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Ski areas, weather and climate: Time series models for New Ski areas, weather and climate: Time series models for New

England case studies England case studies

Lawrence C. Hamilton

University of New Hampshire

, [email protected]

Cliff Brown

This is the pre-/peer reviewed version of the following article: Hamilton, L.C., Brown, C., Keim, B.D. Ski areas, weather

and climate: Time series models for New England case studies. (2007) International Journal of Climatology, 27 (15),

pp. 2113-2124, which has been published in ?nal form at https://dx.doi.org/10.1002/joc.1502. This article may be

used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.

Recommended Citation Recommended Citation

Hamilton, L.C., Brown, C., Keim, B.D. Ski areas, weather and climate: Time series models for New England

case studies. (2007) International Journal of Climatology, 27 (15), pp. 2113-2124.

This Article is brought to you for free and open access by the Sociology at University of New Hampshire Scholars'

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Lawrence C. Hamilton

Sociology Department

University of New Hampshire

Cliff Brown

Sociology Department

University of New Hampshire

Barry D. Keim

Department of Geography and Anthropology

Louisiana State University

ABSTRACT

models that predict day-to-day variations in skier attendance from a combination of mountain

and urban weather, snow cover and cyclical factors. They explain half to two-thirds of the

variation in these highly erratic series, with no residual autocorrelation. Substantively, model

results confirm the “backyard hypothesis” that urban snow conditions significantly affect skier

activity; quantify these effects alongside those of mountain snow and weather; show that

previous-day conditions provide a practical time window; find no monthly effects net of weather;

and underline the importance of a handful of high-attendance days in making or breaking the

season. Viewed in the larger context of climate change, our findings suggest caution regarding

the efficacy of artificial snowmaking as an adaptive strategy, and of smoothed yearly summaries

to characterize the timing-sensitive impacts of weather (and hence, high-variance climate change)

winter-recreation areas often saw departures from their historical climates. In some mountain

and northern regions snow cover was lighter, arrived later in fall, or left earlier in spring; it

became more restricted to higher elevations or latitudes; it more often confronted warm spells,

snow drought or rain (e.g., Huntington et al. 2004; Laternser and Schneebeli 2003; Mote et al.

2005; Nolan and Day 2006; Scherrer et al. 2004). Global climate models suggest that greater

changes lie ahead, driven by greenhouse gas buildup (e.g., IPCC 2001). Regional modeling

applications explore impacts of climate change for particular winter-recreation areas (e.g.

Elsasser and Bürki 2002; Scott forthcoming). The growing literature on this topic includes both

retrospective studies analyzing impacts of recent observed change, and prospective studies

exploring implications of future warming. Studies of both types often take a regional view,

because the geography of climate change and winter tourism vary on fine scales. Specific winter-

tourism regions of interest have included Eastern North America (Scott et al. 2006a), the Great

Lakes (McBoyle and Wall 1992), New England (Scott 2006), New Hampshire (Palm 2001;

Hamilton et al. 2003a), Vermont (Badke 1991), Ontario (Scott et al. 2003), Quebec (Scott et al.

2006b), the European Alps (OECD 2007), Switzerland (Beniston et al. 2003a, 2003b; Elsasser

and Messerli 2001; Koenig and Abegg 1997), Austria (Breiling and Charamaza 1999; Hantel

2000), Australia (Galloway 1988; Koenig 1999) and Japan (Fukushima et al. 2002).

indirect impacts ripple as well. Ski areas in marginal snow areas become stressed first, and many

have in fact gone out of business (NELSAP 2006; Hamilton et al. 2003a). Others survive

through escalating investments in snowmaking, which raise the cost of staying in business—and

of skiing. Future prosperity for downhill ski areas will depend on more snowmaking, although

other snow sports such as cross-country skiing and snowmobiling might not have this option

(Scott 2006; Scott et al. 2006a). In recent years, many ski areas have diversified into real estate

and year-round recreation, to supplement their snow-season income. If snow-season income

declines, other seasons could expand to make up business, but the goals of year-round revenue

and employment, and a driver for real estate values, both are challenged. Scott and McBoyle

(2006) analyze such diversification strategies and constraints as part of their comprehensive

climate change, make this topic particularly appropriate for interdisciplinary analyses of

snow falling yesterday, or the day before that? How consequential is snow in the nearest major

city, compared with snow on the ski slopes themselves? Ski areas experience great variations in

business from one day to the next, as weekend and holiday cycles interact with unpredictable

weather at different locations. Daily resolution could also become more important if, as some

models predict and recent observations suggest, climate change involves shifts not just in means

but in variances, affecting the probabilities of extreme events such as winter thaws, droughts or

rain. Like annual data, daily data allow us to use time as an integrating dimension across social

and natural-science domains. Daily data, however, contain far more observations, hence more

information or degrees of freedom—new power for hypotheses tests and effect estimation within

dynamic multivariate models. The forecasting capabilities of mulivariate daily models could

prove to have practical applications as well.

We present two case studies below, exploring the feasibility of this general approach. Time

series models are constructed for daily attendance at two New Hampshire ski areas. The highly

erratic-appearing fluctuations in daily ski-area attendance, through multiple seasons, prove to be

reasonably well predicted from weekly cycles overlaid by irregular snow-cover and weather

effects. Because snow and weather follow deeper trends in climate, such work also has

implications for understanding the potential future consequences of climate change

Our southern site, Gunstock Mountain Resort, is situated below mid-latitude near Lake

Winnipesaukee. Both resorts developed during the Great Depression of the 1930s, when large

government programs such as the Civilian Conservation Corps and the Works Progress

Administration employed thousands in support of new forest, conservation and development

initiatives. In New Hampshire, these efforts included the construction of ski trails and resort

infrastructure that provided a template for the industry’s subsequent growth (Gunstock Mountain

Resort 2006; New England Ski Museum 2006). Although they are comparable in size and

origins, our sites differ in their topography, elevation, average annual snowfall and proximity to

metropolitan markets.

is quite accessible, although it is more distant from Boston (about 140 miles or 225 kilometers)

and other cities than ski areas located in the lower half of the state. Cannon has 55 trails and nine

lifts, a base elevation of 2000 feet (610 meters), and a vertical drop of 2146 feet (654 meters).

The resort reports an average of 156 inches (396 centimeters) of snowfall each year. Operated by

the New Hampshire Division of Parks and Recreation, the site is also home to the New England

Ski Museum (Cannon Mountain 2006; New England Ski Guide 2006; New England Ski Museum

2006; Ski NH 2006a).

Gunstock Mountain Resort, our southern site, is located in the town of Guilford and dates to

1935. It was created with help from the Works Progress Administration and is owned by

Belknap County. Gunstock is about 100 miles (161 kilometers) from Boston. It offers 51 trails,

seven lifts, a base elevation of 900 feet (274 meters), and a vertical drop of 1400 feet (427

meters). Gunstock reports receiving an average of 100 inches (254 centimeters) of snowfall

annually. In keeping with industry-wide trends, both areas have extensive snowmaking

capability and offer year-round activities including camping, summer sports, and day camps for

children (Gunstock Mountain Resort 2006; New England Ski Guide 2006; Ski NH 2006a).

With the assistance of resort personnel, we were able to obtain records of daily attendance

Weather and snow-condition indicators include daily snowfall, snowdepth and temperature for

Boston, Massachusetts, and Lakeport and Bethlehem, New Hampshire. These sites were selected

based on geography, and for data completeness and quality. The underlying dataset comes from

Climatological Data—New England, published monthly by the National Climatic Data Center,

and was provided in digital form by the Southern Regional Climate Center at Louisiana State

University. The nuances involved in the collection of snowfall and snowdepth data are fully

recognized (Doesken and Judson 1997). We view the Lakeport and Bethlehem weather-station

records as imperfect but demonstrably useful proxies for snowfall, snowdepth and temperature

conditions at the Gunstock and Cannon ski areas, respectively. Similarly, Boston provides a very

rough indicator of conditions in the urban and suburban regions of southern New Hampshire and

more accurate predictions, enhancing the models’ practical value.

as well, but these complicated the models without significant improvements in fit, and were

subsequently set aside.

Searching for predictability behind day-to-day fluctuations in ski-area attendance, we estimated

ARMAX models (autoregressive moving-average models with exogenous variables). The

exogenous variables in this case are cyclical factors and present or lagged values of daily

weather/snow indicators. The disturbances, standing for “everything else” that affects daily ski-

area attendance, were modeled explicitly through autoregressive (AR) and/or moving-average

(MA) terms, plus uncorrelated white-noise errors. AR terms reflect the influence on the

disturbance of past disturbances (or equivalently, of past values of the dependent variable). MA

terms reflect the influence of past random errors. Parameter estimation involves an iterative

maximum-likelihood procedure using the Kalman filter (Harvey 1989; Hamilton 1994). Robust

standard errors and hypothesis tests for individual coefficients, not requiring the usual (but

unrealistic) assumption of homoskedasticity, were obtained via “sandwich” variance estimates

(Huber 1967; White 1980, 1982; Royall 1986). Robust standard errors tend to be larger than the

usual standard errors, so in this sense our hypothesis tests are more conservative.

Substantial exploratory work informed the modeling process. We show results below from two

independent datasets—which should be straightforward.

Some key findings have been visualized in displays influenced by Edward Tufte’s call (1990,

1997, 2001) for designing clear, information-rich graphics that allow viewers to draw their own

comparisons and examine details of relationships between variables. All graphical, database and

modeling work was conducted with Stata (Stata 2005a, 2005b; Mitchell 2004; for an overview

see Hamilton 2006).

the ski season against the cumulative percentage of days. A consistent pattern appears: at both

importance of just a handful of good days each season. These critical days usually include the

post-Christmas and February school vacations, but weather can depress those periods or elevate

others.

To characterize the patterns behind good and bad days, we begin with “full” models predicting

daily attendance across seven or nine seasons (roughly 870 or 1,030 days), based on:

(1) daily snowdepth, snowfall and temperature recorded at a “mountain” weather station not far

from the ski area;

(2) daily snowdepth, snowfall and temperature recorded in the city of Boston, the nearest major

metropolitan area (about 161 kilometers from Gunstock, and 225 from Cannon);

effects proved nonsignificant, however, after controlling for weather and snow conditions.

Unlike weekend cycles, the seasonal cycles appear mainly climate-driven.

The time structure of weather effects on skier activity was not known in advance. For example,

how is skier activity today affected by snow falling today? Or by snow falling yesterday, or the

day before that? In the full models we covered these possibilities by including weather

conditions from the same day (lag 0), previous day (lag 1), and two days previous (lag 2), for all

six “mountain” and “city” weather indicators. Through experiments, we determined that

disturbances in the full models were best specified as regular and multiplicative “seasonal”

(weekly, not yearly) first-order autoregressive and moving average processes:

ARIMA(1,0,1)×(1,0,1)

. Residuals from both full models, tested up to lag 24, do not differ

significantly from white noise. Squared correlations between observed and predicted values

equal .67 for Gunstock and .55 for Cannon. Individual full-model regression coefficients on the

weather variables appear unstable (high standard errors) and difficult to interpret, due to

multicollinearity among closely-related lagged values such as yesterday’s and today’s snowdepth.

most snowy and highest-attendance in Figure 5. Conversely, the warm winter of 1999–00 was

among the least snowy and lowest-attendance. Within each season, moreover, days with less

snow often also are warmer, which can complicate snowmaking when it is needed the most.

Skiers individually might adapt to weather by waiting until poor conditions improve, or by skiing

more frequently once conditions become good. But such behavioral flexibility evidently is not

enough to overcome the impact of low-snow winters, as seen in Figure 5. We saw no large-scale

pattern of skiers adapting to a poor start of the season by increasing their attendance later on. At

both Cannon and Gunstock, total early-season (November through January) attendance exhibited

a weak positive correlation with late-season (February through April) attendance, instead of the

negative correlation one might expect if many skiers were compensating within seasons. Daily

autocorrelations appear predominantly positive or zero, as well.

Figure 5, like the modeling results in Table I, confirms that skier activity still depends upon

weather. Snowdepth in the mountains matters, controlling for temperature (noteworthy because

low temperatures permit artificial snowmaking). Moreover, both snowdepth and snowfall in the

city matter, although they do not necessarily reflect snow conditions in the mountains. If this

backyard effect reflects ignorance, then education is the cure—skiers could be persuaded that

by an average of 0.08EC/decade over the past century, a trend that steepens to 0.25EC/decade in

the past three decades, and becomes even more pronounced, 0.70EC/decade, if we focus

specifically on winters. The Northeast’s observed winter warming has been accompanied by

decreases in snowfall amounts, snowpack depth, and ratio of snow to total precipitation (Hayoe

et al. 2006). Both the observed trends and the consensus of nine atmosphere-ocean general

circulation models (AOGCMs) support a conclusion that “the impacts of climate change are

already being experienced across the NE” (Hayoe et al. 2006).

Earlier studies noted similar warming trends in New England (NERA 2001) and New Hampshire

(Hamilton et al. 2003a) specifically. Over the period of historical records from 1896 through

(Hayoe et al. 2006, in review; also see NECIA 2006) and also to the more general rise in global

Looking forward, the New England Regional Assessment report (NERA 2001) described results

from two AOGCMs that project rises of 3 to 7EC in minimum winter temperature over 21st

century, assuming that greenhouse gas concentrations rise by 1% of current levels per year.

Regional models also project decreasing winter snow depth in the 21st century, including the

particular locations of our two case-study ski areas (Scott, personal communication). Hayoe et

al. (2006, in review) note that, although an ensemble of eight current AOGCMS generally do

well in modeling historical Northeastern US temperature trends, none succeed in reproducing the

rapid 0.7EC/decade increase in winter temperatures observed over 1970–2000. This difficulty

might reflect their limitations in modeling regional snow cover. The (possibly conservative)

Nearly three decades ago, as global warming began its not-yet-recognized takeoff, Dunlap and

Catton (1979:243) described the emergence of environmental sociology, which asserted that

“physical environments can influence (and in turn be influenced by) human societies and

behavior.” The development signaled, in principle, a rejection of the idea that researchers can

explain social facts only in terms of other social facts. Perhaps most of us now agree, but in

practice the goal of integrating environmental indicators as variables in social research has not

been simple. Much environmental sociology remains focused within the social domain, making

progress in research on environment-related policies, movements, attitudes or behavior.

Environmental conditions themselves then appear indirectly, as background concerns or objects

of social construction, instead of direct measures that covary as cause or effect with human

activities. More formal integration has been limited by the fact that environmental and social

data tend to be observed across different units, at different scales, and have different dynamics.

The two obvious dimensions for integrating environmental variables are time and space. Spatial

et al. 2006; Jorgenson 2004; Rasker 2006; Rudel 1999; York, Rosa and Dietz 2003).

Environmental circumstances such as climate-change vulnerability can be considered among the

background factors affecting individual survey respondents whose locations are known (e.g.,

Zahran et al. 2006). Recent advances in modeling and remote sensing have made technically-

defined spatial units such as grid cells or satellite-image pixels available for integrated research

(e.g., Grove et al. 2006). Spatially-integrated data of most types can be mapped or, where

enough observations exist, analyzed through multiple regression and related methods.

Alternatively, we might employ time as the integrating dimension, using years, months or days

for our units of analysis. Yearly time series of aggregated social data are widely available, as are

our attention on change. Such data tend to be limited, however, in the length of available

however, the rich information contained in hundreds of daily observations could open new

analytical doors. This paper began as a “test of concept,” investigating whether ARMAX

modeling of daily time series could yield practical new information regarding the specialized

topic of climate impacts on ski areas. Time series modeling provides a toolkit that might prove

broadly useful for this and other types of detailed impact studies.

Our first results are encouraging, although it is too soon to generalize from the findings.

Whether our two case studies will turn out to be representative of other ski areas, and how things

differ elsewhere, are questions best addressed through replications using more diverse samples.

As steps in that direction, we are currently exploring other Northeastern case studies, as well as

parallel work in Colorado where trends in mountain snowpack have been a concern (Mote et al.

2005). A more ambitious step will be to develop ways to look forward from daily-attendance

models, driving them with future winter days generated stochastically from place-adjusted

models under alternative climate scenarios. Such integration should yield new insights about the

role of variability in this very quick-response domain.

NOTES

{2} Although the same set of years comprises the data points in both panels of Figure 5, some

years (notably 2001–02) plot at different relative x-axis positions, reflecting divergent snow

experiences at two mountain locations less than 50 miles (80 km) apart. This observation

highlights snow variability and the importance of location-specific analyses.

Adeola, F. 2001. Environmental injustice and human rights abuse: The States, MNCs, and

Repression of Minority Groups in the World System. Human Ecology Review 8:39–59.

Badke, C. 1991. Climate Change and Tourism: The Effect of Global Warming on Killington,

Vermont. Unpublished undergraduate thesis, Deparment of Geography. Waterloo, Canada:

University of Waterloo.

Beniston, M., F. Keller, B. Kofi, and S. Goyette. 2003a. Snow pack in the Swiss Alps under

changing climatic conditions: An empirical approach for climate impact studies. Theoretical

and Applied Climatology 74:19–31.

Beniston, M., F. Keller, B. Kofi, and S. Goyette. 2003b. Estimates of snow accumulation and

volume in the Swiss Alps under changing climatic conditions. Theoretical and Applied

Climatology 76:125–140.

Breiling, M., and U.P. Charamaza. 1999. The impact of global warming on winter tourism and

skiing: A regionalised model for Austrian snow conditions. Regional Environmental Change

Carson, R., Y. Jeon, and D. McCubbin. 1997. The relationship between air pollution emissions

and income: U.S. data. Environment and Development Economics 2: 433–450.

Dietz, T. and E. Rosa. 1997. Environmental impacts of population and consumption. In

Environmentally Significant Consumption: Research Directions, P. Stern, T. Dietz, V. Ruttan, R.

Socolow, and J. Sweeney eds., 92–99. Washington, D.C.: National Academy Press.

Doesken, N.J., and A. Judson. 1997. The Snow Booklet: A Guide to the Science, Climatology,

and Measurement of Snow in the United States. Colorado Climate Center, Department of

5:243–273.

Elsasser, H. and P. Messerli. 2001. The vulnerability of the snow industry in the Swiss Alps.

Mountain Research and Development 21(4):335–339.

Fukushima T., M. Kureha, N. Ozaki, Y. Fujimori, and H. Harasawa. 2002. Influences of air

temperature change on leisure industries: Case study on ski activities. Mitigation and

Adaptation Strategies for Global Change 7(2):173–189.

Galloway, R. 1988. The potential impact of climate changes on Australian ski fields. In

Greenhouse: Planning for Climatic Change, ed. G. Pearlman, 428–437. Melbourne, AU:

CSIRO.

Gössling, S., and C. Hall, eds. 2005. Tourism and Global Environmental Change; Ecological,

Social, Economic and Political Inter-relationships. London: Routledge.

Grove, J.M., M.L. Cadenasso, W.R. Burch, Jr., S.T.A. Pickett, K. Schwartz, J. O’Neil-Dunne, M.

Wilson, A. Troy and C. Boone. 2006. Data and Methods Comparing Social Structure and

Vegetation Structure of Urban Neighborhoods in Baltimore, Maryland. Society and Natural

Gunstock Mountain Resort. 2006. http://www.gunstock.com/about_us/, accessed

4 August 2006.

Hamilton, J. D. 1994. Time Series Analysis. Princeton: Princeton University Press.

Hamilton, L. C. 2006. Statistics with Stata 9. Belmont, CA: Duxbury.

Hamilton, L.C., P. Lyster and O. Otterstad. 2000. Social change, ecology and climate in 20

century Greenland. Climatic Change 47(1/2):193–211.

Sociology and Social Policy 23(10):52–73.

25(3):195–215.

Hamilton, L.C., S. Jónsson, H. Ögmundardóttir, and I. Belkin. 2004b. Sea changes ashore: The

ocean and Iceland’s Herring Capital. Arctic 57(4):325–335.

Harvey, A. C. 1989. Forecasting, Structural Time Series Models and the Kalman Filter. Camb

ridge: Cambridge University Press.

Hantel, M. 2000. Climate sensitivity and snow cover duration in Austria. International Journal

of Climatology. 20:615–640.

Hayhoe, K., C.P. Wake, J. Bradbury, T. Huntington, L. Luo, M.D. Swartz, J. Sheffields, B.

Anderson, A. DeGaetano, D. Wolfe and E. Wood. 2006. Past and future changes in climate and

hydrological indicators in the U.S. Northeast. Climate Dynamics 28(4):381–407.

Hayoe, K., C. Wake, B. Anderson, J. Bradbury, A. DeGaetano, A. Hertel, X-Z Liang, E. Maurer,

D. Wuebbles and J. Zhu. In review. Quantifying the regional impacts of global climate change:

Evaluating AOGCM simulations of past and future trends in the temperature, precipitation, and

Huber, P. J. 1967. The behavior of maximum likelihood estimates under non-standard

conditions. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and

Probability, 221–233. Berkeley: University of California Press.

Huntington, T.G., G.A. Hodgkins, B.D. Keim, and R.W. Dudley. 2004. Changes in the

proportion of precipitation occurring as snow in New England (1949–2000). Journal of Climate

17(13):2626–2636.

IPCC (Intergovernmental Panel on Climate Change). 2001. Climate Change 2001: Impacts,

Adaptation and Vulnerability. Third Assessment Report. Cambridge: Cambridge University

Network (HCN) Serial Temperature and Precipitation Data. ORNL/CDIAC-30, NDP-019/R1.

New England Regional Assessment Overview, 8–17. Durham, NH: University of New

Hampshire.

Keim, B.D., A. Wilson, C.P. Wake, and T. Huntington. 2003. Are there spurious temperature

Trends in the United States Climate Division Database? Geophysical Research Letters

30(7):10.1029/2002GL016295.

Keim, B.D., M.R. Fischer and A. Wilson. 2005. Are there spurious precipitation trends in the

United States Climate Division Database? Geophysical Research Letters 32, L04702,

doi:10.1029/2004GL021985.

Koenig, U., and B. Abegg. 1997. Impacts of climate change on winter tourism in the Swiss

Alps. Journal of Sustainable Tourism 5(1):46–58.

Koenig, U. 1999. Climate change and snow tourism in Australia. Geographica Helvetica

54(3):147–157.

Jorgenson, A. 2004. Uneven processes and environmental degradation in the world-economy.

Development, A. Gill and R. Hartman eds. Burnaby, BC: Simon Fraser University.

Mitchell, M. N. 2004. A Visual Guide to Stata Graphics. College Station, TX: Stata Press.

Mote, P. W., A. F. Hamlet, M. P. Clark, and D. P. Lettenmaier. 2005. Declining mountain

snowpack in western North America. Bulletin of the American Meteorological Society

86(1):39–49.

NCDC. 2006. National Climate Data Center FTP site. ftp://ftp.ncdc.noaa.gov/pub/data/cirs/,

accessed 30 May 2006.

New Hampshire.

New England Ski Guide. 2006. http://www.newenglandski.com, accessed 4 August 2006.

New England Ski Museum. 2006. http://www.skimuseum.org/, accessed 4 August 2006.

Nolin, A.W. and C. Daly. 2006. Mapping “at risk” snow in the Pacific Northwest. Journal of

Hydrometeorology 7(5):1164–1171.

OECD (Organisation for Economic Co-operation and Development). 2007. Climate Change in

the European Alps: Adapting Winter Tourism and Natural Hazards Management.

http://www.oecd.org/document/45/0,2340,en_2649_34361_37819437_1_1_1_1,00.html

accessed 6 Jauary 2007.

Palm, B. 2001. Skiing with Climate Change: An Analysis of Climate Change and the

Consequences for the Ski Industry of New Hampshire and Vermont. Masters Thesis, Oxford

University.

Rudel, T. 1999. Critical regions, ecosystem management, and human ecosystem research.

Society and Natural Resources 12:257–260.

Scherrer, S.C., C. Appenzeller C and M. Laternser. 2004. Trends in Swiss Alpine snow days:

The role of local- and large-scale climate variability. Geophysical Research Letters 31(13)

doi:10.1029/2004GL020255

Scott, D, D., Dawson, J, Jones, B. forthcoming. Climate change vulnerability of the Northeast

US winter tourism sector. Mitigation and Adaptation Strategies to Global Change.

14(4):376–398.

Scott, D., G. McBoyle, and A. Minogue. 2006b. Climate change and Quebec’s ski industry.

Global Environmental Change doi:10.1016/j.gloenvcha.2006.05.004

Ski NH. 2006a. http://winter.skinh.com, accessed 4 August 2006.

Ski NH. 2006b. http://www.skinh.com/businessresultsrelease.cfm, accessed 4 August 2006.

Stata Corporation. 2005a. Stata Time-Series Reference Manual, release 9. College Station, TX:

Stata Press.

Stata Corporation. 2005b. User’s Guide, release 9. College Station, TX: Stata Press.

Tufte, E.R. 1990. Envisioning Information. Cheshire CT: Graphics Press.

Tufte, E.R. 1997. Visual Explanations: Images and Quantities, Evidence and Narrative.

Cheshire CT: Graphics Press.

White, H. 1982. Maximum likelihood estimation of misspecified models. Econometrica

50:1–25.

World Tourism Organization. 2003. Climate Change and Tourism: Proceedings of the First

International Conference on Climate Change and Toursim. Djerba, Tunisia, 9–11 April.

Madrid, Spain: World Tourism Organization.

York, R., E. Rosa, and T. Dietz. 2003. Footprints on the earth: The environmental consequences

of modernity. American Sociological Review 68:279-300.