Stock markets and meteorological influences
Thesis
Submitted in fulfillment of the requirements for the degree of Master of Science in Business Administration at University of Groningen
By
Arnold Sandor den Ouden1
May, 2011
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Student nr: 1799355
Acknowledgement
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Stock markets and meteorological influences
Arnold Sandor den Ouden
Abstract
In general, studies on the weather-effect focus on stock returns and one or two weather variables. This thesis tests an additional ten other stock variables and seven weather variables. A classical approach is applied with regard to the theoretical framework; meteorological influences are linked to the CCAPM. Weather conditions are believed to alter the demand side by means of changed risk preferences, while stock market returns are considered to be unaffected. This is a fundamental difference from previous studies. The theoretical model is in part supported by empirical evidence of the Dutch stock market.
JEL codes: C12, G12, G14
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Weather affects mood; as is obvious from daily experience, songs and formal psychological research (e.g. Howarth and Hoffman (1984)). But does the weather affect stock markets? Traditional finance literature assumes markets are efficient and stock market returns include all information, moreover information on the weather. Hence abnormal returns due to weather conditions are not likely. Besides its impact on expected returns, weather can affect stock market variables reflecting risk2. The weather effect has been investigated before, especially with a focus on stock market returns (Saunders (1993), Hirshleifer and Shumway (2003)). In contrast, risk preferences influenced by the weather are an underexplored area of interest. This thesis fills in this existing research gap, both theoretical and empirical. A theoretical elaboration on changed risk preference caused by meteorological influences based upon the classical CCAPM is presented. Empirical research is conducted to test the theoretical model on the Dutch stock market. Data is applied for a period up to 23 years (1987-2010).
Stock market changes influenced by the weather can be explained from various perspectives, in particular from a supply and demand side, the consumer demand on the one side and the production/ economic supply on the other side. From the supply side weather is able to influence real economic output. For example an industry with output clearly influenced by the weather is the agricultural sector. Economic output can increase due to favorable weather conditions or be destroyed by a single storm. A well-known costly storm is the hurricane Katrina that hit primarily the southern part of the United States in 2005. According to the Insurance Journal, hurricane Katrina caused $41.1 billion in insured losses3. Considering this substantial amount of monetary loss caused by the weather, it is not surprising the derivative market based upon weather conditions has grown over the years. Already back in 1997 the first over-the-counter weather derivatives were introduced. Even a special organization, The Weather Risk Management Association, has been formed to serve the interest of weather risk management industry by setting up, for instance, standards and proving education4.
Instead fundamental economic changes in the supply side, the demand side may also be taken as central perspective. From the demand side perspective weather conditions influence consumer mood (Eagles (1994)), in turn their risk preferences (Slovic et al. (2002)), which finally affect stock market variables reflecting risk. This perspective diverges from the traditional finance literature in which consumers are assumed to be fully rational. Previous studies in general focus on returns affected by weather conditions. However, those studies only refer to individual consumer
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Albeit, arbitrage prevents prices to deviate from their fundamentals; it does not prevent changes in trading volumes or bid-ask spreads.
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behavior deviating from unbounded rationality. They do not provide a theoretical framework in which changes in security markets are explained. This thesis develops a theoretical framework in which weather conditions are linked to security markets, which is tested on empirical grounds. Generally, empirical tests are based upon US data. In contrast this thesis applies data of the Dutch stock market, which is relatively rare.
The remainder of this thesis is organized as follows. First, previous studies on the weather effect and critical remarks as explanation to conflicting outcomes are discussed in section I. Next the theoretical framework is developed in which the CCAPM is linked to the weather variables in section II. Section III presents the applied methodology. Section IV elaborates on the applied weather and stock data. Section V provides and interprets the empirical results and proposes an alternative theoretical model. Finally the summary and conclusion are presented in section VI.
I. Literature review
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argued to be rational. In case the general perception is the same amongst consumers, weather influences on risk perception can be considered to be both “correct” and “normatively acceptable”.
Several authors have investigated the relationship between weather and the stock market before. Saunders (1993) was the first to examine the influence of weather on stock returns (Keef and Roush (2007)). Over the years rather conflicting results with regard to the weather effect are presented. Some have found supporting evidence of a relation between the weather and stock markets while others couldn’t support the existence of such a relationship. For instance Hirshleifer and Shumway (2003) and Saunders (1993) present results demonstrating sunshine, or absence of cloud cover, is significantly correlated with stock returns. On the other hand Pardo & Valor (2004) find no correlation at all.
Table 1: Summary results of leading papers on weather and the stock market. Sauders (1993) was the first to report, and
confirm, the weather effect with over 60 years of New York stock exchange data. In a diversity of regions, over several different time frames several authors have conducted comparable studies with rather conflicting outcomes. Results are summarized in this table.
Author Year of
publication
Years investigated
Region Relationship between weather and stock
market
Chang, et al. 2007 1994-2004 New York Yes, cloud cover has influence on market open.
Goetzmann & Zhu
2005 1991-1996 New York No link with individual consumer. But link with risk-aversion of NYSE specialist.
Hirshleifer & Shumway
2003 1982-1997 Worldwide Yes, morning sunshine has effect. Rain/ snow: no effect.
Jacobsen & Marquering
2008 1988-2004 Worldwide No, but found seasonal effect. Keef &
Roush
2007 1992-2003 Sydney No, wind and cloud cover. Yes, temperature.
Krämer & Runde
1997 1960-1990 Germany Depends on statistical method applied. Loughran &
Schultz
2004 1984-1997 U.S.A. No weather effect on the location where company is headquartered.
Pardo & Valor
2003 1981-2000 Spain No effect is present.
Saunders 1993 1927-1989 New York Yes, cloud cover effect is present. Shu & Hung 2009 1994-2004 Europe Yes, especially wind.
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clear critical remark; according to their article results depend on formulation and the statistical method applied. By adjusting hypothesis formulation and statistical methods applied, opposing results can occur. Five other critical remarks regarding research on the weather effect are made in the following paragraphs.
Firstly the percentage of orders submitted from the local market is of great importance for the weather effect to become visible. However, orders are submitted from all over the world, not just from the city where the stock exchange is located. Globalization increases the presence of this obstacle. Globalization is in part overcome by the phenomenon of home country bias. Consumers in general prefer to trade stocks situated in their surrounding area. Home country bias can be applied as a measure of local trading. In comparison with other countries around the globe, the Netherlands has a relatively low home country bias. One of the possible indicators is the Domestic Equity Share (DES), defined as: “the percentage of a country’s equity portfolio that is made up of domestic equity” (Foad (2006), p.27). The DES in the Netherlands was 49.7% in 2004. While for instance, neighboring country Belgium has a DES of 89.7% and the USA 87.4%5. Especially in the Netherlands this percentage has decreased substantially when comparing 2004 data (49.7%) with 1997 (71.8%) (Foad (2006)). Saunders (1993) applied relatively old data (1927-1989) which possibly overcomes the obstacle of globalization and explains his significant results.
Another obstacle in measuring the effect of local weather is country size. Just as mentioned by Loughran and Schultz (2004), the weather in cities like Brussels or Copenhagen reflects the weather faced by most consumers in the whole country. However, in bigger countries like Australia and the US, weather at the stock market location may differ substantially from other parts of the country. Due to the small size of the Netherlands, weather conditions are almost the same across the whole country. The size of a country and differences in weather conditions can explain why Krämer and Runde (1997) find no clear evidence of weather effects in Germany (that in comparison to the Netherlands is over eight times larger). Despite the fact orders are submitted from a wider region, they are executed by local market makers, they are also allowed to exploit their own interest and could in this way be collectively influenced by the weather (Hasbrouck (1995)). Since the abandoning of open-outcry trading and introduction of screen trading, influence of agents has decreased, but is still present.
The third critical remark; investors are inside a building at the times they put through their orders. Although it is clear they are inside - to a lesser extent being exposed to the weather - their behavior can still be influenced by the weather. A clear example of consumer mood being influenced by the weather without even being outside is found in Rind’s (1996) experiment. The psychologist
5 Other comparisons can be made with the average Euro-Area: 72.9%, Non-Euro-Area: 74.7%, Non-Europe:
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conducted an experiment in a hotel where many of the rooms did not have windows. When a guest, of a room without windows, ordered room service, the waiter mentioned the weather outside. The waiter received an average tip of 18.8% on rainy days, 24.4% on cloudy days and 29.4% on sunny days. Expressed differently, people raise their tip by over 50% on sunny days in comparison with rainy days, without actually being exposed to the weather. In line with the waiter mentioning the weather to hotel guests, weathermen mention weather conditions during news bulletins throughout the day to trading consumers.
The fourth remark relates to the extent to which differences in weather conditions occur. As described before, previous studies have presented contrasting results in different places around the world. In cases of minimal observable weather differences, no weather effect can be observed either. For instance the weather in Singapore differs only to a small extent from summer to winter. Average monthly maximum temperatures differ only 2°C between the warmest (June, 31°C) and coldest month (January, 29°C)6. On the other hand New York winters differ substantially from summers. Difference between the warmest and coldest monthly average daytime temperature is 25°C (July 29°C, January 4°C)7. The Netherlands is in-between those two extremes, a difference of 16°C between the warmest and coldest monthly average daytime temperature is observed (July 21°C and January 5°C)8.
In addition to the extent with which weather differences occur, cultural differences are of importance as well, which is the fifth critical remark. Hofstede (1983) has described cultural differences in a five dimension model, containing the following five dimensions: power distance, individualism versus collectivism, masculinity versus femininity, uncertainty avoidance, and long/ short-term orientation. The dimension of uncertainty avoidance is of special importance here, its definition is: “the extent to which people feel threatened by uncertainty and ambiguity and try to avoid these situations” (Mooij and Hofstede (2010), p.89). This dimension can be linked to changed risk perceptions due to the weather. In the case of a culture scoring relatively high on this dimension it is likely consumers respond stronger to the weather in comparison with countries scoring low on this dimension. The Netherlands (53) scores below average (68) on this dimension9. This average is based upon 78 countries worldwide. The low score can be regarded as an indicator for a relatively low observable weather effect.
As is obvious from table 1 research in general investigates the U.S.A. or a wider selection of countries on a more general basis (Hirshleifer (2003)). Research on the weather effect with a focus
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specific on the Netherlands is rare; to fill up the existing gap, this thesis focuses in specific on the Netherlands.
II. Theoretical framework: Weather and the CCAPM
One of the well-established cornerstones of financial theory is the Capital Asset Pricing Model (CAPM), developed by Sharpe (1964) and Lintner (1965)10. Fundamental to the CAPM is the Consumer Based Capital Asset pricing model (CCAPM). Instead of firms on the supply side, the CCAPM takes consumers on the demand side as central perspective. Capital supply basically comes from consumer savings. Their capital surplus needs to be invested, which makes them investors themselves, or otherwise (in)directly in charge of investors. The (C)CAPM assumes an optimizing consumer in markets that are frictionless, have homogeneous beliefs which can only be possible in case information is costless and homogeneously distributed amongst market participants. Following from the consumer’s optimal consumption and savings behavior, in equilibrium the expected return for security is determined by three components; the risk-free rate plus the security’s beta multiplied by the risk premium. The CAPM is formally presented in (1)
( ) ( ( ) ) (1)
where ( ) is the expected return on security , is the risk-free rate, ( ) is the expected return on the market portfolio and is a measure of the movement with the expected market return. The is determined by the covariance between return on security and the market portfolio divided by the variance on the market portfolio, or more formally stated in (2)
( )
( ) (2)
Moreover, due to diversification, the market portfolio’s firm specific risk is entirely eliminated. Only systemic risk remains. In line with Saunders (1993), on a market scale weather only influences the systemic part of the stock market. Changes in market variables (one of them the risk-free rate) influenced by the weather, make the position of the capital market line and utility function move as expressed in Figure 1.
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Figure 1: Utility function movement due to changes in the market place. The figure expresses a movement of the utility
function due to the weather. The risk-free rate and capital market line move in response to the changed utility function position.
Nonetheless it is interesting to consider the weather as an extra variable influencing both the left and right hand side of (1). Clearly, in case both sides of (1) are equally influenced, the weather effect can be cancelled out by simplification. Addition of the weather effect is stated in (3) and followed up by a simplification in (4).
( ) ( ( ) ) (3)
( ) ( ( ) ) (4)
Psychological evidence shows weather influences consumer mood (Eagles (1994)) and attributes such as patience (Howarth and Hoffman (1984)). Considering patience attributes to the preferred level of risk (Slovic et al. (2002)) and taking into consideration consumer intertemporal choice between utility of consumption today or at a future period in time (Cochrane (2005)), weather thus affects stock markets. In this line of thought weather influences on the stock market can be observed by variables reflecting risk preferences instead of market returns. Based upon the previous, the following hypothesis will be tested on empirical grounds: The null hypothesis is in line with previous research on the weather effect, weather does influence prices (5). Those prices are reflected by daily returns of the indices AEX, AMX and AScX. The alternative hypothesis states weather does not influence prices (6), but it changes risk preferences (7). In the alternative hypothesis, risk is measured by stock variables volume/ value, bid-ask spreads and volatility.
Risk Expected
Return
𝑟𝑓
Efficient frontier Capital market line
Movement of utility function
Market portfolio
𝑟𝑓′
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(5)
(6)
(7)
where is a price change, expresses a change in risk preference and is the sensitivity to weather conditions.
III. Methodology
In measuring the influence of weather variables on the stock market, the most commonly applied measures are cloud cover and stock return (Saunders (1993)). To be able to reject the hypothesis weather variables affect stock market returns, first of all, stock market returns are investigated. In addition to those general applied variables seven additional weather variables and ten other stock market variables are investigated as well. Stock variables reflecting consumer level of preferred risk are applied to test the demand side hypothesis on empirical grounds; weather influences the risk perception of consumers. In line with general practice, stock variables are based upon indices instead of individual stocks to mitigate the idiosyncratic risk of individual firms. By eliminating idiosyncratic risk only systemic risk remains.
Just as most previous scholars in this field of interest have done, for instance Jacobsen and Marquering (2008) and Saunders (1993), an Ordinary Least Square (OLS) regression is applied. The regression measuring a weather effect is presented in (8)
( ) (8)
where ( ) is the expected daily market return on day t, represented by three separate Dutch
indices. Indices with different firm size are applied to detect any possible firm size effect. Applied indices are ordered from large to smaller market capitalization respectively AEX, AMX and AScX. The constant is denoted by , sensitivity to weather conditions is denoted by , is represented by eight different weather variables. Those weather variables are: hourly mean wind speed, temperature, global radiation, hourly precipitation amount, air pressure, horizontal visibility, cloud cover and finally humidity. The last symbol represents the OLS term, which assumes:
I. ( ) The expected errors have zero mean.
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IV. ( ) There is no relationship between the error term and corresponding weather variate.
V. ( ) The error terms are normally distributed.
A. Stock market return
Stock market returns can be calculated in several manners, Pardo and Valor (2003) calculate the return between close prices of consecutive days. However, market open differs substantially from the previous day’s closing price. Differences between market open and the previous day’s closing price are for the applied dataset on average AEX: 0,54%, AMX: 0,52% and AScX: 0,49%. To come up with those numbers negative differences are multiplied by -1 to prevent positive and negative differences canceling out each other. Those differences are perceived not only to be caused by measured weather conditions at 9:00. Taking those differences into account, daily returns are based upon open/close values of the same day instead of close prices of consecutive days. Those returns are considered to be a better measure due to not taking post-market close and pre-market open orders into account. Formally stated daily returns of three stock market indices, are calculated as expressed in (9)
(
) (9)
where expresses the return on a particular day, and expresses respectively the prices at market open and market close on a particular day. Based upon Chang et al. (2007) results demonstrating the weather effect being the strongest just after market open, the first hour of trading is investigated as well. Which is calculated as expressed in (10)
(
) (10)
where expresses the return in the first hour of trading, expresses the price at 10:00 a.m. on a particular day, and expresses the price at market open on the same particular day. In addition to the generally applied return measures, several other stock market variables reflecting preferred risk are investigated as well. The next paragraph discusses those variables in more detail.
B. Measures of preferred risk
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applied measures of preferred risk. Mcinish and Wood (1992) mention, besides other factors, risk as determinant of bid-ask spreads. Goetzmann and Zhu (2005) report a widening of NYSE bid-ask spreads during cloudy days. According to them, widening is primarily caused by market-makers. Those market-makers are assumed to be located in the city hosting the exchange and reflect their risk perception on the bid-ask spread. Based upon their significant results the bid-ask spread is applied as a stock variable reflecting preferred risk. To arrive at the daily bid-ask spread, first the daily bid-ask spread of each individual firm listed on the particular index is calculated. Following Goetzmann and Zhu’s (2005) reasoning the market spread is calculated as the equal weighted average of all individual stocks. Equal weighted is chosen instead of value-weighted because it better reflects the average market makers behavior. Due to, increased market efficiency, bid-ask spreads have decreased substantially over the investigated period of time (AEX: -79.21%, AMX: -71.49% and AScX: -53.85%). To overcome possible biased results, changes relative to the previous day and deviations from the yearly average are investigated as well.
Other measures reflecting perceived risk by consumers are trading volume and value. Trading value and volume correlate to a large extent due to the fact that traded value is a result of volume multiplied by the value of each traded stock. When trading volume changes, the traded value in general changes in the same direction. Following this reasoning both trading volume and value are investigated for total market and AMX index. Considering both trading values/ volumes fluctuate to a large extent from one year to another, and increased substantially over the investigated period of 23 years, results can be biased when only absolute values are applied. To control for those changes two different adjustments are made. The first of the adjustments is calculating the deviation of the year’s average. The second adjustment is calculating the log change in comparison with the previous day. Which is calculated as, presented in (11):
(
) (11)
where is the value at time and is the value at the day preceding . By applying a log scale
instead of a percentage scale a more even distribution is obtained. As a result of changed risk preference, besides trading volumes/ values and bid-ask spreads, market volatility can change as well. In this manner volatility is applied as the third measure of the preferred level of risk. Volatility is applied with regard to the AEX index.
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market risk, on the other hand bid-ask spreads shorten by increased volume, due to a higher liquidity. Volume in turn increases with a higher risk preference, due to consumer willingness to make a deal at times of increased risk, stemming from, for instance, heat stress (Tong (2009)). In conclusion, it can be postulated risk both widens and indirectly shortens the bid-ask spread. This rather ambiguous relation is a clear example of the so called micro- to-macro problem. Translating individual behavior into the macro level yields conflicting outcomes.
C. Frequency of data
First of all the dataset is analyzed on a seasonal basis by comparing the seasonal weather pattern with a seasonal stock market pattern. Jacobsen and Marquering (2008) argue a low frequency can be a better proxy due to the excluding of possible noise. Seasonal data is one of the lowest frequencies possible to apply in this field of interest. A total of twelve values depicting the seasonal weather and stock pattern are calculated by summing all separate month (Jan, Feb, …, Dec) values of the whole investigated period, and dividing them by the number of years, expressed in (12)
̅ ( ) ( ) ( )
(12)
where ̅ expresses the arithmetic average month (Jan, Feb, …, Dec) value over the investigated period of 23 years, ( ) expresses the average month value in year one, ( ) expresses the average month value in year two, etc. The same holds for the other eleven months. Side effects of seasonal data weather effects on smaller periods of time are eliminated as well. Weather circumstances do certainly change at a faster pace than on a monthly basis. To overcome the elimination of weather effects on smaller periods of time, the dataset is investigated on a daily basis as well. The side effect of included noise is in part overcome by excluding the largest outliers. Between the seasonal and daily frequency lies weekly data, this is investigated as well. Both the stock and weather variables on a weekly basis are calculated as presented in (13)
̅ ( ) ( ) (13)
where ̅ ( )is the weekly arithmetic mean of week , in which has 52 values each year. Mon, Tue,
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dataset does not suffer from “missing” data, each weekly variable is based upon the average of five observations.
D. Adjustments
Both the weather and stock market are fluctuating to a large extent from season to season and from day to day. Due to seasonal patterns in the weather two separate adjustments are made. As set out by Goetzmann and Zhu (2005) consumers evaluate the weather in relation to the seasonal average. This reasoning is in line with the prospect theory, in which individuals act relative to a certain reference point (Nofsinger (2011)), in this case the seasonal average. The adjustment is made by calculating the average weather value over the observed years for each month from January through December, as in (12). Next the daily deviation from this value is calculated, a daily abnormal variable relative to the seasonal pattern results, more formally stated in (14)
̅ ( ) (14)
where is the abnormal weather variable on a particular day, is the weather variable on a particular day and ̅ ( ) represents the average weather of the concerning month calculated over
the time period 1951-2010, as expressed in (12). Equal to the weather a seasonal pattern in stock markets exists as well. An example of a seasonal pattern is the January-effect (Anderson, Gerlach and DiTraglia (2007)). To control for seasonal patterns in the stock market, the same method is applied as to the weather. Where is replaced by , represented by stock variables: market return, bid-ask spread, volume/ value and volatility.
In line with Nofsinger’s (2011) elaboration on individuals acting relative to a certain reference point, a second adjustment is made. Regressions consisting of stock market changes as a dependent variable and weather changes as an independent variable are run as well. It is possible individuals respond positively to a perceived weather improvement. And in turn respond in the opposite direction to weather deterioration. Change relative to the previous day is calculated as in (15)
(15)
where is weather change relative to the previous day, is weather on a particular day, and
is weather at the previous day. In case of stock market variables, is replaced by , expressing
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IV. Data and descriptive statistics
A. Stock dataStock data is retrieved from both Yahoo! Finance11 and Thomson Datastream. Some features of the applied stock data are discussed in this paragraph. A full list of detailed descriptive statistics for stock data, both on a daily as well as a weekly basis is presented in Tables A.1, A.2 and A.3 in Appendix A. By adjusting the daily data into weekly data several changes to the dataset are observed. As expected, several statistics are less extreme on a weekly basis in comparison with daily basis. This can be explained by reversion to their mean; relatively high and relatively low values are averaged out of the dataset. By applying weekly values the number of observations decreases by factor of five, due to a trading week consisting of five days. To avoid results being manipulated by outliers, occurring especially in daily data, several outliers are excluded from the dataset. Daily returns of >5% and <-5%, as well as AMX volume changes of >10% and <-10% are excluded from the applied dataset. Weather conditions are expected to influence stock variables only to a relatively small extent. Large outliers are not caused by weather conditions. A substantial difference is observed between minimum and maximum bid-ask spreads (AEX: 0.187, AMX: 0.585, AScX: 0.659). The differences can be explained by the lengthy observation period. Over the years both market liquidity and efficiency have increased, as a consequence bid-ask spreads have become smaller. The larger spreads are observed in the beginning of the applied period and the smaller spreads are observed at the end of the applied period. Liquidity differences between three indices clearly remain visible by comparison of AEX bid-ask spreads (mean: 0.04) with the AMX (mean: 0.08) and AScX (mean 0.12).
B. Weather data
Weather data is retrieved from the Royal Netherlands Meteorological Institute12. Weather observations from 1951 till 2010 are obtained from weather station Schiphol. By covering such a long period the dataset is not completely homogenous. This limitation is caused by measurement technique adjustments and changes in the weather station’s exact location. Weather station Schiphol is situated at 11.9km distance from the Amsterdam stock exchange13. The close distance makes it a sound representative of weather at the stock exchange. The Netherlands as a relatively small country makes Schiphol weather representative of weather conditions at the rest of the country as well. The same local circumstances guarantee consumers to be homogeneously exposed to weather conditions and weather predictions. Homogeneous information is one of the mentioned assumptions
11
See, www.finance.yahoo.com
12
See, www.knmi.nl/klimatologie
13 KNMI weather station number 240 located at Schiphol airport LON4.77 LAT52.30, the stock market is located
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underlying the CCAPM. Based on the same set of information consumers form homogeneous beliefs. As representation of relatively small distances in the Netherlands, Figure 2 depicts the longest distances in three distinct directions. The city of Vaals, in the province Limburg, is situated at the longest distance of Schiphol at a relatively close 191 km. The two other distances are Nieuweschans at 190km in the province of Groningen and Eede at 149km in the province of Zeeland. In addition to those small distances over half of the Dutch population is situated in the dense populated area called “de Randstad”, situated in the surrounding area of Schiphol.
Figure 2: Small distances in the Netherlands. Relatively small distances in the Netherlands are visualized. The Amsterdam
stock exchange is located at 11.9 km from weather station Schiphol. The city located at the longest distance from weather station Schiphol is Vaals at 191km. Those relatively close distances justify the application of one weather station as a representative of local weather all over the country.
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Table 2: Measurement information applied weather variables. Additional measurement information concerning the
applied weather variables is presented. Table is based upon descriptives of the Royal Netherlands Meteorological
Institute14.
Weather variable Additional measurement information Hourly mean wind speed Measured in 0.1 m/s.
Temperature In 0.1 degrees Celsius, at 1.50 m at the time of observation.
Temperature change Calculated based upon temperature as stated in the row above, by: in which is the
temperature change, is the temperature on a particular day and is the temperature on the previous day.
Global radiation In J/cm2, during the hourly division. Hourly precipitation amount In 0.1 mm (-1 for <0.05 mm).
Air pressure In 0.1 hPa, reduced to mean sea level, at the time of observation.
Horizontal visibility At the time of observation (0=less than 100m, 1=100-200m, 2=200-300m,..., 49=4900-5000m, 50=5-6km, 56=6-7km, 57=7-8km, ..., 79=29-30km, 80=30-35km, 81=35-40km,..., 89=more than 70km).
Cloud cover In octants, at the time of observation (0=sky clear, 9=sky invisible). Humidity Relative atmospheric humidity (in %) at 1.50 m at the time of observation.
Most weather variables can be interpreted in a black-white fashion of good versus bad weather. For instance a nice sunny day has a clear blue sky with no cloud cover. The opposite, a high amount of cloud cover can be considered as bad weather. Air pressure is less clear cut; high air pressure was historically interpreted as pleasant weather, low air pressure as unpleasant weather. Over the years it has become evident that an explicit separation is not in line with reality. For instance high air pressure can result in thunder and lightning, generally interpreted as unpleasant instead of pleasant weather. The same ambiguously holds for temperature. Psychological research by Pilcher et al. (2002) has found heat affects mental capabilities, above a certain temperature mental capabilities decrease. Warm summer days do not only relax people, they can increase stress and in turn consumers risk preference.
On first review the obtained KNMI dataset contained a wide range of 21 weather variables. Considering the existence of high correlations between several of those weather variables a selection is made. For instance the variable “hourly mean wind speed” and the variable “mean wind speed during the 10-minute period preceding the time of observation” present a correlation coefficient of 0.97. Inclusion of both, approximately the same variables would not add any value. A side mark to the correlation coefficient; due to differences in the unit of measurement correlation coefficients are applied throughout this thesis instead of covariance. As can be expected from logical reasoning, several other weather variables have strong correlations amongst each other as well. Some correlations are positive while others are negative. For instance cloud cover and global radiation present a negative correlation (-0.54). This can be explained by clouds blocking the radiation from the sun. Cloud cover and humidity present the opposite correlation, namely positive (0.49). This can
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be explained by clouds preventing humidity from fading away from the air. A variety of correlations is supported by the correlation diagram for the applied eight weather variables in Table 3. Although several correlations are relatively high, due to the high number of observations (6199) correlations can be considered as low in comparison with fewer observations. By applying average values based upon weekly instead of daily data, the noise decreases and correlations increase significantly. This is supported by Table B.4 in Appendix B. Existence of correlations between weather variables causes the problem of multicollinearity. Due to the fact variables are not orthogonal to each other, inclusion of more than one weather variable into one regression would result in loss of precision. Following this argumentation only regressions based upon one single weather variable are run.
Table 3: Correlation coefficients for eight applied weather variables. As can be expected from logical reasoning several
weather variables present higher/ lower correlations while others present positive/ negative coefficients. For instance temperature and global radiation correlate to a large extent. Coefficients are based upon 6199 observations from 01-01-1987 to 06-10-2010. Coefficients of ≤-0.4 and ≥0.4 are accentuated.
Wind speed Temperature Global
radiation Precipitation Air pressure
Horizontal
visibility Cloud cover Humidity
Wind speed 1.00 -0.06 -0.17 0.09 -0.40 0.18 0.17 -0.01 Temperature -0.06 1.00 0.67 -0.01 -0.05 0.34 -0.17 -0.48 Global radiation -0.17 0.67 1.00 -0.17 0.15 0.44 -0.54 -0.76 Precipitation 0.09 -0.01 -0.17 1.00 -0.20 -0.12 0.15 0.19 Air pressure -0.40 -0.05 0.15 -0.20 1.00 -0.04 -0.24 -0.13 Horizontal visibility 0.18 0.34 0.44 -0.12 -0.04 1.00 -0.28 -0.62 Cloud cover 0.17 -0.17 -0.54 0.15 -0.24 -0.28 1.00 0.49 Humidity -0.01 -0.48 -0.76 0.19 -0.13 -0.62 0.49 1.00
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V. Results and interpretation
A. Several data frequenciesWith regard to the interpretation of the results, it is interesting to note weather variables are completely exogenously determined. Human activities do not influence day to day weather conditions. It is out of question if weather influences the stock market or if it is the other way around. Exogenously increases the ease of interpretation. Interpretation of separate weather variables on the other hand is harder. High correlation coefficients between several weather variables make it difficult to determine if it is one single weather variable influencing the stock market or if it is a combination of several weather variables. Possibly two variables are present at the same time but only one variable impacts the stock market. The other variable can be present, however, does not have any impact on the stock market. For instance at times cloud cover is low, which is directly observable by the human eye, global radiation is high at the same time, but in contrast this variable is not directly observable by the human eye and possibly does not influence the stock market. The example of observability is clear, but does not need to hold in practice. As stated in the literature review, the human body responds to the amount of (unobservable) sunlight.
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Figure 3: Is a seasonal pattern present? As visually presented, no relationship is indicated between the variables
temperature and AEX return. The correlation coefficients are -0.01 on daily basis and -0.10 on monthly basis. In line with the theoretical framework, a variable measuring stock market returns (AEX) does not correlate with a weather variable (temperature). Figure is based upon monthly average observations in the period 04-01-1993 to 06-10-2010.
Figure 4: Is a seasonal pattern present? As is visually presented, an indication of a relationship is present between the two
variables presence of rainfall and volatility. During months in which observation was preceded by a relatively frequent presence of rainfall, volatility was high as well. The accompanied correlation coefficient is 0.79 on a monthly basis. In line with the theoretical framework, a variable measuring perceived risk (volatility) correlates with a weather variable (presence of rainfall). The figure is based upon monthly average observations in the period 03-01-2000 to 06-10-2010.
After analyzing the data on a seasonal basis the next step is to look at a more detailed level of the dataset, namely on a daily basis. First, regressions containing daily stock market returns as a dependent variable and eight weather variables as explanatory variables are conducted. The AEX, AMX and AScX indices represent the daily stock market returns. As presented in Table 4, except for the regression between AMX daily return and wind speed, no coefficients with a significance level below 5% are present between the weather variables and daily stock return. Those results
-0,40% -0,30% -0,20% -0,10% 0,00% 0,10% 0,20% 0,30% 0,40% 0 2 4 6 8 10 12 14 16 18 20 1 2 3 4 5 6 7 8 9 10 11 12 A EX r e tu rn Tem p e ratu re 0C Month
Temperature AEX Return
18 20 22 24 26 28 30 32 0,13 0,15 0,17 0,19 0,21 0,23 0,25 0,27 0,29 0,31 0,33 1 2 3 4 5 6 7 8 9 10 11 12 Vo latil ity Pr e sen ce o f r ai n fal l Month
20
empirically confirm the alternative hypothesis, which states no relationship is present between weather variables and stock market returns.
Table 4: Regression results for weather variables and daily returns. Only one weather variable presents significant
coefficients, of which AScX is significant at the 10% level. The absence of more significant coefficients confirm the theoretical framework; stock market returns are unaffected by the weather. AEX is based upon 4554 observations in the period 10-10-1992 till 06-10-2010. AMX is based upon 1251 observations in the period 03-03-2005 till 06-10-2010. AScX is based upon 1259 observations in the period 03-03-2005 till 06-10-2010. *, ** and *** indicate statistical significance at the 10%, 5% and1% levels, respectively.
Absolute AEX Return AMX Return AScX Return
Coefficient Adjusted R2 Coefficient Adjusted R2 Coefficient Adjusted R2
Hourly mean wind speed -3.29E-6 -0.000 -2.70E-5** 0.003 -1.90E-5* 0.002
Temperature -2.19E-6 -0.000 -3.04E-6 -0.000 -2.58E-6 -0.000
Temperature change -2.15E-6 -0.000 -1.78E-5 0.001 -1.19E-5 0.001
Global radiation -4.83E-7 -0.000 -2.55E-6 -0.001 1.73E-6 -0.001
Hourly precipitation amount 5.60E-6 -0.000 4.28E-5 -0.000 -4.54E-6 -0.001
Air pressure 1.71E-6 0.000 2.16E-6 -0.000 1.82E-6 -0.000
Horizontal visibility -1.14E-5 0.000 -3.30E-5 0.001 -1.42E-5 -0.000
Cloud cover -2.21E-5 -0.000 -3.34E-6 -0.001 -5.27E-5 -0.000
Humidity 9.48E-6 -0.000 1.85E-5 -0.000 3.00E-6 -0.001
21
interpreted as better weather causing lower volatility. In turn this can be interpreted as a lower level of risk.
Other variables reflecting risk are trading volumes and values. Stemming from the theoretical framework, those variables need to have a stronger link to weather variables in comparison with daily returns as well. The theoretical framework is indeed supported by the empirical results. Results of those regressions are presented in Table 5. Six weather variables regressed against trading volume do show significant coefficients. Of those coefficients four are even significant at the 1% level.
Table 5: Regression results for unadjusted weather variables and total market volume and value. A wide range of weather
variables present significant coefficients for both trading volume and trading value. Results confirm the hypothesis weather affects variables reflecting preferred risk. Volume and value are based upon 6033 observations in the period 01-01-1987 till 06-10-2010. *, ** and *** indicate statistical significance at the 10%, 5% and1% levels, respectively.
Absolute Total market volume Total market value Coefficient Adjusted R2 Coefficient Adjusted R2
Hourly mean wind speed -5,240 * 0.000 4,670 -0.000
Temperature 4,648*** 0.002 9,897*** 0.002
Temperature change -4,571 -0.000 -1,411 -0.000
Global radiation 2,599** 0.001 1,946 -0.000
Hourly precipitation amount 1,217 -0.000 5,208 0.000
Air pressure -2,364*** 0.001 -9,041*** 0.004
Horizontal visibility 3,053*** 0.007 -2,632* 0.000
Cloud cover 2,528 -0.000 15,436** 0.001
Humidity -3,602*** 0.006 7,014*** 0.006
In addition to the seasonal and daily frequencies Tables in Appendix F, G and H, present results of regressions based upon weekly data. Although weekly data in part eliminates noise it does not yield substantially different results in comparison with daily data. In line with daily data, especially regressions with volume and value result in several significant coefficients. As mentioned earlier those variables can be considered as representatives of consumers risk perception. While as predicted by the theoretical framework, regressions trying to explain stock market returns yield a relatively low number of significant results.
B. Adjustments
22
previous day had a positive 3% return, 1.5% can be considered as low. As presented in the Tables of Appendix D, a relative low amount of significant coefficients is present for regressions on changes relative to the previous day. According to the presented significance levels, consumers do not respond to changes in weather variables with changes in stock returns and neither do they with changes in variables representing risk perception.
This chapter started by elaborating on the seasonal weather pattern and the possible existence of a seasonal pattern in the stock market. The relationship between weather conditions and stock market on a seasonal basis is not strongly supported. It is possible traders respond to deviations of the seasonal weather pattern by causing deviations from the seasonal stock market pattern. For instance above average cloud coverage in June my cause above average trading volumes in the same month. Regressions are run for a variety of weather and stock variables. Results are different for both regressions with absolute values and regressions with changes relative to the previous day. Primarily, trading volume and value do present higher significance levels. Those results confirm the theoretical model, which states consumers respond to weather variables by changes in their risk preference. Coefficients accompanied by their significance levels of market volume and value are presented in Table 6. Results of nine other stock variables are presented in Appendix F.
Table 6: Regression results for daily weather deviations of seasonal pattern and trading volume and value. Remarkably
high significance levels for a wide range of weather variables do occur, which confirms the expectations of the theoretical framework. Except for global radiation (5828), volume and value are based upon 6033 observations from the period 01-01-1987 till 06-10-2010. *, ** and *** indicates statistical significance at the 10%, 5% and1% levels, respectively.
Seasonal adjusted Total market volume Total market value
Coefficient Adjusted R2 Coefficient Adjusted R2
Hourly mean wind speed -5,854,714** 0.000 2,928,263 -0.000
Temperature change 1,584,220*** 0.008 1,584,220*** 0.008
Global radiation 5,451,869*** 0.001 -3,073,727 -0.000
Hourly precipitation amount 1,003,572 -0.000 1,003,572 -0.000
Air pressure -2,219,071*** 0.001 -8,701,893*** 0.004
Horizontal visibility 3,493,047*** 0.008 3,493,047*** 0.008
Humidity -5,134,525*** 0.008 -5,134,525*** 0.008
It needs to be mentioned all reported adjusted R2’s are relatively low. Those low adjusted R2’s are in line with previous studies on the weather effect, for instance by Saunders (1993). An attempt is made to increase adjusted R2’s by adding a stock market variable to the regressions. Based upon the strongly significant results of Shu et al. (2009) in addition to (8), the parameter is added in
(16) to control for first order autocorrelation.
23
Although controlling for first order autocorrelation sounds logical, it is in contradiction to the CAPM. The CAPM implicitly assumes the Markov property holds; only the present value of a variable is relevant for predicting the future, the past history of the variable and the way that the present has emerged from the past is irrelevant. However, as can be concluded from Table D.6 Appendix D, the coefficient of the added lagged variable is significant at the 5% level and adjusted R2‘s increase, they are, however, still relatively low. Regressions containing weather variables air pressure and wind speed result in coefficients with a significance level below the 5% level.
In addition to the previous adjustments, regressions are run to test if afternoon weather observations result in higher significance levels in comparison with morning weather observations. This can be the case due to the fact trading volumes, values and volatilities result from a whole trading day, not just a couple of hours in the morning or afternoon. Appendix G presents the results of those regressions for volume, value and volatility. As can be expected from high correlation coefficients between morning and afternoon weather in Table B.3 of Appendix B, no substantial differences are observed between regressions with morning or afternoon weather observations.
C. Are the results period consistent?
24
D. Which variable is it?
As represented by the correlation diagram in Table B.4, Appendix B, most weather variables correlate, to a large extent, amongst each other. Those high correlations make it hard to interpret which variables or combinations of variables actually influence consumer risk preference. For instance global radiation negatively correlates with humidity (correlation: -0.76). Presented results confirm a correlation between weather variables and consumer risk preference. The question remains which of the weather variables actually influences consumer risk preference.
E. Remark on applied measurement scale
Several presented coefficients can be considered as relatively low. However, measurement scales of both weather data and stock data can be considered as ambiguous. The “correct” scale to apply can be a point of discussion without a clear answer resulting. After a single adjustment in measurement scale the coefficients can be increased artificially. For instance stock market trading volume is measured in a 105 times larger scale in comparison with stock market returns. By adjusting the measurement scale the significance level and adjusted R2’s are not affected, only reported coefficients can be increased.
F. Alternative theoretical framework
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Figure 5: Utility function movement due to the weather. Movement of utility function alongside the capital market line
due to a changed risk preference is expressed, which is caused by changed weather circumstances. Weather circumstances change at a faster pace in comparison to the risk-free rate. By assuming the actual risk-free rate is fixed over short periods of time, the utility function can only move alongside the capital market line in response to changed consumer risk preference. By moving alongside the capital market line individual consumers reach their preferred level of risk accompanied by the highest possible return. This is achieved by an optimal combination of the tangency portfolio and the risk-free asset.
VI. Summary and conclusion
Based on empirical findings, Dutch stock market returns are not affected by weather variables. This is in contrast to the null-hypothesis, formulated in line with several earlier studies (Hirshleifer (2003) and Saunders (1993)). However, variables representing the preferred level of risk do show a highly significant relation with several weather variables. This is in line with the alternative hypothesis. To incorporate those findings into a theoretical framework an alternative model is proposed, which elaborates on the effect of weather circumstances on consumer behavior. Consumers respond to weather conditions by changing risk preferences. By considering changes in weather variables occurring at a faster pace than the risk-free rate, this rate is assumed to be fixed over short periods of time relative to the weather. In case consumer risk preferences change in response to weather conditions and the risk-free rate is fixed, consumers are only able to move their utility functions alongside the capital market line. This movement makes consumers arrive at their preferred expected level of risk accompanied by the highest possible return. With this reasoning, weather variables are included in the CCAPM without the mentioned drop out due to simplification.
Several critical remarks regarding research on the weather effect can be made. With regard to measurability of the local weather effect the percentage of orders submitted from the local market is of great importance for the weather effect to become visible. This percentage is relatively
Risk Expected Return 𝑟𝑓 Fixed Efficient frontier Capital market line Movement of
utility function
26
low in the Netherlands. Another obstacle in measuring the effect of local weather is country size. Due to the small size of the Netherlands, weather conditions are almost the same across the whole country. The third critical remark; investors are inside a building at the times they put through their orders, can be mitigated by Rind’s (1996) tipping experiment. The fourth remark relates to the extent to which differences in weather conditions occur. In cases of minimal observable weather differences, no weather effect can be observed either. For instance the weather in Singapore differs only to a small extent (2°C) from summer to winter. On the other hand New York winters differ substantially (25°C) from summers. The Netherlands is in-between those two extremes, a difference of 16°C is present. In addition to the extent with which weather differences occur, cultural differences amongst countries are of importance as well.
As a critical remark, empirical results can be criticized based on the presented adjusted R2’s. Although several adjustments are made, of which an added stock market variable to the regressions, reported adjusted R2‘s are in line with earlier papers on the weather effect relatively low (Saunders (1993)).
Knowledge of market returns not being influenced by weather conditions does not improve trading strategies. However, knowledge of risk perceptions being influenced by weather conditions can be valuable information. Consumers can profit from knowledge of increasing or decreasing market liquidity and changes of bid-ask spreads. In addition to having the advantage of market knowledge, consumers can profit by becoming aware of their own behavior.
27
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VII. Appendix A: Summary of statistics
Table A.1: Summary of statistics applied stock data: on both a daily as well as a weekly basis, as can be expected, several statistics except for minimum values, are lower on a weekly basis in comparison with a daily basis due to the fact that values are reverted to their mean. AEX is based on the period 10-10-1992 till 06-10-2010. AMX and AScX are based on the period 03-03-2005 till 06-10-2010., and AEX return in the first hour of trading is based on observations in the period 19-05-2003 till 06-10-2010. *, ** and *** indicate statistical significance at the 10%, 5% and1% levels, respectively.
AEX return AScX return AMX return AEX return first hour Daily Weekly Daily Weekly Daily Weekly Daily Weekly
Number of observations 4,554 938 1,273 264 1,265 264 1,895 356 Mean -0.00 -0.00 -0.00 -0.00 -0.00 -0.00 -0.00 -0.00 Median 0.00 0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 Maximum 0.049 0.020 0.035 0.16 0.041 0.017 0.47 0.0079 Minimum -0.049 -0.028 -0.037 -0.022 -0.049 -0.023 -0.42 -0.016 Standard deviation 0.011 0.00 0.0090 0.0049 0.011 0.0060 0.0062 0.0025 Skewness -0.20 -0.83 -0.59 -0.64 -0.67 -0.68 -0.41 -1.012 Kurtosis 5.80 6.59 5.30 5.58 5.03 4.29 9.08 9.31 Jarque-Bera 1,516.17 613.49 354.96 91.27 310.91 38.8 2,973.89 650.89 Probability 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Table A.2: Summary of statistics applied stock data: on both a daily as well as a weekly basis, as can be expected, several statistics except for minimum values are lower on a weekly basis in comparison with a daily basis due to the fact that values are reverted to their mean. Total market volume and value are based on observations in the period 01-01-1987 till 06-10-2010. AEX volatility is based on the period 03-01-2000 till 06-10-2010. *, ** and *** indicate statistical significance at the 10%, 5% and1% levels, respectively.
Volume total market Value total market Value AMX AEX Volatility
Daily Weekly Daily Weekly Daily Weekly Daily Weekly
Number of observations 6,033 1,239 6,033 1,239 6,199 1,239 2,805 561 Mean 69,187 68,558 1,596,746 1,586,512 23,158.35 23,161.24 25.58 25.59 Median 62,162 65,104 1,339,544 1,383,026 20,878 20,815.80 22.61 22.67 Maximum 501,863 302,522 11,430,020 6,895,984 82,482 80,001.40 81.22 71.12 Minimum 0.000 2,097 17.00 68,299 1,878 1,961.80 10.12 11.21 Standard deviation 62,131 59,471 1,479,304 1,419,898 17,148.61 17,139.08 11.67 11.59 Skewness 0.813 0.555 1.382 1.131 0.78 0.77 1.50 1.47 Kurtosis 3.680 2.498 5.389 3.897 3.13 3.11 5.21 4.99 Jarque-Bera 781.631 76.587 3,353.97 305,612 627.76 123.38 1,628.88 294.43 Probability 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Table A.3: Summary of statistics applied stock data: on both a daily as well as a weekly basis, as can be expected, several statistics except for minimum values, are lower on a weekly basis in comparison with a daily basis due to the fact values are reverted to their mean. Outliers are excluded, all data is observed in the period 28-08-2001 till 06-10-2010.*, ** and *** indicate statistical significance at the 10%, 5% and 1% levels, respectively.
AEX bid-ask AMX bid-ask AScX bid-ask Daily Weekly Daily Weekly Daily Weekly
30
Table A.4: Summary of statistics weather data: on both a daily as well as a weekly basis, as can be expected, several statistics except for minimum values are lower on a weekly basis in comparison with a daily basis due to the fact that values are reverted to their mean. Global radiation is observed from 14-09-1987 till 06-10-2010. Other variables are observed from 01-01-1987 till 06-10-2010 at 9:00. *, ** and *** indicate statistical significance at the 10%, 5% and1% levels, respectively.
Hourly mean wind speed Temperature Global radiation Hourly precipitation amount Daily Weekly Daily Weekly Daily Weekly Daily Weekly
Number of observations 6,199 1,239 6,199 1,239 6,071 1,200 6,199 1,239 Mean 53.22 53.22 110.96 110.95 78.52 78.46 0.81 0.81 Median 50 50.4 112 112 57 71.20 0 0 Maximum 216 139 292 265.40 260 230 92 19.40 Minimum 0 10 -139 -92.00 0 0 -1 -1 Standard deviation 27.62 17.65 67.33 64.32 69.50 59.36 4.23 2.01 Skewness 0.85 0.72 -0.15 -0.16 0.71 0.42 7.55 3.50 Kurtosis 4.10 3.80 2.56 2.34 2.26 2.04 86.30 19.61 Jarque-Bera 1066.25 140.88 72.95 28.33 648.02 81.47 18,512.32 16778.71 Probability 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Table A.5: Summary of statistics weather data: on both a daily as well as a weekly basis, as can be expected, several statistics except for minimum values are lower on a weekly basis in comparison with a daily basis due to the fact that values are reverted to their mean. All data is observed from 01-01-1987 till 06-10-2010 at 9:00. *, ** and *** indicate statistical significance at the 10%, 5% and1% levels, respectively.
Air pressure Horizontal visibility Cloud cover Humidity Daily Weekly Daily Weekly Daily Weekly Daily Weekly
Number of observations 6,199 1,239 6,198 1,239 6,199 1,239 6,199 1,239 Mean 10,156 10,156 61.59 61.59 5.51 5.51 81.15 81.15 Median 10,164 10,160 64 64 7 5.80 83 82.60 Maximum 10,452 10,405 89 82.6 9 8.40 100 99.40 Minimum 9,660 9,882 0.00 11.8 0 0 31 43 Standard deviation 105.72 85.65 17.03 11.26 2.82 1.65 13.17 10.16 Skewness -0.42 -0.23 -1.40 -1.07 -0.84 -0.78 -0.62 -0.60 Kurtosis 3.43 3.26 5.03 4.30 2.17 3.26 2.81 2.90 Jarque-Bera 230.47 14.52 3,088.82 322.55 909.12 125.52 400.40 75.00 Probability 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
VII. Appendix B: Correlation diagrams
Table B.1: Correlation coefficients weather variables and stock variables: Statistics are based on seasonal observations. Applied values are obtained by calculating both the average monthly weather and stock variables over the available years. Coefficients of ≤-0,4 and ≥0,4 are accentuated. In line with firm size expectations AScX return presents remarkably higher correlation coefficients in comparison with both the AEX return and AMX return.
AEX return AMX return AScX return totmk Vollume Vallue AEX Vollatility Vollatility change Windspeed -0.09 -0.05 0.08 0.19 0.26 0.10 -0.22 Temperature -0.10 0.11 0.14 0.07 0.11 -0.15 0.46 Temperature change 0.10 0.20 0.54 0.29 0.41 -0.21 0.01 Global radiation -0.07 0.36 0.43 0.01 0.24 -0.47 0.31
Rainfall in past hour -0.02 -0.45 -0.44 0.06 -0.25 0.53 0.24
Air pressure -0.35 0.03 0.14 -0.33 -0.27 -0.57 0.29
Air pressure change 0.43 0.67 0.74 -0.22 0.01 -0.39 -0.39
Horizontal sight -0.07 0.28 0.35 0.01 0.17 -0.39 0.38
Cloud cover 0.10 -0.43 -0.51 -0.20 -0.43 0.41 -0.44
Cloud cover change -0.08 -0.03 -0.08 -0.01 -0.09 0.08 -0.13
Humiddity 0.05 -0.44 -0.52 0.01 -0.26 0.54 -0.30
Fog 0.02 -0.36 -0.41 0.00 -0.17 0.38 -0.34
Rain present or not 0.27 -0.44 -0.54 0.05 -0.36 0.79 -0.36
Snow present or not -0.18 0.08 0.08 -0.07 0.05 -0.10 -0.17
