1 Cointegration The VAR models discussed so fare are appropriate for modeling I(0) data, like asset returns or growth rates of macroeconomic time series. Economic theory, however, often implies equilibrium relationships between the levels of time series variables that are best described as being I(1). Similarly, arbitrage arguments imply that the I(1) prices of certain financial time series are linked. The statistical concept of cointegration is required to make sense of regression models and VAR models with I(1) data.
2 Spurious Regression If some or all of the variables in a regression are I(1) then the usual statistical results may or may not hold. One important case in which the usual statistical results do not hold is spurious regression, when all the regressors are I(1) and not cointegrated. That is, there is no linear combination of the variables that is I(0). Example: Granger-Newbold JOE 1974 Consider two independent and not cointegrated I(1) processes y 1t and y 2t y it = y it 1 + ε it, ε it GWN(0, 1), i =1, 2 Estimated levels and differences regressions y 1 = y 2, R 2 =0.21 (0.39) (0.05) y 1 = y 2, R 2 =0.00 (0.07) (0.06)
3 Statistical Implications of Spurious Regression Let Y t =(y 1t,...,y nt ) 0 denote an (n 1) vector of I(1) time series that are not cointegrated. Write Y t =(y 1t, Y 0 2t )0, and consider regressing of y 1t on Y 2t giving y 1t = ˆβ 0 2Y 2t +û t Since y 1t is not cointegrated with Y 2t true value of β 2 is zero The above is a spurious regression and û t I(1).
4 The following results about the behavior of ˆβ 2 in the spurious regression are due to Phillips (1986): ˆβ 2 does not converge in probability to zero but instead converges in distribution to a non-normal random variable not necessarily centered at zero. This is the spurious regression phenomenon. The usual OLS t-statistics for testing that the elements of β 2 are zero diverge to ± as T. Hence, with a large enough sample it will appear that Y t is cointegrated when it is not if the usual asymptotic normal inference is used. The usual R 2 from the regression converges to unity as T so that the model will appear to fit well even though it is misspecified. Regression with I(1)data only makes sense when the data are cointegrated.
5 Intuition Recall, with I(1) data sample moments converge to functions of Brownian motion. Consider two independent and not cointegrated I(1) processes y 1t and y 2t : Then y it = y it 1 + ε it, ε it WN(0,σ 2 i ), i =1, 2 T 2 T X T 2 T X t=1 t=1 y 2 it σ 2 i Z 1 y 1t y 2t σ 1 σ 2 Z 1 0 W i(r) 2 dr, i =1, 2 0 W 1(r)W 2 (r)dr where W 1 (r) andw 2 (r) are independent Wiener processes.
6 In the regression y 1t = ˆβy 2t +û t Phillips derived the following convergence result using the FCLT and the CMT: ˆβ = T 2 T X Ã σ 2 2 y 2 2t t=1 Z W 2(r) 2 dr T 2 T X t=1 y 1t y 2t! 1 σ 1 σ 2 Z 1 Therefore, ˆβ 9 p 0 ˆβ random variable 0 W 1(r)W 2 (r)dr
7 Cointegration Let Y t =(y 1t,...,y nt ) 0 denote an (n 1) vector of I(1) time series. Y t is cointegrated if there exists an (n 1) vector β =(β 1,...,β n ) 0 such that β 0 Y t = β 1 y 1t + + β n y nt I(0) In words, the nonstationary time series in Y t are cointegrated if there is a linear combination of them that is stationary or I(0). The linear combination β 0 Y t is often motivated by economic theory and referred to as a long-run equilibrium relationship. Intuition: I(1) time series with a long-run equilibrium relationship cannot drift too far apart from the equilibrium because economic forces will act to restore the equilibrium relationship.
8 Normalization The cointegration vector β is not unique since for any scalar c c β 0 Y t = β 0 Y t I(0) Hence, some normalization assumption is required to uniquely identify β. A typical normalization is so that or β =(1, β 2,..., β n ) 0 β 0 Y t = y 1t β 2 y 2t β n y nt I(0) y 1t = β 2 y 2t + + β n y nt + u t u t I(0) = cointegrating residual In long-run equilibrium, u t = 0 and the long-run equilibrium relationship is y 1t = β 2 y 2t + + β n y nt
9 Multiple Cointegrating Relationships If the (n 1) vector Y t is cointegrated there may be 0 <r<nlinearly independent cointegrating vectors. For example, let n =3andsupposetherearer =2 cointegrating vectors Then β 1 = (β 11,β 12,β 13 ) 0 β 2 = (β 21,β 22,β 23 ) 0 β 0 1 Y t = β 11 y 1t + β 12 y 2t + β 13 y 3t I(0) β 0 2 Y t = β 21 y 1t + β 22 y 2t + β 23 y 3t I(0) and the (3 2) matrix B 0 = Ã β 0 1 β 0 2! = Ã β11 β 12 β 13 β 21 β 22 β 33 forms a basis for the space of cointegrating vectors. The linearly independent vectors β 1 and β 2 in the cointegrating basis B are not unique unless some normalization assumptions are made. Furthermore, any linear combination of β 1 and β 2,e.g. β 3 = c 1 β 1 + c 2 β 2 where c 1 and c 2 are constants, is also a cointegrating vector.!
10 Examples of Cointegration and Common Trends in Economics and Finance Cointegration naturally arises in economics and finance. In economics, cointegration is most often associated with economic theories that imply equilibrium relationships between time series variables: The permanent income model implies cointegration between consumption and income, with consumption being the common trend. Money demand models imply cointegration between money, income, prices and interest rates. Growth theory models imply cointegration between income, consumption and investment, with productivity being the common trend.
11 Purchasing power parity implies cointegration between the nominal exchange rate and foreign and domestic prices. Covered interest rate parity implies cointegration between forward and spot exchange rates. The Fisher equation implies cointegration between nominal interest rates and inflation. The expectations hypothesis of the term structure implies cointegration between nominal interest rates at different maturities. The present value model of stock prices states that a stock s price is an expected discounted present value of its expected future dividends or earnings.
12 Remarks: The equilibrium relationships implied by these economic theories are referred to as long-run equilibrium relationships, because the economic forces that act in response to deviations from equilibriium may take a long time to restore equilibrium. As a result, cointegration is modeled using long spans of low frequency time series data measured monthly, quarterly or annually. In finance, cointegration may be a high frequency relationship or a low frequency relationship. Cointegration at a high frequency is motivated by arbitrage arguments. The Law of One Price implies that identical assets must sell for the same price to avoid arbitrage opportunities. This implies cointegration between the prices of the same asset trading on different markets, for example.
13 Similar arbitrage arguments imply cointegration between spot and futures prices, and spot and forward prices, and bid and ask prices. Here the terminology long-run equilibrium relationship is somewhat misleading because the economic forces acting to eliminate arbitrage opportunities work very quickly. Cointegration is appropriately modeled using short spans of high frequency data in seconds, minutes, hours or days.
14 Cointegration and Common Trends If the (n 1) vector time series Y t is cointegrated with 0 <r<ncointegrating vectors then there are n r common I(1) stochastic trends. For example, let Y t = (y 1t,y 2t ) 0 I(1) ε t = (ε 1t,ε 2t,ε 3t ) 0 I(0) and suppose that Y t is cointegrated with cointegrating vector β =(1, β 2 ) 0. This cointegration relationship may be represented as y 1t = β 2 tx y 2t = s=1 tx s=1 ε 1s + ε 3t ε 1s + ε 2t The common stochastic trend is P t s=1 ε 1s.
15 Notice that the cointegrating relationship annihilates the common stochastic trend: β 0 Y t = y 1t β 2 y 2t = β 2 tx s=1 ε 1s + ε 3t β 2 = ε 3t β 2 ε 2t I(0). tx s=1 ε 1s + ε 2t
16 Some Simulated Cointegrated Systems Cointegrated systems may be conveniently simulated using Phillips (1991) triangular representation. For example, consider a bivariate cointegrated system for Y t =(y 1t,y 2t ) 0 with cointegrating vector β =(1, β 2 ) 0. A triangular representation has the form y 1t = β 2 y 2t + u t, where u t I(0) y 2t = y 2t 1 + v t, where v t I(0) The first equation describes the long-run equilibrium relationship with an I(0) disequilibrium error u t. The second equation specifies y 2t as the common stochastic trend with innovation v t : y 2t = y 20 + tx j=1 v j.
17 In general, the innovations u t and v t may be contemporaneously and serially correlated. The time series structure of these innovations characterizes the short-run dynamics of the cointegrated system. The system with β 2 = 1, for example, might be used to model the behavior of the logarithm of spot and forward prices, spot and futures prices, stock prices and dividends, or consumption and income.
18 Example: Bivariate system with β =(1, 1) 0 y 1t = y 2t + u t y 2t = y 2t 1 + v t u t = 0.75u t 1 + ε t, ε t iid N(0, (0.5) 2 ), v t iid N(0, (0.5) 2 ) Note: y 2t defines the common trend
19 Trivariate cointegrated system with 1 cointegrating vector β =(1, β 1,β 2 ) 0 y 1t = β 1 y 2t + β 2 y 3t + u t, u t I(0) y 2t = y 2t 1 + v t, v t I(0) y 3t = y 3t 1 + w t, w t I(0) An example of a trivariate cointegrated system with one cointegrating vector is a system of nominal exchange rates, home country price indices and foreign country price indices. A cointegrating vector β = (1, 1, 1) 0 implies that the real exchange rate is stationary.
20 Example: Trivariate cointegrated system β =(1, 0.5, 0.5) 0 y 1t = 0.5y 2t +0.5y 3t + u t, u t = 0.75u t 1 + ε t,ε t iid N(0, (0.5) 2 ) y 2t = y 2t 1 + v t, v t iid N(0, (0.5) 2 ) y 3t = y 3t 1 + w t, w t iid N(0, (0.5) 2 ) Note: y 2t and y 3t are the common trends
21 Simulated trivariate cointegrated system with 2 cointegrating vectors A triangular representation for this system with cointegrating vectors β 1 =(1, 0, β 13 ) 0 and β 2 =(0, 1, β 23 ) 0 is y 1t = β 13 y 3t + u t, u t I(0) y 2t = β 23 y 3t + v t, v t I(0) y 3t = y 3t 1 + w t, w t I(0) An example in finance of such a system is the term structure of interest rates where y 3 represents the short rate and y 1 and y 2 represent two different long rates. The cointegrating relationships would indicate that the spreads between the long and short rates are stationary.
22 Example: Trivariate system with β 1 = (1, 0, 1) 0, β 2 =(0, 1, 1) 0 y 1t = y 3t + u t, u t = 0.75u t 1 + ε t,ε t iid N(0, (0.5) 2 ) y 2t = y 3t + v t, v t = 0.75v t 1 + η t,η t iid N(0, (0.5) 2 ) y 3t = y 3t 1 + w t, w t iid N(0, (0.5) 2 ) Note: y 3t defines the common trend.
23 Cointegration and Error Correction Models Consider a bivariate I(1) vector Y t =(y 1t,y 2t ) 0 and assume that Y t is cointegrated with cointegrating vector β =(1, β 2 ) 0 so that β 0 Y t = y 1t β 2 y 2t is I(0). Engle and Granger s famous (1987) Econometrica paper showed that cointegration implies the existence of an error correction model (ECM) of the form y 1t = c 1 + α 1 (y 1t 1 β 2 y 2t 1 ) + X j ψ j 11 y 1t j + X j ψ j 12 y 2t j + ε 1t y 2t = c 2 + α 2 (y 1t 1 β 2 y 2t 1 ) + X j ψ j 21 y 1t j + X j ψ j 22 y 2t j + ε 2t The ECM links the long-run equilibrium relationship implied by cointegration with the short-run dynamic adjustment mechanism that describes how the variables react when they move out of long-run equilibrium.
24 Let y t denote the log of real income and c t denote the log of consumption and assume that Y t =(y t,c t ) 0 is I(1). The Permanent Income Hypothesis implies that income and consumption are cointegrated with β =(1, 1) 0 : c t = μ + y t + u t μ = E[c t y t ] u t I(0) Suppose the ECM has the form y t = γ y + α y (c t 1 y t 1 μ)+ε yt c t = γ c + α c (c t 1 y t 1 μ)+ε ct The first equation relates the growth rate of income to the lagged disequilibrium error c t 1 y t 1 μ, and the second equation relates the growth rate of consumption to the lagged disequilibrium as well. The reactions of y t and c t to the disequilibrium error are captured by the adjustment coefficients α y and α c.
25 Consider the special case y t = γ y +0.5(c t 1 y t 1 μ)+ε yt, c t = γ c + ε ct. Consider three situations: 1. c t 1 y t 1 μ =0. Then E[ y t Y t 1 ] = γ y E[ c t Y t 1 ] = γ d 2. c t 1 y t 1 μ>0. Then E[ y t Y t 1 ]=γ y +0.5(c t 1 y t 1 μ) >γ y Here the consumption has increased above its long-run mean (positive disequilibrium error) and the ECM predicts that y t will grow faster than its long-run rate to restore the consumption-income ratio its long-run mean.
26 3. c t 1 y t 1 μ<0. Then E[ y t Y t 1 ]=γ y +0.5(c t 1 y t 1 μ) <c y Here consumption-income ratio has decreased below its long-run mean (negative disequilibrium error) and the ECM predicts that y t will grow more slowly than its long-run rate to restore the consumptionincome ratio to its long-run mean.
27 Tests for Cointegration Let the (n 1) vector Y t be I(1). Recall, Y t is cointegrated with 0 <r<ncointegrating vectors if there exists an (r n) matrixb 0 such that B 0 Y t = β 0 1 Y t. β 0 ry t = u 1t. u rt I(0) Testing for cointegration may be thought of as testing for the existence of long-run equilibria among the elements of Y t.
28 Cointegration tests cover two situations: There is at most one cointegrating vector Originally considered by Engle and Granger (1986), Cointegration and Error Correction: Representation, Estimation and Testing, Econometrica. They developed a simple two-step residual-based testing procedure based on regression techniques. There are possibly 0 r<ncointegrating vectors. Originally considered by Johansen (1988), Statistical Analysis of Cointegration Vectors, Journal of Economics Dynamics and Control. He developed a sophisticated sequential procedure for determining the existence of cointegration and for determining the number of cointegrating relationships based on maximum likelihood techniques.
29 Residual-Based Tests for Cointegration Engle and Granger s two-step procedure for determining if the (n 1) vector β is a cointegrating vector is as follows: Form the cointegrating residual β 0 Y t = u t Perform a unit root test on u t to determine if it is I(0). The null hypothesis in the Engle-Granger procedure is no-cointegration and the alternative is cointegration.
30 There are two cases to consider. 1. The proposed cointegrating vector β is pre-specified (not estimated). For example, economic theory may imply specificvaluesfortheelementsinβ such as β =(1, 1) 0. The cointegrating residual is then readily constructed using the prespecified cointegrating vector. 2. The proposed cointegrating vector is estimated from the data and an estimate of the cointegrating residual ˆβ 0 Y t =û t is formed. Note: Tests for cointegration using a pre-specified cointegrating vector are generally much more powerful than tests employing an estimated vector.
31 Testing for Cointegration When the Cointegrating Vector Is Pre-specified Let Y t denote an (n 1) vector of I(1) time series, let β denote an (n 1) prespecified cointegrating vector and let u t = β 0 Y t = cointegrating residual Thehypothesestobetestedare H 0 : u t = β 0 Y t I(1) (no cointegration) H 1 : u t = β 0 Y t I(0) (cointegration) Anyunitrootteststatisticmaybeusedtoevaluate the above hypotheses. The most popular choices are the ADF and PP statistics, but one may also use the more powerful ERS and Ng- Perron tests. Cointegration is found if the unit root test rejects the no-cointegration null.
32 It should be kept in mind, however, that the cointegrating residual may include deterministic terms (constant or trend) and the unit root tests should account for these terms accordingly.
33 Testing for Cointegration When the Cointegrating Vector Is Estimated Let Y t denote an (n 1) vector of I(1) time series and let β denote an (n 1) unknown cointegrating vector. The hypotheses to be tested are H 0 : u t = β 0 Y t I(1) (no cointegration) H 1 : u t = β 0 Y t I(0) (cointegration) Since β is unknown, to use the Engle-Granger procedure it must be first estimated from the data. Before β can be estimated some normalization assumption must be made to uniquely identify it. A common normalization is to specify Y t =(y 1t, Y 0 2t )0 where Y 2t =(y 2t,...,y nt ) 0 is an ((n 1) 1) vector and the cointegrating vector is normalized as β =(1, β 0 2 )0.
34 Engle and Granger propose estimating the normalized cointegrating vector β 2 by least squares from the regression y 1t = γ 0 D t + β 0 2 Y 2t + u t D t = deterministic terms and testing the no-cointegration hypothesis with a unit root test using the estimated cointegrating residual û t = y 1t ˆγ 0 D t ˆβ 2 Y 2t The unit root test regression in this case is without deterministic terms (constant or constant and trend). For example, if one uses the ADF test, the test regression is û t = πû t 1 + px j=1 ξ û t j + error
35 Distribution Theory Phillips and Ouliaris (PO) (1990) show that ADF and PP unit root tests (t-tests and normalized bias) applied to the estimated cointegrating residual do not have the usual Dickey-Fuller distributions under the null hypothesis of no-cointegration. Due to the spurious regression phenomenon under the null hypothesis, the distribution of the ADF and PP unit root tests have asymptotic distributions that are functions of Wiener processes that Depend on the deterministic terms in the regression used to estimate β 2 Depend on the number of variables, n 1, in Y 2t.
36 These distributions are known as the Phillips-Ouliaris (PO) distributions, and are described in Phillips and Ouliaris (1990).
37 To further complicate matters, Hansen (1992) showed the appropriate PO distributions of the ADF and PP unit root tests applied to the residuals also depend on the trend behavior of y 1t and Y 2t as follows: Case I: Y 2t and y 1t are both I(1) without drift and D t = 1. The ADF and PP unit root test statistics follow the PO distributions, adjusted for a constant, with dimension parameter n 1. Case II: Y 2t is I(1) with drift, y 1t may or may not be I(1) with drift and D t = 1. The ADF and PP unit root test statistics follow the PO distributions, adjusted for a constant and trend, with dimension parameter n 2. If n 2 = 0 then the ADF and PP unit root test statistics follow the DF distributions adjusted for a constant and trend.
38 Case III: Y 2t is I(1) without drift, y 1t is I(1) with drift and D t =(1,t) 0. The resulting ADF and PP unit root test statistics on the residuals follow the PO distributions, adjusted for a constant and trend, with dimension parameter n 1. Example: PO Critical Values PO Critical Values: Case I n-1 1% 5%
39 Regression-Based Estimates of Cointegrating Vectors and Error Correction Models Least Square Estimator Least squares may be used to consistently estimate a normalized cointegrating vector. However, the asymptotic behavior of the least squares estimator is nonstandard. The following results about the behavior of ˆβ 2 if Y t is cointegrated are due to Stock (1987) and Phillips (1991): T (ˆβ 2 β 2 ) converges in distribution to a nonnormal random variable not necessarily centered at zero. The least squares estimate ˆβ 2 is consistent for β 2 and converges to β 2 at rate T instead of the usual rate T 1/2.Thatis,ˆβ 2 is super consistent.
40 ˆβ 2 is consistent even if Y 2t is correlated with u t so that there is no asymptotic simultaneity bias. In general, the asymptotic distribution of T (ˆβ 2 β 2 ) is asymptotically biased and non-normal. The usual OLS formula for computing avar(ˆβ d 2 )isincorrect and so the usual OLS standard errors are not correct. Even though the asymptotic bias goes to zero as T gets large ˆβ 2 may be substantially biased in small samples. The least squres estimator is also not efficient. The above results indicate that the least squares estimator of the cointegrating vector β 2 could be improved upon. A simple improvement is suggested by Stock and Watson (1993).
41 What causes the bias and non-normality in ˆβ 2? Assume a triangular representation of the form y 1t = Y 0 2t β 2 + u 1t Y 2t = Y 2t 1 + u 2t The bias and non-normality is a function of the time series structure of u t =(u 1t, u 0 2t )0. Assume a Wold structure for u t Ã u1t! u 2t Ã! ε1t ε 2t Ã ψ11 (L) = Ψ 21 (L) ÃÃ 0 iid N 0 Ψ 12 (L) Ψ 22 (L)!!Ã! ε1t ε 2t!!, Ã σ11 σ 12 σ 21 Σ 22 Result: There is no asymptotic bias if u t WN(0, I n )
42 Stock and Watson s Efficient Lead/Lag Estimator Stock and Watson (1993) provide a very simple method for obtaining an asymptotically efficient (equivalent to maximum likelihood) estimator for the normalized cointegrating vector β 2 as well as a valid formula for computing its asymptotic variance. Let Y t = (y 1t, Y2t 0 )0 Y 2t = (y 2t,...,y nt ) 0 β = (1, β 0 2 )0
43 Stock and Watson s efficient estimation procedure is: Augment the cointegrating regression of y 1t on Y 2t with appropriate deterministic terms D t with p leads and lags of Y 2t y 1t = γ 0 D t + β 0 2 Y 2t + px j= p = γ 0 D t + β 0 2 Y 2t + ψ 0 0 Y 2t ψ 0 j Y 2t j + u t +ψ 0 p Y 2t+p + + ψ 0 1 Y 2t+1 +ψ 0 1 Y 2t ψ 0 p Y 2t p + u t Estimate the augmented regression by least squares. The resulting estimator of β 2 is called the dynamic OLS estimator and is denoted ˆβ 2,DOLS. It will be consistent, asymptotically normally distributed and efficient (equivalent to MLE) under certain assumptions (see Stock and Watson (1993))
44 Asymptotically valid standard errors for the individual elements of ˆβ 2,DOLS are given by the OLS standard errors multiplied by the ratio Ã! ˆσ 2 1/2 u clrv(u t ) where ˆσ 2 u is the OLS estimate of var(u t ) and clrv(u t ) is any consistent estimate of the long-run variance of u t using the residuals û t from. Alternatively, the Newey-West HAC standard errors mayalsobeused. An alternative method to correct the standard errors utilizes a Cochrane-Orcutt GLS transformation of the error term. This is called the dynamic GLS estimator. Recently, Okagi and Ling (2005) have utilized this estimator to produce improved tests for cointegration based on Hausman-type tests.
45 Estimating Error Correction Models by Least Squares Consider a bivariate I(1) vector Y t =(y 1t,y 2t ) 0 and assume that Y t is cointegrated with cointegrating vector β =(1, β 2 ) 0 so that β 0 Y t = y 1t β 2 y 2t is I(0). Suppose one has a consistent estimate ˆβ 2 (by OLS or DOLS) of the cointegrating coefficient and is interested in estimating the corresponding error correction model for y 1t and y 2t using y 1t = c 1 + α 1 (y 1t 1 ˆβ 2 y 2t 1 ) + X j ψ j 11 y 1t j + X j ψ j 12 y 2t j + ε 1t y 2t = c 2 + α 2 (y 1t 1 ˆβ 2 y 2t 1 ) + X j ψ j 21 y 1t j + X j ψ 2 22 y 2t j + ε 2t Because ˆβ 2 is super consistent it may be treated as known in the ECM, so that the estimated disequilibrium error y 1t ˆβ 2 y 2t may be treated like the known disequilibrium error y 1t β 2 y 2t.
46 Since all variables in the ECM are I(0), the two regression equations may be consistently estimated using ordinary least squares (OLS). Alternatively, the ECM system may be estimated by seemingly unrelated regressions (SUR) to increase efficiency if the number of lags in the two equations are different.
Estimation and Inference in Cointegration Models Economics 582 Eric Zivot May 17, 2012 Tests for Cointegration Let the ( 1) vector Y be (1). Recall, Y is cointegrated with 0 cointegrating vectors if there
Cointegration Basic Ideas and Key results Egon Zakrajšek Division of Monetary Affairs Federal Reserve Board Summer School in Financial Mathematics Faculty of Mathematics & Physics University of Ljubljana
Chapter 5: Bivariate Cointegration Analysis 1 Contents: Lehrstuhl für Department Empirische of Wirtschaftsforschung Empirical Research and und Econometrics Ökonometrie V. Bivariate Cointegration Analysis...
SYSTEMS OF REGRESSION EQUATIONS 1. MULTIPLE EQUATIONS y nt = x nt n + u nt, n = 1,...,N, t = 1,...,T, x nt is 1 k, and n is k 1. This is a version of the standard regression model where the observations
Department of Economics Discussion Paper 2004-19 Business Cycles and Natural Gas Prices Apostolos Serletis Department of Economics University of Calgary Canada and Asghar Shahmoradi Department of Economics
I J A B E R, Vol. 13, No. 4, (2015): 1525-1534 TEMPORAL CAUSAL RELATIONSHIP BETWEEN STOCK MARKET CAPITALIZATION, TRADE OPENNESS AND REAL GDP: EVIDENCE FROM THAILAND Komain Jiranyakul * Abstract: This study
ERC Working Paper in Economic 03/10 November 2003 Testing The Quantity Theory of Money in Greece: A Note Erdal Özmen Department of Economics Middle East Technical University Ankara 06531, Turkey firstname.lastname@example.org
Provided by the author(s) and NUI Galway in accordance with publisher policies. Please cite the published version when available. Title Are the US current account deficits really sustainable? Author(s)
A Trading Strategy Based on the Lead-Lag Relationship of Spot and Futures Prices of the S&P 500 FE8827 Quantitative Trading Strategies 2010/11 Mini-Term 5 Nanyang Technological University Submitted By:
Business cycles and natural gas prices Apostolos Serletis and Asghar Shahmoradi Abstract This paper investigates the basic stylised facts of natural gas price movements using data for the period that natural
Unit Labor Costs and the Price Level Yash P. Mehra A popular theoretical model of the inflation process is the expectationsaugmented Phillips-curve model. According to this model, prices are set as markup
Is the Forward Exchange Rate a Useful Indicator of the Future Exchange Rate? Emily Polito, Trinity College In the past two decades, there have been many empirical studies both in support of and opposing
Working Papers No. 2/2012 (68) Piotr Arendarski Łukasz Postek Cointegration Based Trading Strategy For Soft Commodities Market Warsaw 2012 Cointegration Based Trading Strategy For Soft Commodities Market
Volume 24, Number 2, December 1999 Empirical Properties of the Indonesian Rupiah: Testing for Structural Breaks, Unit Roots, and White Noise Reza Yamora Siregar * 1 This paper shows that the real exchange
Chapter 6: Multivariate Cointegration Analysis 1 Contents: Lehrstuhl für Department Empirische of Wirtschaftsforschung Empirical Research and und Econometrics Ökonometrie VI. Multivariate Cointegration
MPRA Munich Personal RePEc Archive Why the saving rate has been falling in Japan Yoshiaki Azuma and Takeo Nakao January 2009 Online at http://mpra.ub.uni-muenchen.de/62581/ MPRA Paper No. 62581, posted
THE PRICE OF GOLD AND STOCK PRICE INDICES FOR THE UNITED STATES by Graham Smith November 2001 Abstract This paper provides empirical evidence on the relationship between the price of gold and stock price
An Empirical Study on the Relationship between Stock Index and the National Economy: The Case of China Ming Men And Rui Li University of International Business & Economics Beijing, People s Republic of
2012, Vol. 4, No. 2, pp. 103-112 ISSN 2152-1034 Relationship between Stock Futures Index and Cash Prices Index: Empirical Evidence Based on Malaysia Data Abstract Zukarnain Zakaria Universiti Teknologi
7. IS THERE A LONG-RUN RELATIONSHIP BETWEEN TAXATION AND GROWTH: THE CASE OF TURKEY Salih Turan KATIRCIOGLU Abstract This paper empirically investigates long-run equilibrium relationship between economic
Página 1 de 12 Unit Root Testing The theory behind ARMA estimation is based on stationary time series. A series is said to be (weakly or covariance) stationary if the mean and autocovariances of the series
Minimum LM Unit Root Test with One Structural Break Junsoo Lee Department of Economics University of Alabama Mark C. Strazicich Department of Economics Appalachian State University December 16, 2004 Abstract
THE EFFECTS OF BANKING CREDIT ON THE HOUSE PRICE * Adibeh Savari 1, Yaser Borvayeh 2 1 MA Student, Department of Economics, Science and Research Branch, Islamic Azad University, Khuzestan, Iran 2 MA Student,
The Power of the KPSS Test for Cointegration when Residuals are Fractionally Integrated Philipp Sibbertsen 1 Walter Krämer 2 Diskussionspapier 318 ISNN 0949-9962 Abstract: We show that the power of the
Bias in the Estimation of Mean Reversion in Continuous-Time Lévy Processes Yong Bao a, Aman Ullah b, Yun Wang c, and Jun Yu d a Purdue University, IN, USA b University of California, Riverside, CA, USA
ECONOMICS 266, Spring, 1997 Bent E. Sørensen March 1, 2005 1 Cointegration. The survey by Campbell and Perron (1991) is a very good supplement to this chapter - for further study read Watson s survey for
Technical Paper Series Congressional Budget Office Washington, DC FORECASTING DEPOSIT GROWTH: Forecasting BIF and SAIF Assessable and Insured Deposits Albert D. Metz Microeconomic and Financial Studies
The price-volume relationship of the Malaysian Stock Index futures market ABSTRACT Carl B. McGowan, Jr. Norfolk State University Junaina Muhammad University Putra Malaysia The objective of this study is
Time Series Analysis and Spurious Regression: An Error Correction Peter K. Enns Takaaki Masaki Nathan J. Kelly email@example.com firstname.lastname@example.org email@example.com Cornell University Cornell University
The Long-Run Relation Between The Personal Savings Rate And Consumer Sentiment Bradley T. Ewing 1 and James E. Payne 2 This study examined the long run relationship between the personal savings rate and
EVIEWS tutorial: Cointegration and error correction Professor Roy Batchelor City University Business School, London & ESCP, Paris EVIEWS Tutorial 1 EVIEWS On the City University system, EVIEWS 3.1 is in
SEEDS Surrey Energy Economics Discussion paper Series SURREY ENERGY ECONOMICS CENTRE Electricity Demand for Sri Lanka: A Time Series Analysis Himanshu A. Amarawickrama and Lester C Hunt October 2007 SEEDS
Pricing Corn Calendar Spread Options by Juheon Seok and B. Wade Brorsen Suggested citation format: Seok, J., and B. W. Brorsen. 215. Pricing Corn Calendar Spread Options. Proceedings of the NCCC-134 Conference
INDIRECT INFERENCE (prepared for: The New Palgrave Dictionary of Economics, Second Edition) Abstract Indirect inference is a simulation-based method for estimating the parameters of economic models. Its
Applied Time Series Analysis ANALYSIS OF EUROPEAN, AMERICAN AND JAPANESE GOVERNMENT BOND YIELDS Stationarity, cointegration, Granger causality Aleksandra Falkowska and Piotr Lewicki TABLE OF CONTENTS 1.
How do oil prices affect stock returns in GCC markets? An asymmetric cointegration approach. Mohamed El Hedi AROURI (LEO-Université d Orléans & EDHEC, firstname.lastname@example.org) Julien FOUQUAU (ESC
MPRA Munich Personal RePEc Archive Testing for Granger causality between stock prices and economic growth Pasquale Foresti 2006 Online at http://mpra.ub.uni-muenchen.de/2962/ MPRA Paper No. 2962, posted
PITFALLS IN TIME SERIES ANALYSIS Cliff Hurvich Stern School, NYU The t -Test If x 1,..., x n are independent and identically distributed with mean 0, and n is not too small, then t = x 0 s n has a standard
November, 2004 The Effect of Infrastructure on Long Run Economic Growth David Canning Harvard University and Peter Pedroni * Williams College --------------------------------------------------------------------------------------------------------------------
Nonlinear Error-Correction Models for Interest Rates in the Netherlands Dick van Dijk æ Tinbergen Institute, Erasmus University Rotterdam and Philip Hans Franses Rotterdam Institute for Business Economic
Overview of Violations of the Basic Assumptions in the Classical Normal Linear Regression Model 1 September 004 A. Introduction and assumptions The classical normal linear regression model can be written
University of Wollongong Research Online Applied Statistics Education and Research Collaboration (ASEARC) - Conference Papers Faculty of Engineering and Information Sciences 2011 Is the Basis of the Stock
Normalization and Mixed Degrees of Integration in Cointegrated Time Series Systems Robert J. Rossana Department of Economics, 04 F/AB, Wayne State University, Detroit MI 480 E-Mail: email@example.com
Lecture 12: Time Series Analysis III MIT 18.S096 Dr. Kempthorne Fall 2013 MIT 18.S096 Time Series Analysis III 1 Outline Time Series Analysis III 1 Time Series Analysis III MIT 18.S096 Time Series Analysis
Chapter 5 Analysis of Multiple Time Series Note: The primary references for these notes are chapters 5 and 6 in Enders (2004). An alternative, but more technical treatment can be found in chapters 10-11
CHAPTER-6 LEAD-LAG RELATIONSHIP BETWEEN SPOT AND INDEX FUTURES MARKETS IN INDIA 6.1 INTRODUCTION The introduction of the Nifty index futures contract in June 12, 2000 has offered investors a much greater
LEAD-LAG RELATIONSHIP BETWEEN ISE 30 SPOT AND FUTURES MARKETS Serhat YANIK* & Yusuf AYTURK* Abstract The lead-lag relationship between spot and futures markets indicates which market leads to the other.
Chapter 4: Vector Autoregressive Models 1 Contents: Lehrstuhl für Department Empirische of Wirtschaftsforschung Empirical Research and und Econometrics Ökonometrie IV.1 Vector Autoregressive Models (VAR)...
The Law of one Price in Global Natural Gas Markets - A Threshold Cointegration Analysis Sebastian Nick a, Benjamin Tischler a, a Institute of Energy Economics, University of Cologne, Vogelsanger Straße
Professor Faik BĐLGĐLĐ, PhD E-mail: firstname.lastname@example.org Department of Economics, Faculty of Economics and Administrative Sciences, Erciyes University, Turkey Assistant Professor Yalçın PAMUK, PhD E-mail:
Chapter Vector autoregressions We begin by taking a look at the data of macroeconomics. A way to summarize the dynamics of macroeconomic data is to make use of vector autoregressions. VAR models have become
Economics Letters 68 (2000) 179 184 www.elsevier.com/ locate/ econbase The information content of lagged equity and bond yields Richard D.F. Harris *, Rene Sanchez-Valle School of Business and Economics,
American Journal of Applied Sciences 2 (5): 996-1002, 2005 ISSN 1546-9239 Science Publications, 2005 Revisiting Share Market Efficiency: Evidence from the New Zealand Australia, US and Japan Stock Indices
AN EMPIRICAL INVESTIGATION OF THE RELATIONSHIP AMONG P/E RATIO, STOCK RETURN AND DIVIDEND YIELS FOR ISTANBUL STOCK EXCHANGE Funda H. SEZGIN Mimar Sinan Fine Arts University, Faculty of Science and Letters
State Space Time Series Analysis p. 1 State Space Time Series Analysis Siem Jan Koopman http://staff.feweb.vu.nl/koopman Department of Econometrics VU University Amsterdam Tinbergen Institute 2011 State
THE U.S. CURRENT ACCOUNT: THE IMPACT OF HOUSEHOLD WEALTH Grant Keener, Sam Houston State University M.H. Tuttle, Sam Houston State University 21 ABSTRACT Household wealth is shown to have a substantial
Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation
C The Journal of Risk and Insurance, 2009, Vol. 76, No. 1, 109-131 LONG-TERM DISABILITY CLAIMS RATES AND THE CONSUMPTION-TO-WEALTH RATIO H. J. Smoluk ABSTRACT Aframeworkforlinkinglong-termdisability(LTD)claimsratestothemacroeconomy
Inflation as a function of labor force change rate: cointegration test for the USA I.O. Kitov 1, O.I. Kitov 2, S.A. Dolinskaya 1 Introduction Inflation forecasting plays an important role in modern monetary
FACULTAD DE CIENCIAS ECONÓMICAS Y EMPRESARIALES GRADO EN ECONOMÍA Is the Forward Rate a True Unbiased Predictor of the Future Spot Exchange Rate? Autor: Elena Renedo Sánchez Tutor: Juan Ángel Jiménez Martín
Time Series Analysis Identifying possible ARIMA models Andrés M. Alonso Carolina García-Martos Universidad Carlos III de Madrid Universidad Politécnica de Madrid June July, 2012 Alonso and García-Martos
Get the latest knowledge from leading global experts. Financial Science Economics Economics Short Courses Presented by the Department of Economics, University of Pretoria WITH 2015 DATES www.ce.up.ac.za
Ministry of Transport Air passenger departures forecast models A technical note By Haobo Wang Financial, Economic and Statistical Analysis Page 1 of 15 1. Introduction Sine 1999, the Ministry of Business,
Advances in Economics and International Finance AEIF Vol. 1(1), pp. 1-11, December 2014 Available online at http://www.academiaresearch.org Copyright 2014 Academia Research Full Length Research Paper MULTIPLE
Hedging Illiquid FX Options: An Empirical Analysis of Alternative Hedging Strategies Drazen Pesjak Supervised by A.A. Tsvetkov 1, D. Posthuma 2 and S.A. Borovkova 3 MSc. Thesis Finance HONOURS TRACK Quantitative
Does Insurance Promote Economic Growth? Evidence from the UK Maurice Kugler and Reza Ofoghi * July 2005 Abstract The first conference of UNCTAD in 1964 acknowledged the development of national insurance
116 THE EFFECT OF MONETARY GROWTH VARIABILITY ON THE INDONESIAN CAPITAL MARKET D. Agus Harjito, Bany Ariffin Amin Nordin, Ahmad Raflis Che Omar Abstract Over the years studies to ascertain the relationship
Christopher F Baum Boston College & DIW August 2007 hristopher F Baum ( Boston College & DIW) NASUG2007 1 / 26 Introduction This presentation discusses two recent developments in time series analysis by
This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution
Co-movements of NAFTA trade, FDI and stock markets Paweł Folfas, Ph. D. Warsaw School of Economics Abstract The paper scrutinizes the causal relationship between performance of American, Canadian and Mexican
International Business Research April, 2008 FDI and Economic Growth Relationship: An Empirical Study on Malaysia Har Wai Mun Faculty of Accountancy and Management Universiti Tunku Abdul Rahman Bander Sungai
4 Unit Root Tests This is page 111 Printer: Opaque this 4.1 Introduction Many economic and financial time series exhibit trending behavior or nonstationarity in the mean. Leading examples are asset prices,
Journal of Contemporary Issues in Business Research ISSN 2305-8277 (Online), 2013, Vol. 2, No. 1, 1-10. Copyright of the Academic Journals JCIBR All rights reserved. COINTEGRATION AND CAUSAL RELATIONSHIP
TOURISM AS A LONG-RUN ECONOMIC GROWTH FACTOR: AN EMPIRICAL INVESTIGATION FOR GREECE USING CAUSALITY ANALYSIS Nikolaos Dritsakis Department of Applied Informatics University of Macedonia Economics and Social
Dynamics of Real Investment and Stock Prices in Listed Companies of Tehran Stock Exchange Farzad Karimi Assistant Professor Department of Management Mobarakeh Branch, Islamic Azad University, Mobarakeh,
IIMK/WPS/155/ECO/2014/13 FORECASTING THE PRICE OF GOLD: AN ERROR CORRECTION APPROACH Kausik Gangopadhyay 1 Abhishek Jangir 2 Rudra Sensarma 3 1 Assistant Professor, Indian Institute of Management Kozhikode,
INTERNATIONAL JOURNAL OF BUSINESS, 8(3), 2003 ISSN:1083-4346 Financial Integration of Stock Markets in the Gulf: A Multivariate Cointegration Analysis Aqil Mohd. Hadi Hassan Department of Economics, College
A Re-examination of the Fragility of Evidence from Cointegration-Based Tests of Foreign Exchange Market Efficiency by John Barkoulas * Department of Economics, P.O. Box 6025, West Virginia University Morgantown,
Economic Activity and Crime in the Long Run: An Empirical Investigation on Aggregate Data from Italy, 1951 1994 ANTONELLO E. SCORCU and ROBERTO CELLINI Department of Economics, University of Bologna, Bologna,
107 INFLATION, INTEREST RATE, AND EXCHANGE RATE: WHAT IS THE RELATIONSHIP? Maurice K. Shalishali, Columbus State University Johnny C. Ho, Columbus State University ABSTRACT A test of IFE (International