Economics 310 Lecture 16 Autocorrelation Continued

Bid-Ask Spread an Example The spread between the bid price for US currency and the ask price for US currency in the Brazilian blackmarket is function of opportunity cost of holding currency and the risk of holding currency. Opportunity cost is interest rate risk is the rate of variability in exchange rate

Breusch-Godfrey Test Test for higher order autocorrelation Estimate model by ols regress residual on independent variables, lagged values of residual n times r-square is chi-square

Breusch-Godfrey Test

Breusch-Godfrey Example |_?ols spread interest sigma / resid=e |_sample |_genr e1=lag(e) |_genr e2=lag(e1) |_genr e3=lag(e2) |_genr e4=lag(e3) |_genr e5=lag(e4) |_genr e6=lag(e5) |_genr e7=lag(e6) |_genr e8=lag(e7) |_genr e9=lag(e8) |_genr e10=lag(e9) |_genr e11=lag(e10) |_genr e12=lag(e11) |_ols e interest sigma e1 e2 e3 e4 e5 e6 e7 e8 e9 e10 e11 e12

Breusch-Godfrey Results VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 31 DF P-VALUE CORR. COEFFICIENT AT MEANS INTEREST E E SIGMA E E E E E E E E E E E E E E CONSTANT |_gen1 lm=$n*$r2..NOTE..CURRENT VALUE OF $N = NOTE..CURRENT VALUE OF $R2 = |_print lm LM

Obtaining Efficient Estimates When rho known, we can use generalized least squares. When rho unknown: First difference method No intercept Berenblutt-Webb test rho based on Durbin Watson statistic Cochrane-Orcutt Iterative Two step Durbin two-step

When structure of autocorrelation is known

Rho unknown - 1st difference

Estimating Rho

Estimating Rho-continued

Estimating our model with Cochrane-Orcutt |_auto spread interest sigma LEAST SQUARES ESTIMATION 58 OBSERVATIONS BY COCHRANE-ORCUTT TYPE PROCEDURE WITH CONVERGENCE = ITERATION RHO LOG L.F. SSE ASYMPTOTIC ASYMPTOTIC ASYMPTOTIC ESTIMATE VARIANCE ST.ERROR T-RATIO RHO VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 55 DF P-VALUE CORR. COEFFICIENT AT MEANS INTEREST E SIGMA CONSTANT

Estimating rho-Cochrane- Orcutt two step |_ols spread interest sigma / resid=e dw |_sample 2 58 |_genr e1=lag(e) |_ols e e1 / noconst VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 56 DF P-VALUE CORR. COEFFICIENT AT MEANS E

Estimating rho Durbin-Watson Statistic |_ols spread interest sigma / resid=e dw REQUIRED MEMORY IS PAR= 32 CURRENT PAR= 500 OLS ESTIMATION 58 OBSERVATIONS DEPENDENT VARIABLE = SPREAD...NOTE..SAMPLE RANGE SET TO: 1, 58 DURBIN-WATSON STATISTIC =

Estimating rho Durbin Two-step |_genr y1=lag(spread) |_genr x1=lag(interest) |_genr x2=lag(sigma) |_ols spread interest x1 sigma x2 y1 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 51 DF P-VALUE CORR. COEFFICIENT AT MEANS INTEREST X E SIGMA X Y CONSTANT

Comparing estimates of rho