Tammy R.
Parker tparker@ulm.edu is an Associate
Professor of Economics and Alumni Endowed Professor of Entrepreneurship,
University of Louisiana at Monroe. Michael E. Parker
mparker@ulm.edu is an Associate Professor
of Finance, University of Louisiana at Monroe.
|
The
paper investigates the comovement between stock indexes of eight Asian countries
in order to ascertain empirical evidence of market inefficiency and the
transmission of financial market occurrences. The study utilizes cointegration and
common serial correlation feature tests to determine the existence of
interrelatedness between the stock market variables. Some empirical evidence is found to
support market inefficiency among these Asian countries. This finding indicates that market
problems in one country would quickly migrate to the other Asian countries.
|
Introduction
The Asian crisis, which began in 1996 and continued through the early part of 1998, marked the end of a decade of average growth rates of 7.4 percent for the countries of Korea, Thailand, Malaysia, Taiwan, Singapore, Hong Kong, Indonesia, and the Philippines. Between 1985 and 1995, these East Asian countries were commonly referred to as the “miracle economies”. These countries first made shoes and garments, but quickly converted to heavy industry and electronics that led to unprecedented growth levels. Beginning in 1996, growth rates weakened, export trade fell, and currencies depreciated as many people lost confidence in the economies of these countries. Thereby, the beginning of the Asian crisis occurred which resulted in loan intervention by the IMF to help bring an end to the chaos.
In the year 2000, the potential for a second Asian crisis was far from over. The Indonesian rupiah, the Thai baht, and the Philippine peso were all down since the beginning of the year. The rupiah was down 25 percent since January, making it the world’s worst performing currency (Einhorn and Shari, 2000). Jittery investors, low consumer spending, high levels of non-performing loans, and high levels of foreign debt all contributed to this situation. In addition, equity investors were hesitant to invest in these stock markets due to the fear of currency depreciation eroding their stock values. For example, the Thai stock market index was down 42 percent in U.S. dollars during the first six months of 2000 and the Indonesia stock market index was down 43 percent during the same time period. The question to be addressed in this research paper is whether the stock markets of these “miracle economies” can help explain or predict the Asian crisis of 1996 -1998 and future Asian turmoil.
This study will investigate comovement of the stock market indexes of Korea, Taiwan, Hong Kong, Singapore, Malaysia, Thailand, Indonesia, and the Philippines by concentrating on the persistence of disturbances and the comovement of various series during the last decade. The tendency of fluctuations in economic activity to synchronize internationally is analyzed by testing whether these features are common across countries. However, as with any asset price, we would expect those prices to be efficiently determined in the market.
The concept of efficient markets was originated by Fama (1965), who described an efficient market as consisting of a large number of profit maximizers and in which prices will reflect all information available so that no profit opportunities are left to be exploited. The Economist (Jan 2, 1998) provides numerous examples of reasons why the Asian stock markets would not be efficiently determined. The basic reasons include the following: 1) families that are quite powerful retain majority stakes in public companies and exercise tight control over the companies; and 2) interests of the management of companies and politicians are closely interwoven. This has led to insider trading, trades occurring at above-market prices; and general biases against minority shareholders.
These countries were chosen due to their pronounced involvement in the Asian crisis that began 1996. If comovement between the stock market indexes is found to exist, not only would this indicate market inefficiency in the sense of asset price efficiency as put forth by Fama (1965), but it would also provide a catalyst for the spread of the financial crisis between the countries being investigated.
Methodology
|
In order to investigate whether the financial markets move together among the countries studied, an analysis of the persistence of disturbances and the comovement of the stock market indexes will be performed. Cointegration is one way to simultaneously model long-run persistence and comovement. However, this investigates forms of comovement which are nonstationary only. Comovement can also be of the stationary nature which would mean that the common shocks are less persistent than unit roots. In order to investigate stationary comovement, common feature tests will be utilized. The existence of a long term relationship among stock market data will be tested using the Johansen (1988) and Johansen and Juselius (1990) methodology for cointegration. The existence of a cointegrating relation would imply comovement of the stock indexes of the countries investigated which would provide evidence of the interconnectedness of the financial markets since series that are cointegrated can be expressed with a causal ordering in at least one direction. [1] This interrelatedness of the financial markets could explain why the Asian financial crisis in 1996-1997 affected so many of the Asian countries. The crisis began in Thailand, but quickly spread to Malaysia, Indonesia, the Philippines, Taiwan, and Korea. The bivariate pairings which do not demonstrate a cointegrating relation will be subjected to a more stringent test for comovement called common serial correlation feature tests developed by Engle and Kozicki (1993). The finding of a common serial correlation between variables implies the existence of stationary comovement of stock indexes and therefore implies at least one way causality. [2] This stationary comovement could also be interpreted as evidence of the interrelatedness of the financial markets of these countries on a macroeconomic level. Similar to the detection of nonstationary comovement, the finding of stationary comovement would provide evidence of market inefficiency and a conduit for the spread of financial chaos between these countries. The use of cointegration tests are relatively common in the literature and the reader is referred to Johansen (1988) and Johansen and Juselius (1990) for a complete discussion. Common feature testing is relatively new to the literature and a brief elaboration on the methodology follows. Cointegration tests investigate long term relationships by analyzing forms of comovement of variables that are nonstationary. In order to investigate the forms of comovement that are stationary, common features can be analyzed. Common feature testing is performed among stationary variables. Many macroeconomic variables in their levels are nonstationary and are stationary in their first differences (Nelson and Plossner, 1982). Therefore, it is necessary to perform common feature tests on the first differences of most variables. Although stationarity tests are performed in the paper, we assume stationarity in first differences of the variables we are considering for methodology exposition purposes. The first differences of the logs of the stock index variables of two countries will share a common feature if comovement of the variables exists between the two countries. The common feature for which we test is serial correlation. The finding of a common serial correlation feature between two stock index variables implies at least one way causality. The finding of such a common feature will indicate persistence and comovement in the system. Common serial correlation will be tested by using the test statistic developed by Engle and Kozicki (1993). The model for a common feature test between the stock index of one country (s1,t) and the stock index of a second country (s2,t) where the common feature is generated by a vector of variable wt is given by
In this model, ct is a constant term and wt is a serial correlation feature which may be common to both series. The error terms are serially uncorrelated. The linear combination, s1,t - d s2,t, can be written in the following way: (2) s1,t - d s2,t=ct(b1-db2)+wt(g1-dg2)+Єt
If there exists a parameter, d, such that g 1-d g2=0, then wt is not a component of the linear combination. In this case, wt is called a common feature. If wt is a serial correlation common feature, then the linear combination s1,t - d s2,t will be serially uncorrelated. The steps involved for the bivariate common serial correlation test are summarized below. First, to test for a bivariate common serial correlation feature, you must first test for the existence of the serial correlation feature in the individual series. Second, you must determine among the pairs identified as having the serial correlation feature within the individual series which of these pairs is the feature due to a common component. That is, estimate the following equation for the pairs identified as having the feature within the individual series:
Estimate this equation using the limited-information maximum likelihood (LIML) approach where the instrument list is an intercept and the lags of s1,t and s2,t. By using the LIML approach the parameter estimate is insensitive to normalization. Then estimate a regression of the residuals from (3) on the lags of s1,t and s2,t given by the following:
The value of the T*R2 (where T equals the number of observations and R2 is the percentage of explained variation divided by total variation in the model) from this model is the relevant test statistic, with a chi-squared distribution, of the common feature test as proposed by Engle and Kozicki (1993). Refer to Engle and Kozicki (1993, p.371-372) for details of the test statistic. The null hypothesis of this test statistic is that the linear combination of the variables does not have the feature, that is, the feature is common for the two variables in question. The alternative hypothesis is that the linear combination of the variables does have the feature and therefore the feature is not common between the two variables. Keep in mind that each individual series must have the feature present before it is relevant to test whether that feature is common between two series. This means that in step one of the procedure, we must reject the null hypothesis of no feature to proceed. However, in the last step of the procedure in which we investigate the existence of the feature for the linear combination of the variables, it is the acceptance of the null hypothesis of no feature that implies that the feature is common between the two series. Recall if the feature is common, this implies at least one-way causality and therefore comovement among the stock indexes being investigated.
|
Data and Empirical Results
The data used in this study are stock market indexes for the countries of Korea, Taiwan, Hong Kong, Singapore, Malaysia, Thailand, Indonesia, and the Philippines. Specifically, the indexes included in the study are the following: the KOSPI Composite Index, the Taipei Stock Index (Taiwan), the Hang Seng Stock Index (Hong Kong), the All-Share Index (Singapore), Kuala Lumpur Composite Index (Malaysia), the SET General Index (Thailand), the Jakarta Composite Index (Indonesia), and the Philippine Stock Index (Philippines). Although the indices used in this study vary on sample, weighting, and computation means, they are still comparable in this context. Each index represents the broad market indicator for their respective countries. Since this methodology looks at comovement and not rates of return from the indexes, the variances in indexes will not affect the outcome of the study. The data is weekday data, and 2,760 data points are contained in each series. The time period investigated is from January 1, 1990 through June 31, 2000. The data was obtained from DRI/McGraw Hill.
Prior to cointegration and common feature testing, the order of integration needs to be ascertained. The order of integration of the individual time series is determined using the augmented Dickey-Fuller test (Fuller, 1976; Dickey and Fuller, 1981), the Phillips-Perron test (Phillips, 1987; Perron, 1988; Phillips and Perron, 1988), and the KPSS test (Kwaitkowski, Phillips, and Shin, 1992). For all of the six countries investigated, the output variable is found to be nonstationary in levels and stationary in first differences. That is, the variables are integrated of order one. The results of the unit root tests are reported in Table One.
To investigate the comovement among the nonstationary variables in their levels, the cointegration test is applied on a bivariate basis. The lag lengths to be used in the bivariate cointegration models were determined by the AIC criteria (Akaike, 1973). The null hypothesis for the trace statistic is that there are r or fewer cointegrating vectors and the alternative hypothesis is that there are at least r+1 cointegrating vectors. The null hypothesis for the maximum eigenvalue statistic is that there are r cointegrating vectors and the alternative hypothesis is that there are r+1 cointegrating vectors. The results of these bivariate cointegration tests are reported in Table Two.
For the trace test with the null hypothesis of no cointegration (r≤0) results range from a high of 19.74 for the pairing of Hong Kong and Taiwan to a low of 1.27 for the pairing of Korea and Thailand. The critical value for the trace test for null hypothesis of r≤0 is 12.53 (10.47) at the 95 percent (90 percent) significance level. The null hypothesis is rejected in five of the possible twenty-eight pairings at the 90 percent level or above. The critical value for the trace test for the null hypothesis of r≤1 is 3.84 (2.86) at the 95 percent (90 percent) significance level. Here, we accept the null hypothesis in most instances. For the pairing of Indonesia and Hong Kong we reject this null hypothesis; however, this result is not in interpretable. Therefore, the trace test supports the finding of one cointegrating vector in five of the pairings.
For the maximum likelihood test with a null hypothesis of r=0, the results range from a high test statistic of 17.01 for the pairing of Hong Kong and Taiwan to a low of 1.00 for Thailand and Taiwan. The critical value for the maximum likelihood test with the null hypothesis of r=0 is 11.44 (9.52) at the 95 percent (90 percent) statistical significance level. The null hypothesis is rejected in six of the possible twenty-eight pairings at the 90 percent level of significance or above. The critical value for the maximum likelihood test with the null hypothesis of r=1 is 3.84 (2.86) at the 95 percent (90 percent) statistical significance level. The results are similar to the trace statistic test results.
Overall, the trace and maximum likelihood tests are in agreement that five of the twenty-eight pairings exhibit a cointegrating vector. That is, the following pairs exhibit comovement among their stock market indexes: Indonesia and Philippines; Indonesia and Singapore; Malaysia and Korea; Korea and Singapore; and Hong Kong and Taiwan. The results of the cointegration test are supportive of nonstationary comovement of stock market indexes between these five pairings of Asian countries. These results provide evidence of inefficient stock markets in these countries as they relate to each other. These inefficiencies and interrelatedness between the countries listed above could facilitate the explaining of the spread an Asian financial crisis among these countries.
The twenty-three pairings not exhibiting nonstationary comovement, as detected by cointegration tests, can be further investigated by analyzing possible stationary comovement between the variables. If additional comovement was indicated among these additional twenty-three pairs the results could be more conclusive regarding overall comovement, that is, market inefficiencies, for these Asian countries.
For the twenty-three bivariate pairings for which no cointegrating relation was found to exist, further comovement tests are performed by investigating the stationary comovement which can be detected by a common serial correlation feature test. The first step of the bivariate common serial correlation feature test is to establish the existence of the feature in each individual series. Equation 1 (above) is estimated, where wt is a vector of the lags of s1,t and s2,t, and the relevant test statistic is presented in Table Three.
Recall the variables are in first difference in order to meet the stationarity criteria. In the table, the LM test statistic is provided and is distributed chi-squared with two degrees of freedom. The null hypothesis is that the feature does not exist within the series and the alternative hypothesis is that the feature does exist within the series. The critical value at the 10 percent level is 4.61. For all pairings, we reject the null hypothesis and conclude that the serial correlation feature does exist within the individual series. Therefore, we proceed to test as to whether the feature, which exists within the individual series, is actually a common feature between the two series referred to in the pairings.
The second step in testing for common features is to test the pairs that were identified in the first step as having the feature individually and to ascertain for which of these pairs the feature is due to a single component. The empirical results of Equation 4 (above) for the twenty-three pairings investigated are summarized in Table Four. Table Four contains four entries. The first entry is the feature test statistic which is distributed chi-squared with one degree of freedom with critical values of 2.71 and 3.84, respectively, at the 10 percent and 5 percent levels. The null hypothesis of the feature test statistic is that no feature exists for the linear combination of the two variables, which signifies that the feature is actually common between the two stock market series. The second entry is the coefficient estimate of d from Equation 3 (above) and the third entry is the t-statistic for this coefficient (for the test to be valid, d needs to be statistically significant). The fourth entry is the Ljung-Box Q(12) statistic for the minimum linear combination error term from Equation 4.
For the twenty-three pairings that are investigated for the existence of a common feature, ten accept the null hypothesis of the LIML common feature test. This implies that for these ten pairings stationary comovement exists between the stock market indexes of these countries on a bivariate basis. These pairings include: Indonesia and Malaysia; Indonesia and Hong Kong; Malaysia and the Philippines; Malaysia and Thailand; Malaysia and Taiwan; Philippines and Hong Kong; Philippines and Taiwan; Korea and Thailand; Singapore and Thailand; and Thailand and Taiwan.
However, thirteen of the pairings reject the null hypothesis of having the feature in common. These pairings include: Indonesia and Korea; Indonesia and Thailand; Indonesia and Taiwan; Malaysia and Hong Kong; Malaysia and Singapore; Philippines and Korea; Philippines and Singapore; Philippines and Thailand; Korea and Hong Kong; Korea and Taiwan; Hong Kong Singapore and Thailand; and Singapore and Taiwan. These thirteen pairings demonstrated consistent lack of comovement as shown by the cointegration tests and the common feature tests. These results do not support comovement of stock market indexes among these thirteen bivariate pairings and would support stock market efficiency for these country pairings. For these thirteen pairings the conveyance of financial crisis across borders is not demonstrated empirically through the stock data investigated.
Conclusion
This study has investigated the comovement between stock indexes of eight Asian countries. The purpose of the study was to ascertain the interrelatedness of these stock indexes as it relates to market efficiency and the transmission of financial crisis across borders. The countries were selected due to their pronounced involvement in the 1996-1997 Asian financial crisis. The study is timely in that, as we proceed into the new millennium, fears of another Asian crisis abound as Asian currencies depreciate and investors’ confidence in Asian financial markets decrease.
All empirical tests were performed on a bivariate basis. So, for the eight countries studied, twenty-eight bivariate pairings exist. The results show that five of the twenty-eight pairings exhibit evidence of a cointegrating vector or nonstationary comovement. Another ten of the twenty-eight pairings exhibit evidence of a common serial correlation feature or stationary comovement. Therefore, overall fifteen of the twenty-eight pairings exhibit either stationary or nonstationary comovement, which implies at least one-way causality between the variables.
The comovement found to exist in these fifteen pairings is indicative of market inefficiency in that one stock index can be used to predict movement in another stock index. This historical comovement of the stock indexes of these fifteen pairings may provide some explanation of the rapid spread of the Asian crisis across financial markets in 1996-1997 and be indicative of future financial transmission between markets.
There are two practical implications arising from the findings of this paper. First, there is comovement in fifteen of the pairings. This would indicate inefficiency between markets, but it says nothing about direction of causality. For the purpose of this study, inefficiency is the critical issue, not the direction of causality. Comovement indicates that market problems in one country would migrate to other markets. Such a process would speed the spread of a crisis. The second implication from this study is the lack of efficiency between markets. From a portfolio standpoint, investors could not use these various markets to reduce their investment correlation and thereby reduce risk because an investor in Asian markets would be exposed to an excessive amount of unsystematic risk.
Table One
Unit
Root Tests
|
|
ADF |
PP |
KPSS(mu) |
KPSS(tau) | ||||
|
|
Level |
1st
diff |
Level |
1st
diff |
Level |
1st
diff |
Level |
1st
diff |
|
|
-2.65 |
-7.52* |
-1.61 |
-42.33* |
14.81* |
.07 |
2.94* |
.10 |
|
|
-1.77 |
-21.97* |
-1.56 |
-49.23* |
11.59* |
.11 |
7.89* |
.10 |
|
|
-1.67 |
-12.18* |
-.56 |
-42.4* |
27.17* |
.26 |
10.54* |
.08 |
|
|
-2.30 |
-9.55* |
-1.84 |
-47.60* |
4.31* |
.1 |
3.99* |
.08 |
|
|
-1.50 |
-16.03* |
-2.11 |
-51.04* |
44.64* |
.09 |
7.73* |
.09 |
|
|
-1.87 |
-44.91* |
-1.64 |
-44.90* |
10.26* |
.08 |
4.74* |
.09 |
|
|
-0.99 |
-8.23* |
-1.14 |
-45.89* |
23.02* |
.22 |
10.30* |
.08 |
|
|
-2.83 |
-8.92* |
-3.04 |
-49.59* |
23.48* |
.17 |
2.55* |
.11 |
|
Critical Value 90%
Level |
-3.43 |
-3.43 |
-3.43 |
-3.43 |
.463 |
.463 |
.146 |
.146 |
Note: “*” denotes rejection of the null hypothesis at the 90
percent
level of statistical significance.
The null hypothesis for the ADF and PP tests is that the series is
nonstationary. The null hypothesis
for the KPSS test is that the series is stationary.
Table Two
Cointegration Test Results
|
|
Trace
Statistic |
Maximum
Eigenvalue |
# of vectors | ||
|
|
r=0 |
r≤0 |
r=0 |
r=1 |
|
|
|
6.56 |
0.13 |
6.42 |
0.12 |
0 |
|
|
11.74* |
0.00 |
11.74** |
0.00 |
1 |
|
|
9.62 |
0.03 |
9.59* |
0.03 |
0 |
|
|
7.34 |
3.13* |
4.21 |
3.13* |
0 |
|
|
13.81** |
0.05 |
13.76** |
0.05 |
1 |
|
|
6.05 |
1.51 |
4.55 |
1.51 |
0 |
|
|
6.97 |
0.00 |
6.97 |
0.00 |
0 |
|
|
5.32 |
0.20 |
5.12 |
0.20 |
0 |
|
|
11.56* |
0.01 |
11.56** |
0.01 |
1 |
|
|
6.45 |
0.91 |
5.54 |
0.91 |
0 |
|
|
9.29 |
0.03 |
9.27 |
0.03 |
0 |
|
|
4.12 |
1.48 |
2.64 |
1.48 |
0 |
|
|
6.97 |
0.08 |
6.89 |
0.08 |
0 |
|
|
4.32 |
0.00 |
4.31 |
0.00 |
0 |
|
|
4.45 |
0.83 |
3.62 |
0.83 |
0 |
|
|
2.82 |
0.19 |
2.64 |
0.19 |
0 |
|
|
5.91 |
1.35 |
4.56 |
1.35 |
0 |
|
|
8.77 |
0.09 |
8.69 |
0.09 |
0 |
|
|
9.92 |
0.63 |
9.29 |
0.63 |
0 |
|
|
12.03* |
0.01 |
12.01** |
0.01 |
1 |
|
|
1.27 |
0.02 |
1.25 |
0.02 |
0 |
|
|
4.22 |
0.04 |
4.18 |
0.04 |
0 |
|
|
9.91 |
0.43 |
9.48 |
0.43 |
0 |
|
|
7.95 |
0.17 |
7.78 |
0.17 |
0 |
|
|
19.74** |
2.74 |
17.01 |
2.74 |
1 |
|
|
2.32 |
0.09 |
2.22 |
0.09 |
0 |
|
|
7.57 |
0.13 |
7.44 |
0.13 |
0 |
|
|
1.49 |
0.49 |
1.00 |
0.49 |
0 |
|
Critical Value at
90% |
10.47 |
2.86 |
9.52 |
2.86 |
|
|
Critical Value at
95% |
12.43 |
3.84 |
11.44 |
3.84 |
|
Note: “*” (“**”) denotes statistical significance at the 90
percent (95 percent)
level of statistical significance.
Table Three
LM
Test Statistic for Serial Correlation within Individual Series
|
Bivariate
Pairing (Independent Variable
Listed First) |
LM Test
Statistic |
Bivariate
Pairing (Independent Variable
Listed First) |
LM Test
Statistic |
|
|
124.99* |
|
29.54* |
|
|
133.19* |
|
141.95* |
|
|
157.81* |
|
24.62* |
|
|
137.30* |
|
6.56* |
|
|
130.19* |
|
65.82* |
|
|
149.06* |
|
62.08* |
|
|
23.80* |
|
163.01* |
|
|
13.68* |
|
27.35* |
|
|
30.91* |
|
6.56* |
|
|
36.65* |
|
68.92* |
|
|
21.33* |
|
59.90* |
|
|
10.12* |
|
35.01* |
|
|
133.47* |
|
7.11* |
|
|
161.09* |
|
7.11* |
|
|
186.25* |
|
65.64* |
|
|
164.92* |
|
58.26* |
|
|
127.18* |
|
15.04* |
|
|
39.11* |
|
14.77* |
|
|
49.50* |
|
71.66* |
|
|
36.10* |
|
67.28* |
|
|
25.71* |
|
12.58* |
|
|
10.94* |
|
72.48* |
|
|
15.86* |
|
72.20* |
|
|
70.29* |
|
119.79* |
|
|
63.18* |
|
43.76* |
|
|
54.97* |
|
22.71* |
Note: The critical value is 4.61 for the LM test statistic. “*” denotes statistical significance at
the 90 percent level or above.
Table Four
LML Approach Common Feature Test Results
|
|
Λ2(1) |
d |
T-Statistic for
d
|
Q(12) |
|
|
0.55 |
1.84 |
5.42 |
33.10 |
|
|
12.03** |
2.77 |
3.55 |
21.92 |
|
|
0.27 |
4.24 |
2.62 |
37.81 |
|
|
4.92** |
1.29 |
7.42 |
10.75 |
|
|
5.20** |
3.58 |
2.28 |
33.33 |
|
|
0.27 |
0.41 |
4.92 |
53.18 |
|
|
4.10** |
3.43 |
1.67 |
37.09 |
|
|
2.73* |
1.07 |
6.42 |
59.51 |
|
|
0.03 |
0.54 |
4.69 |
49.48 |
|
|
1.09 |
0.44 |
2.83 |
35.77 |
|
|
13.13** |
2.63 |
3.62 |
18.128 |
|
|
0.82 |
4.90 |
2.59 |
40.52 |
|
|
7.66** |
2.47 |
8.01 |
16.30 |
|
|
3.83* |
1.48 |
7.35 |
24.92 |
|
|
1.91 |
2.50 |
3.58 |
26.75 |
|
|
3.28* |
1.96 |
3.22 |
27.16 |
|
|
0.55 |
0.72 |
5.45 |
28.09 |
|
|
2.74* |
1.42 |
2.77 |
19.98 |
|
|
4.10** |
0.46 |
3.02 |
36.05 |
|
|
6.84** |
0.33 |
3.18 |
36.08 |
|
|
0.82 |
0.47 |
8.64 |
15.59 |
|
|
3.01* |
0.69 |
5.51 |
26.47 |
|
|
0.27 |
1.46 |
4.32 |
18.44 |
Note: “*” (“**”) denotes statistical significance at the 90 percent (95 percent) level of statistical significance for the common feature test statistic. Rejection of the null hypothesis implies that the linear combination still has the feature and therefore the feature is not common between the two variables.
References
Akaike, H. "Information Theory and the Extension of the Maximum Likelihood Principle. " In 2nd International Symposium on Information Theory, B.N. Petrov and F. Csaki, eds., Budapest. 1973.
"Asia’s Stockmarket Nightmare.” The Economist. December 20, 1997-January 2, 1998.
Dickey, D. A. and Fuller, W. A. "Likelihood ratio statistics for autoregressive time series with a unit root." Econometrica 49: 1057-1072.
Einhorn, B. and Shari, M. “Currency Crisis, Part Two?” Business Week. July 31, 2000, page 62.Engle, R. F. and Granger, C. "Cointegration and error correction: representation, estimation and testing." Econometrica. 1987. 55: 251-276.
Engle, R. F. and Kozicki, S. "Testing for common features," Journal of Business and Economic Statistics. 1993 11 (4):369-395.
Fama, E. F. "The behavior of stock market prices." Journal of Business. 1965 38: 34-105.
Fuller, W. A. Introduction to Statistical Time Series. New York: Wiley. 1976.
Granger, C. "Developments in the study of cointegrated economic variables." Oxford Bulletin of Economics and Statistics. 1986 48: 213-225.
Hansen, H. and Juselius, K. "CATS in RATS: Cointegration Analysis of Time Series, Evanston: Estima. 1995.
Johansen, S. "Statistical analysis of cointegrating vectors," Journal of Economic Dynamics and Control. 1988 12: 231-254.
Johansen, S. and Juselius, K. "Maximum likelihood estimation and inference on cointegration--with applications to the demand for money," Oxford Bulletin of Economics and Statistics. 1990 52: 169-210.
Kwiatkowski, D., Phillips, P., Schmidt, P., and Shin, Y. “Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root.” Journal of Econometrics. 1992 54(1-3):167-210.
Nelson, C. And C. Plosser, “Trends and Random Walks in Macroeconomic Time Series: Some Evidence and Implications,” Journal of Monetary Economics, 1982 10(2), 139-62.
Osterwald-Lenum, M. "A note with fractiles of the asymptotic distribution of the maximum likelihood cointegration rank test statistics: four cases." Oxford Bulletin of Economics and Statistics. 1992 54: 1361-1401.
Perron, P. "Trend and random walks in macroeconomic time series: further evidence from a new approach,)Journal of Economic Dynamics and Control. 1988 12: 297-332.
Phillips, P. "Time series regression with a unit root," Econometrica. 1987 55: 277-301.
Phillips, P. and Perron, P. "Testing for a unit root in time series regression," Biometrika. 1988 75: 335-346.
End Notes
1. See Granger (1986, p.218).
2. See Engle and Kozicki (1993, p. 373).
To change the background color use the scroll bar to find a color you prefer and click on it.
Return to the top of the page.
