s around 3year band. For the longer periods and until the 1980s poultry is led by beef, but in the 1990s poultry starts replacing beef. This change in the way meat consumption is dis tributed across beef and poultry signalize the occurrence of shifts in consumer preferences. This finding coincides with the increased consumers’ awareness with health, safety, and nutritional issues during the 1980s and 1990s, when US consumers started to see beef as less desirable than poultry in terms of fat, cholesterol, calorie content, artificial ingredients, convenience characteristics, store display, and price (too expensive) [2,4,19]. Figure 4(m) reveals a strong dependence of beef con sumption to changes in pork price, especially around 10 year band. These timeseries mutually interact in a way that beef consumption is actually influenced by pork prices. Moreover, Figure 4(n) demonstrates dependence of beef prices to changes in pork consumption in the 8 year band, when pork consumption during the 1980s and 1990s leads beef prices. Figure 4(o) also shows that beef and pork prices are highly interrelated and negatively correlated. A strong interrelationship between beef and fish con sumption is also observed in Figure 4(d), which is espe cially evident for the large cycle periodicity of 30 years. It seems that fish in the long run might evolve from being an unimportant commodity to a good that will be an im portant future protein opponent to meat. In fact, Wohl genant [19] pointed out that during the mid 1970s, the relationship between beef and fish changed from one of substitutability to one of complementarity. Nevertheless, our results demonstrate that this relationship has been prolonged to the end of 2000s. The relationship between pork and poultry consump tion, Figure 4(c), is very synchronous (inphase) around the 16year band and for all time periods, demonstrating similar movement of their consumption cycles. The sec tors outside the cone of influence and above the 5% sig nificance level are not a reliable indicator of correlation, however, the significant area of is so large that it is very unlikely to be simply by chance, revealing again substi tution between these two meats. Figure 4(e) shows that the coherence of pork and fish consumption is very sig nificant for a periodicity of 8 years at the beginning of the century and until the 1950s, as well as in the 3  4 year periodicity during the 1970s. These two series are negatively correlated (in antiphase), where fish con sumption lags behind pork consumption. However, the behavior of these two timeseries changes completely during the late 1990s and 2000s, exhibiting a synchro nized pattern. This suggests that unlike the period until the 1980s, when fish and pork consumption alternate, sub stituting one another, during the 1990s and 2000s they tend to fluctuate in a similar manner. These are signifi cant results that again point to the exceptional behavior of pork consumption cycles, which may be related to the fact that in the 1990s pork contained more lean and less fat due to the new production practices, in which the US pork industry actually capitalized by promoting pork as a light and nutritious alternative to poultry—“Pork: The Other White Meat” [8]. Comparing the results for the relationship between meat and fish consumption and in come (Figures 3 and 4), we see that the larger areas stand out as being significant, showing a positive (in phase) relationship between the aforementioned time series, suggesting that meat and fish consumption ac company changes in income. The beef, pork, and poultry consumption cycles with periodicities around 20 years are strongly correlated with income cycles. In Figure 4 the regions of higher coherence at lower to medium scales may point to what is perhaps the most interesting element of change regarding the relationship between income and meat consumption (beef and poul try). While income and beef consumption, as well as in come and poultry consumption, show high mutual de pendence at medium to high scales and for most of the period, the relationship between income and pork con sumption is more concentrated at higher scales. The in creased sensitivity of beef and poultry consumption to changes in income, and decreased sensitivity of pork consumption to income again points to uniqueness of pork consumption cycles. The US pork industry has man aged to tackle the challenge of meeting the consumer demands regarding pork that seems to be an entirely dif ferent product in the eyes of the consumers [8]. Unlike the association between income and meat con
An Application of Wavelet Analysis to Meat Consumption Cycles 260 sumption, the relationship between income and fish con sumption accounts for much smaller regions of coher ence mostly at medium scales. This occurs during the decade of the 1970s until the late 1980s, when the rela tionship between fish consumption and income displays a strong crosscorrelation that points to fish becoming an important protein source at par with meat. Our results show that meat consumption timeseries can significantly alter both in time and frequency and that wavelet tools are good indicators of these alterations. The finding that the beginning of 1960s represents an important turning point in the evolution of US meat con sumption cycles, and that this significant structural change was not completed until the decade of the 2000s, is a rather important contribution to the research on meat consumption cycles. Moreover, the wavelet analysis un dertaken here demonstrates not only changes of the meat consumption cycles in time, but also in frequency. The findings of the different meat consumption patterns is also particularly interesting, especially pork consumption cycles that exhibit more stability at the shorter cycles, showing no evidence of long cycles, and thus pointing to the fact that the pork consumption is less sensitive to external shocks. 4. Conclusions This paper has used wavelet analysis to understand char acteristic features, patterns and changes in the meat con sumption cycles for the United States data. The real world data, such as meat consumption timeseries, often have complex dynamics that dominate their behavior. Wavelet analysis has the potential to deal with nonsta tionary data, while most econometric methods assume stationarity, which may or may not be apparent in eco nomic data. Furthermore, wavelets ability to separate out the dynamics in a timeseries over a different time hori zons, can reveal interesting insights into cycles at differ ent time scales. Besides common analysis in the time domain that can be done using other techniques, wavelet analysis can also capture the hidden information on con sumption cycles in the frequency domain, where the evolution of the wavelet transform from one scale to an other is easy to follow and reconstruct, isolating very fine details or changes that occur in a shortrun (using high frequencies), and very large details or changes that occur in a longrun (using low frequencies). By applying the wavelet approach, we have shown its potential in exam ining meat consumption cycles, as well as interactions between different timeseries, representing them in a timefrequency plane where features and patterns (we could not otherwise see) can be observed in an analytical way. The US meat industry has been a major force in US agriculture and is currently undergoing significant change. In order to be able to respond to consumer demand and adapt production patterns and practices it is important to capture any systematic pattern that eventually occurs in the meat consumption cycles, especially at coarse scales which determine global trends, as they influence global environment. Our analysis has demonstrated significant structural change in meat consumption cycles initiated in the 1960s and not completed until the decade of the 2000s, patterns of two types of prevailing cycles: longer with 8year periodicity and shorter with 2  4year perio dicity characterized by greater volatility. Moreover, we have shown that pork consumption exhibit more stability at the shorter cycles, showing no evidence of long cycles. Facing changes in the meat sector the identification and understanding of the specificities of these global trends could help the meat industry to make this information useful and effective. Moreover, found patterns occurring in the short time at fine scales that do not affect overall run are also of concern as they give the information on the shocks that occurred and might occur in the shortrun. Not only do identified patterns describe meat consump tion cycles, but they also encompass the overall dynam ics and the short and longrun effects of income and prices along years that might lead to unexpected trends and (rather) local instability. In other words, wavelet analysis besides identifying patterns in the meat con sumption cycles can help us to conclude if these patterns exist in other factors, like prices and income, and if such relations evolve over time. Through simple observation of the wavelet estimates it has found a mutual interaction and similar patterns between beef consumption and pork price, especially with 10year periodicity. On the other hand, it has been demonstrated that pork consumption leads beef prices with the 8year periodicity. The capac ity of demystifying the nature and detecting the dominant features and patterns in the meat consumption cycles is significant for understanding of changes in the meat sec tor. This may assist in designing policies affecting the other food sectors, as well as industry and economies where meat production and processing are important economic activities. The insights from wavelet analysis on meat consump tion cycles may come handy for further improvements of the existent models currently used in the analyses of meat demand. Generally, this will involve complementing these models with the frequency dimension which can point to the underlying patterns in meat consumption which can not be seen otherwise. What would be especially perti nent, and what is generally missing in demand models, as well as in our analysis, are variables describing product attributes and consumer characteristics that may influ ence the meat consumption cycles. The identification of these additional variables, other than prices and income, could further contribute to a better understanding of Copyright © 2013 SciRes. FNS
An Application of Wavelet Analysis to Meat Consumption Cycles Copyright © 2013 SciRes. FNS 261 changes in the meat consumption cycles and factors be hind these alterations. This challenging task could further enable more appropriate industry responses to shifts in consumer preferences. Thereby, if these latter are exis tent and point toward higher dietary and health con sciousness then meat industry could allocate appropriate resources to research, product development and adver tising. On the other hand, if the shifts in consumer pref erences are nonexistent and changes in meat consump tion can be explained only by alterations in prices and income then the industry could concentrate to producing more competitive alternatives. 5. Acknowledgements M. Banović is supported by Fundação para a Ciência e a Tecnologia through grant SFRH/BPD/63067/2009. REFERENCES [1] J. Chavas, “Structural Change in the Demand for Meat,” American Journal of Agricultural Economics, Vol. 65, No. 1, 1983, pp. 148153. doi:10.2307/1240351 [2] G. Moschini and D. Meilke, “Parameter Stability and the US Demand for Beef,” Western Journal of Agricultural Economics, Vol. 9, No. 2, 1984, pp. 271282. [3] B. Goodwin, “Multivariate Gradual Switching Systems and the Stability of US Meat Demands: A Bayesian Ana lysis,” Structural Change and Economic Dynamics, Vol. 3 No. 1, 1992, pp. 155166. doi:10.1016/0954349X(92)900322 [4] E. W. Anderson and S. M. Shugan, “Repositioning for Changing Preferences—The Case of Beef versus Poul try,” Journal of Consumer Research, Vol. 18, No. 2, 1991, pp. 219232. doi:10.1086/209254 [5] J. Eales and L. Unnevehr, “Demand for Beef and Chicken Products: Separability and Structural Change,” American Journal of Agricultural Economics, Vol. 70, No. 3, 1988, pp. 521532. doi:10.2307/1241490 [6] R. Robenstein and W. Thurman, “Health Risk and the Demand for Red Meat: Evidence from Futures Markets,” Review of Agricultural Economics, Vol. 18, No. 4, 1996, pp. 629641. [7] G. Tonsor and N. Olynk, “Impacts of Animal WellBeing and Welfare Media on Meat Demand,” Journal of Agri cultural Economics, Vol. 62, No. 1, 2010, pp. 5972. doi:10.1111/j.14779552.2010.00266.x [8] A. Resurreccion, “Sensory Aspects of Consumer Choices for Meat and Meat Products,” Meat Science, Vol. 66, No. 1, 2001, pp. 1120. doi:10.1016/S03091740(03)000214 [9] P. Crowley, “A Guide to Wavelets for Economists,” Jour nal of Economic Surveys, Vol. 21, No. 2, 2007, pp. 207 267. doi:10.1111/j.14676419.2006.00502.x [10] A. Rua and L. Nunes, “International Comovement of Stock Market Returns: A Wavelet Analysis,” Journal of Em pirical Finance, Vol. 16, No. 4, 2001, pp. 632639. doi:10.1016/j.jempfin.2009.02.002 [11] A. Grinsted, J. Moore and S. Jevrejeva, “Application of the Cross Wavelet Transform and Wavelet Coherence to Geophysical Time Series,” Nonlinear Processes in Geo physics, Vol. 11, No. 5/6, 2004, pp. 561566. doi:10.5194/npg115612004 [12] V. Arsenijevic, “A New Insight into the Classification of Type Ia Supernovae,” Monthly Notices of the Royal As tronomical Society (MNRAS), Vol. 414, No. 2, 2011, pp. 16171624. doi:10.1111/j.13652966.2011.18493.x [13] V. Arsenijevic, S. Fabbro, A. M. Mourão and A. J. Rica da Silva, “Diversity of Supernovae Ia Determined Using Equivalent Widths of Si II 4000,” Astronomy & Astro physics, Vol. 492, No. 2, 2008, pp. 535544. doi:10.1051/00046361:200810675 [14] C. B. Singh, R. Choudhary, D. S. Jayas and J. Paliwal, “Wavelet Analysis of Signals in Agriculture and Food Quality Inspection,” Food and Bioprocess Technology, Vol. 3, No. 1, 2010, pp. 212. doi:10.1007/s1194700800937 [15] P. Jackman, D.W. Sun and P. Allen, “Comparison of Various Wavelet Texture Features to Predict Beef Palat ability,” Meat Science, Vol. 83, No. 1, 2009, pp. 8287. doi:10.1016/j.meatsci.2009.04.003 [16] I. Daubechies, “Ten Lectures on Wavelets,” 9th Edition, Society for Industrial and Applied Mathemathics, Phila delphia, 1992. doi:10.1137/1.9781611970104 [17] C. Torrence and G. Compo, “A Practical Guide to Wave let Analysis,” Bulletin of the American Meterological So ciety, Vol. 79, No. 1, 1998, pp. 6178. doi:10.1175/15200477(1998)079<0061:APGTWA>2.0. CO;2 [18] C. Torrence and P. Webster, “The Annual Cycle of Per sistence in the El NiñoSouthern Oscillation,” Quarterly Journal of the Royal Meteorological Society, Vol. 124, No. 550, 1998, pp. 19852004. doi:10.1002/qj.49712455010 [19] M. Wohlgenant, “Estimating Cross Elasticities of De mand for Beef,” Western Journal of Agricultural Eco nomics, Vol. 10, No. 2, 1985, pp. 322329.
