The change in the behavior of odd-lot short sellers.

Marks, Barry R. ; McCormack, Joseph P.

ABSTRACT

Technical indicators of individual investor behavior using odd-lot short selling have been widely studied. Contrarians employ these indicators in their investment strategies because they feel that individual investors who utilize odd-lot short selling tend to get into or out of the market at precisely the wrong times. These technical indicators have even appeared in popular investments textbooks. The current study indicates that these indicators are no longer valid indicators of individual investor behavior.

Daily odd-lot short selling is examined for the period 1970 through 1995 using a generalized autoregressive conditional heteroscedatic (GARCH) model. Results for the period 1970 through 1985 are consistent with previous studies of individual investor behavior. Both a day of the week effect and a turn of the year effect were present. Additionally, odd-lot short selling was significantly related to the previous day's price change.

Results for the period 1986 through 1995 differ significantly from the earlier period. The evidence indicates that individual investors no longer dominate this market. Professional traders now dominate this market. Neither the day of the week effect nor the turn of the year effect were statistically significant, and odd-lot short sales were not related to the previous day's price change.

INTRODUCTION

Technical trading rules based upon odd-lot short sales assume that the trades are being done by unsophisticated individual investors. Heavy odd-lot short selling by individuals is interpreted as a bullish signal to other, more informed, investors (Reilly & Brown, 2000; Colby & Meyers, 1988). Conversely, light odd-lot short selling by individuals is interpreted as a bearish signal.

Today odd-lot sales are just as likely to be made by professional traders as by individuals. One of the requirements of short selling is that it can be accomplished only after an uptick. However, odd-lot short sellers are guaranteed of being able to sell at the next uptick. Professional traders can use odd-lot short selling in an attempt to make arbitrage profits. In fact, Norris (1986) claims that the dominant traders in odd-lot short sales are professional traders rather than unsophisticated individuals.

This study investigates the day of the week effect, the turn of the year effect, the holiday effect, and the previous day price change effect for the period 1970 through 1995. The total sample was split into two parts. One part covered the period 1970 through 1985 and the other part covered the period 1986 through 1995. The results indicate the existence of a day of the week effect, a turn of the year effect, and a previous day price change effect in the first period. The day of the week effect and a turn of the year effect have been documented for individual investors by many other researchers. This day of the week effect, turn of the year effect, and previous day price change effect are not statistically significant during the later period of the study.

We employ a generalized autoregressive conditional heteroscedasticity (GARCH) model. This statistical methodology is an improvement over an equality of means test. Equality of means tests implicitly assume (1) that each daily observation is independent of observations from previous days and (2) that the variance is constant over the time period of the study. Although this approach is widely used to investigate the day of the week effect, the turn of the year effect, and the holiday effect in rate-of-return studies, such a statistical approach may be invalid in studies where the dependent variable is dependent upon observations from prior days or where the variance of the error in the model is not constant. Furthermore, an equality of means type test cannot easily be extended to consider simultaneous effects that variables may have on each other. The GARCH model corrects for these weaknesses. The empirical results from this study indicate that odd-lot short sales follow such a model.

This paper consists of the following five sections. The first section is a review of the literature on the behavior of the individual trader. The second and third sections describe the data and the methodology respectively. The fourth section presents the results of the study and is followed by a summary and conclusion.

REVIEW OF THE LITERATURE

Recent studies on stock market activity have investigated the relationship between the behavior of individual investors and certain stock market anomalies. Lakonishok and Maberly (1990) argue that individual investors are likely a cause of the negative returns observed on Mondays because individual investors analyze and/or evaluate their portfolios on the weekend and then institute their trades on Mondays. Lakonishok and Maberly find that the ratio of odd-lot sales minus odd-lot purchases divided by New York Stock Exchange (NYSE) trading volume was highest on Mondays indicating that individual investors sell more shares on Monday than on any other day of the week and therefore appear to have more influence on the market on Mondays. They also find that NYSE block volume as a percentage of total NYSE volume was lowest on Mondays indicating that institutional investors tend to be less active in the market on Mondays.

Dyl and Maberly (1992) suggest that the January effect is influenced by the trading of individual investors. They observe that the ratio of odd-lot sales to odd-lot purchases is dramatically higher at the close of the year relative to the beginning of the subsequent year. Ritter (1988) finds the mean daily buy/sell ratio of cash account customers of Merrill Lynch, Pierce, Fenner, and Smith is lower at the end than at the beginning of the year. Ritter suggests that this activity may be related to the tax-loss selling in December following bear markets and the parking of the proceeds until January.

Dyl and Maberly also notice that the ratio of odd-lot sales to odd-lot purchases is extremely high two days before Christmas and two days before New Year's Day. They suggest that this behavior may explain the high positive returns on the trading day immediately preceding these two holidays (Pettengill, 1989; Ariel, 1990).

DATA

Aggregate daily odd-lot short selling data for the NYSE were obtained from various issues of Barron's for the period 1970 through 1995. Daily short sales figures were checked for errors against both weekly totals for odd-lot short selling, which appear in Barron's, and against daily odd-lot short selling, which appear in the Wall Street Journal. Aggregate daily trading volume of the NYSE and the level of the NYSE Composite Index were obtained from Barron's.

METHODOLOGY

Generalized autoregressive conditional heteroscedastic (GARCH) models have frequently been applied to the analysis of financial time series (Engle et al., 1987; De Jong et al., 1992; Kodres, 1993; Vlaar & Palm, 1993). The GARCH model allows the conditional variance of the error term in a linear regression model to evolve over time.

The following GARCH model was investigated in this paper:

LPSHORTt = [beta]0 + [beta]1LPSHORTt-1 + [beta]2LPSHORTt-2 + [beta]3LPSHORTt-3 + [beta]7M + [beta]8T + [beta]9W + [beta]10F + [beta]11DEC + [beta]12JAN + [beta]13PREH1 + [beta]14PREH2 + [beta]15POST1 + [beta]16POST2 + [beta]17LNYSE1 + vt vt = et - 1vt-1 - 2vt-2 - 3vt-3 - 4vt-4 - 5vt-5 - 6vt-6 - 7vt-7 - 8vt-8 9vt-9 - 10vt-10 - 11vt-11 - 12vt-12 - 13vt-13 - 14vt-14 - 15vt- 15 16vt-16 - 17vt-17 - 18vt-18 - 19vt-19 - 20vt-20, et = ut ht, ht = 0 + 1et-12 + 1ht-1 + 2ht-2,

where ut is an independent normally distributed random variable at time t with a mean of zero and a variance of one. The variables in the above equation are defined in Table 1. The variance vt is the conditional error at time t. It has both an autoregressive component and heteroscedastic component. The coefficients in the equation for the heteroscedastic component ht are constrained to be greater than or equal to zero in the maximum likelihood estimation procedure to ensure that ht is always positive.

The dependent variable LPSHORTt is the natural logarithm of one plus the rate of change in the number of aggregate odd-lot shares sold short on the NYSE. Since the number of odd-lot shares sold short increased dramatically over the period from 1970--1995, the rate of change is a more appropriate dependent variable then simply the number of odd-lot shares sold short. The number of odd-lot shares sold short each day was highly variable. For instance, the sales on day t might be 100,000 shares, the sales on day t+1 might be 400,000 shares, and the sales on day t+2 might revert back to 100,000 shares. The rate of change from day t to day t+1 is 3.00, while the rate of change from day t+1 to day t+2 is -.75. Because of this asymmetric movement in the rate of change, the dependent variable was chosen to be the natural logarithm of one plus the rate of change in the number of odd-lot shares sold. In this case, the dependent variable for the rate of change from day t to day t+1 is ln(1+3.00), which is 1.3863, and the dependent variable for the rate of change from day t+1 to day t+2 is ln(1-.75), which is -1.3863.

The first set of independent variables in the model consists of LPSHORTt-1, LPSHORTt-2, and LPSHORTt-3. These variables are the dependent variable at time t lagged one through three days, respectively. The variables M, T, W, and F are zero-one independent variables representing days of the week. Since no variable is defined for Thursday, the coefficients of variables M, T, W, and F represent the difference in the dependent variable on those days compared to the level of the dependent variable on Thursday. Lakonishok and Maberly (1990) observe that the ratio of odd-lot sales minus odd-lot purchases divided by New York Stock Exchange (NYSE) trading volume is highest on Mondays. If any of the current coefficients are statistically significant, then a day of the week effect exists in the behavior of odd-lot short sellers.

Two variables are assigned to represent odd-lot short sales in either December or January. These zero-one dummy variables are DEC and JAN. Dyl and Maberly (1992) report that the ratio of odd-lot sales to odd-lot purchases is dramatically higher at the close of the year relative to the beginning of the next year. Brent et al. (1990) suggest that individual investors may increase their short selling in December for tax reasons. Investors who want to postpone payment of taxes on gains from holding common stock may sell short common stocks which they own to lock in their profit for the year. Investors would then recognize their gain in the next tax year by closing out their positions in the next year. Researchers have also observed that the month of January is unique because it has higher excess returns and stock price volatility than other months (Glosten, et al., 1993).

Variables PREH2, PREH1, POST1, and POST2 capture the potential holiday effect. These variables are zero-one variables which identify the day two days before a holiday, one day before a holiday, one day after a holiday, and two days after a holiday respectively. Dyl and Maberly (1992) observe different behavior of individual investors in purchases and sales of odd-lots on the NYSE prior to the Christmas and New Years Day holidays but did not investigate investor behavior around other holidays. If any of the four variables above are statistically significant, then a holiday effect exists for odd-lot short sellers.

Another independent variable is VOLD, which is the natural logarithm of one plus the rate of change in volume of shares traded on the New York Stock Exchange (NYSE) on day t. This variable measures the change in the level of trading by all investors on the NYSE for day t. The change in odd-lot short sales should be positively related to this variable.

The last independent variable is LNYSE1, which is the natural logarithm of one plus the rate of change in the NYSE stock price index for the previous day. This variable was included in the model to determine whether odd-lot short sellers react in a belated manner to changes in stock prices. Some researchers argue that short sellers are contrarians (Hanna, 1976). If this is indeed the case, then short selling should increase as stock prices increase and the coefficient of this variable should be positive. However, if individual investors react in concert with the market in a belated manner, their short selling will increase after the market falls and decrease after the market rises. This behavior will be reflected by a negative coefficient.

RESULTS

This section is divided in two parts. The first portion contains some descriptive information about the dependent variable, while the second portion discusses the results from the GARCH model. Table 2 shows the mean and standard deviation for the dependent variable broken down by day of the week, month of the year, and holiday effect. The first section of the table analyzes the day of the week effect. Although the means vary across days of the week, the analysis of variance test for the equality of means across days of the week does not reject the null hypothesis that the means are the same across all days of the week at the .05 significance level. The second section of the table gives the mean of the dependent variable grouped into three different categories, December, January, and all other months. The null hypothesis that the means are the same across the three categories cannot be rejected at the .05 significance level. The third section is related to the holiday effect. The dependent variable was broken down into five different categories. The null hypothesis that the means are the same across the five categories is rejected at the .01 level. The hypothesis tests discussed in this section may be inaccurate because the analysis of variance test assumes that each daily observation is independent of observations for the prior days and that the variance is constant over time. These weaknesses do not exist in the GARCH model.

The results from the GARCH model for the entire 1970-1995 period are presented in Table 3. The parameters presented in Table 3 were obtained by maximizing the likelihood function for the model. The likelihood ratio test was performed to determine if additional variables should be added to the equations for LPSHORTt, vt and ht. The two variables considered for inclusion in the equation for LPSHORTt were LPSHORTt-4 and ht, while vt-21 was tested for inclusion in the equation for vt. The variables et-22 and ht-3 were considered for addition to the equation for ht. The coefficients for the terms in the equation for ht were constrained to be positive in the estimation process. Therefore, the likelihood ratio test criterion for verifying the null hypothesis was taken from the table in Kodde and Palm (1986). The addition of either et-22 or ht-3 to the equation for ht did not increase the explanatory power of the model. Vlaar and Palm (1993) applied this procedure to select the number of lag terms for their GARCH model. The likelihood ratio test could not reject the null hypothesis (at the .05 significance level) for any of the above mentioned cases.

The empirical evidence indicates the dependent variable is related to its value one through three days earlier. Hence, the dependent variable does not appear to be independent of previous observations, which is assumed in an analysis of variance test for differences in the mean. The level of trading volume on the NYSE (LVOLD) is positively related to odd-lot selling activity. Since two of the coefficients related to the day of the week effect are significant, a day of the week effect is apparent. The change in odd-lot selling from Friday to Monday is statistically higher than the default level of trading from Wednesday to Thursday. Similarly, the change in odd-lot selling from Monday to Tuesday is statistically lower than trading from Wednesday to Thursday. These results are consistent with the observation of Lakonishok and Maberly (1990) that the ratio of odd-lot sales minus odd-lot purchases divided by NYSE trading volume was highest on Mondays.

A turn of the year effect is also evident in the data. The change in daily trading is smaller in December, while the change in daily trading is higher in January. Hence, the demand for odd-lot short selling is more stable in December which is consistent with the tax hedging hypothesis. The demand for odd-lot short selling is more variable in January which is consistent with the higher market volatility and excess stock returns in January (Glosten, et al., 1993). The change in daily odd-lot short selling increases one trading day after a holiday. Such a result is not consistent with the Dyl and Maberly observation that the ratio of odd-lot sales to odd-lot purchases is high two trading days before Christmas and New Year's Day. But, the current study examined all holidays.

The change in odd-lot short selling was also related to the previous day price change. If prices rise on the NYSE, then short selling declines the next day; if prices fall on the NYSE, then short selling increases the next day.

The intricate modeling of the error term in the GARCH model had a major impact on the results. Neither the turn of the year, or holiday effect coefficients were significant at the .05 level in the ordinary least square regression equation, but one of the days of the week coefficients (Tuesday) was significant. The moving average terms in the equation for the conditional error variance vt were statistically significant at the .01 level in the GARCH model. Furthermore, each of the coefficients in the equation for ht was significant at the .05 level.

The heteroscedastic component, ht, increased dramatically starting in 1985. The level and variability of odd-lot short selling increased around this time. Norris (1986) stated: "Now the odd-lot shorting is done largely by professionals, but they act only when there is such a negative attitude in the futures pits that such shorting can lock in arbitrage profit."

The original sample was broken into two parts. One part covers the period 1970 through 1985 and the other part covers the period 1986 through 1995. Empirical results for the first period are given in Table 4. Except for the first day after a holiday, all the independent variables in the equation for LPSHORTt, which were significant in the total sample, are significant in the sample for the period 1970 through 1985. The first day after a holiday is not statistically significant--but the second day after a holiday is significant at the .05 level.

For the early subsample, each of the moving average terms in the equation for the conditional error variance, vt, were statistically significant at the .05 level. Furthermore, each of the coefficients in the equation for ht was significant at the .05 level. The main difference between the early subsample and the entire sample is related to the timing of the post holiday effect.

For the subsample covering the years 1986-1995 in Table 5, both the day of the week effect and the turn of the year effect are no longer significant. Also the change in odd-lot short selling is no longer related to the change in stock prices from the previous day. The post holiday effect is, however, significant for both days after a holiday. The absence of the day of the week effect and the turn of the year effect is inconsistent with the results obtained by Lakonishok and Maberly (1990) and Dyl and Maberly (1992) respectively.

For the later subsample, each of the moving average terms in the equation for the conditional error variance vt were statistically significant at the .01 level, except for vt-20. Furthermore, only the coefficient for et-12 and for ht-1 in the equation for ht were significant at the .05 level.

SUMMARY AND CONCLUSION

Lakonishok and Maberly (1990) and Dyl and Maberly (1992) track the aggregate behavior of odd-lot sales and purchases of stocks on the NYSE. They believe that analyzing this data would lead to a better understanding of the behavior of individual investors. Lakonishok and Maberly observed a day of the week effect, and Dyl and Maberly found a turn of the year effect.

This paper investigates the aggregate behavior of odd-lot short sellers on the NYSE. We also found a day of the week effect and a turn of the year effect for 1970-1985. However, these effects were not statistically significant for 1986-1995. The results for the 1986-1995 time period support the Norris' assertion that professional traders now dominate the market for odd-lot short sales. This assertion is further strengthened by the fact that during 1970-1985, odd-lot short selling was significantly related to the previous day's price change, whereas it was not significant during the 1986-1995 time period. The results indicate that individual investors no longer dominate the odd-lot short selling market. These findings indicate that the use of odd-lot short selling as an indicator of individual investor behavior may no longer be valid.

The generalized autoregressive heteroscedasticity technique (GARCH) improved the explanatory power of the model. The dependent variable in the model was dependent on observations from prior days and the variance of the error term did vary over the time period of this study. The results from this study indicate that the GARCH model should be applied to other studies of individual investor behavior.

REFERENCES

Ariel, R. A. (1990). High stock returns before holidays: existence and evidence on possible causes. Journal of Finance, 45(5), 1611-1626.

Brent, A., D. Morse & E. K. Stice (1990). Short interest: explanations and tests. Journal of Financial and Quantitative Analysis, 25(2), 273-289.

Colby, R. W. & T. A. Meyers (1988). The encyclopedia of technical market indicators. Homewood, IL: Dow-Jones. De Jong, F., A. Kemna & T. Kloek (1992). A contribution to event study methodology with an application to the Dutch stock market. Journal of Banking and Finance, 16(1), 11-36.

Dyl, E. & E. Maberly (1992). Odd-lot transactions around the turn of the year and the january effect. Journal of Financial and Quantitative Analysis, 27(4), 591-604.

Engle, R. F., D. M. Lilien & R. P. Robins (1987). Estimating time varying risk premia in the term structure: the Arch-M model. Econometrica, 55(2), 391-407.

Glosten, L. R., R. Jagannathan & D. E. Runkle (1993). On the relation between the expected value and volatility of the nominal excess return on stocks. Journal of Finance, 48(5), 1779-1801.

Hanna, M. (1976). A stock price predictive model based on changes in ratios of short interest to trading volume. Journal of Financial and Quantitative Analysis, 11(5), 965-985.

Kodde, D. & F. Palm (1986). Wald criteria for jointly testing equality and inequality restrictions. Econometrica, 54(5), 1243-1248.

Kodres, L. E. (1993). Tests of unbiasedness in foreign exchange futures markets: An examination of price limits and conditional heteroscedasticity. Journal of Business, 66(3), 463-490.

Lakonishok, J. & E. Maberly (1990). The weekend effect: trading patterns of individual and institutional investors. Journal of Finance, 45(1), 231-243.

Norris, F. (1986, August 25). Odd-lot short sales: an old indicator's new lease on life. Barron's, 21 & 36.

Pettengill, G. N. (1989). Holiday closings and security returns. Journal of Financial Research, 12(1), 57-67.

Reilly, F. & K. Brown (2000). Investment analysis and portfolio management, 6th edition. Fort Worth, TX: Dryden Press.

Ritter, J. (1988). The buying and selling behavior of individual investors at the turn of the year. Journal of Finance, 43(3), 710-717.

Vlaar, P. J.G. & F. C. Palm (1993). The message in weekly exchange rates in the European monetary system: mean reversion, conditional heteroscedasticity, and jumps. Journal of Business and Economic Statistics, 11(3), 351-360.

Barry R. Marks, University of Houston-Clear Lake

Joseph P. McCormack, University of Houston-Clear Lake

Table 1: Variable Definitions

LPSHORTt = Natural logarithm of one plus the rate of change in short
selling for day t.

LVOLD = Natural logarithm of one plus the rate of change for volume
of trading on the NYSE for day t.

M = 1 if day t is Monday; 0 otherwise.

T = 1 if day t is Tuesday; 0 otherwise.

W = 1 if day t is Wednesday; 0 otherwise.

F = 1 if day t is Friday; 0 otherwise.

DEC = 1 if day t is in December; 0 otherwise.

JAN = 1 if day t is in January; 0 otherwise.

PREH1 = 1 if day t is one day prior to a holiday; 0 otherwise.

PREH2 = 1 if day t is two days prior to a holiday; 0 otherwise.

POST1 = 1 if day t is one day after a holiday; 0 otherwise.

POST2 = 1 if day t is two days after a holiday; 0 otherwise.

LNYSE1 = Natural logarithm of one plus the rate of change in the NYSE
stock price index for day t-1.

Table 2: Test for Differences in Means
Years 1970-1995

Days of the Week Standard Number of
Variable Mean Deviation Observations

M .00262 .80235 1256
T -.00179 .78624 1341
W .03801 .70422 1345
R -.01638 .72510 1318
F -.02015 .74393 1310

Analysis of Variance Test for Equality of Means

F = 1.25

Month of the Year Standard Number of
Variable Mean Deviation Observations

December -.00823 .68586 548
January .01983 .77827 550
All other months -.00043 .75667 5472

Analysis of Variance Test for Equality of Means

F = .22

Holiday Effect Standard Number of
Variable Mean Deviation Observations

Two days prior to holiday .02330 .71878 209
One day prior to holiday -.16097 .86568 210
One day after holiday .11686 .96554 208
Two days after holiday .09546 .79968 207
All other days -.00194 .73799 5736

Analysis of Variance Test for Equality of Means

F = 4.55 *

* Significant at .01 level.

Table 3: Estimates of Model Parameters
Years 1970-1995

Variable Coefficient t-Statistic

Equation LPSHORTt

Intercept -.01293 -.980
LPSHORTt-1 .13583 3.906 *
LPSHORTt-2 -.09133 -2.546 **
LPSHORTt-3 -.11862 -3.211 *
LVOLD .63361 20.516 *
M .09598 5.149 *
T -.06978 -3.704 *
W .02318 1.005
F .01966 .865
DEC -.02827 -5.595 *
JAN .01810 3.655 *
PREH1 -.04764 -1.432
PREH2 -.02411 -.822
POST1 .09814 2.887 *
POST2 -.03638 1.208
LNYSE1 -2.9949 -7.926 *

Equation vt

vt-1 .71317 19.743 *
vt-2 .48629 9.752 *
vt-3 .28189 6.351 *
vt-4 .24389 7.312 *
vt-5 .23331 9.573 *
vt-6 .22453 11.927 *
vt-7 .20521 10.519 *
vt-8 .19751 9.809 *
vt-9 .17143 8.471 *
vt-10 .15018 7.865 *
vt-11 .14695 8.086 *
vt-12 .13840 7.570 *
vt-13 .15407 8.401 *
vt-14 .13366 7.347 *
vt-15 .12999 7.128 *
vt-16 .12121 6.706 *
vt-17 .10213 5.759 *
vt-18 .07518 4.380 *
vt-19 .05293 3.302 *
vt-20 .03509 2.696 *

Equation ht

Intercept .00070 2.843 *
et-12 .05899 9.594 *
ht-1 .29463 9.308 *
ht-2 .64465 20.294 *

* Significant at .01 level.

** Significant at .05 level.

Table 4: Estimates of Model Parameters
Years 1970-1985

Variable Coefficient t-Statistic

Equation LPSHORTt

Intercept -.01580 -1.098
LPSHORTt-1 .14752 3.253 *
LPSHORTt-2 -.08667 -2.536 **
LPSHORTt-3 -.10444 -2.246 **
LVOLD .60674 17.690 *
M .11677 5.989 *
T -.06964 -3.518 *
W .02266 .920
F .01440 .590
DEC -.02976 -5.180 *
JAN .01850 3.008 *
PREH1 -.03283 -.891
PREH2 -.04544 -1.386
POST1 .06717 1.809
POST2 .06620 1.995 **
LNYSE1 -3.06898 -7.489 *

Equation vt

vt-1 .72961 15.291 *
vt-2 .49826 10.816 *
vt-3 .30001 5.360 *
vt-4 .24630 5.534 *
vt-5 .23451 7.078 *
vt-6 .22580 9.193 *
vt-7 .19323 7.723 *
vt-8 .17886 7.105 *
vt-9 .15799 6.128 *
vt-10 .14580 5.847 *
vt-11 .14584 5.779 *
vt-12 .14073 5.715 *
vt-13 .15186 6.339 *
vt-14 .13248 5.708 *
vt-15 .12418 5.322 *
vt-16 .12679 5.572 *
vt-17 .10078 4.505 *
vt-18 .06595 3.098 *
vt-19 .04548 2.297 **
vt-20 .04231 2.606 *

Equation ht

Intercept .00096 1.861
et-12 .05620 6.490 *
ht-1 .16636 2.175 **
ht-2 .77257 10.358 *

* Significant at .01 level.

** Significant at .05 level.

Table 5: Estimates of Model Parameters
Years 1986-1995

Variable Coefficient t-Statistic

Equation LPSHORTt

Intercept .00167 .047
LPSHORTt-1 .13300 1.326
LPSHORTt-2 -.16937 -2.079 **
LPSHORTt-3 -.09346 -1.031 *
LVOLD .81005 9.151 *
M -.00982 -.195
T -.08140 -1.520
W .02018 .344
F .05528 .939
DEC -.01902 -1.450
JAN .01313 .942
PREH1 -.10414 -1.256
PREH2 .09042 1.190
POST1 .29249 3.324 *
POST2 -.16399 -2.033 **
LNYSE1 -1.19552 -1.120

Equation vt

vt-1 .69593 6.812 *
vt-2 .40857 3.417 *
vt-3 .24462 2.920 *
vt-4 .25120 3.846 *
vt-5 .24884 6.956 *
vt-6 .21867 6.323 *
vt-7 .21169 5.775 *
vt-8 .21440 6.067 *
vt-9 .19036 5.534 *
vt-10 .15943 4.853 *
vt-11 .15217 4.951 *
vt-12 .12776 4.454 *
vt-13 .14926 5.419 *
vt-14 .12578 4.508 *
vt-15 .13634 5.064 *
vt-16 .10694 4.054 *
vt-17 .09251 3.628 *
vt-18 .07599 3.033 *
vt-19 .06089 2.594 *
vt-20 .02209 1.063

Equation ht

Intercept .00041 .647
et-12 .05188 4.261 *
ht-1 .54453 2.266 **
ht-2 .40307 1.724

* Significant at .01 level.

** Significant at .05 level.