I am studying stock prices. Let Pt be price of stock at time t. While Pt is non stationary, the return, rt=log(Pt/Pt-1) is stationary.
However, when I study on rt, I decide on an ARMA(0,1) without intercept process rather than ARMA(0,0).
I am confused with this result. I was expecting rt to be an ARMA(0,0) process which supports Pt to be a white noise.
However, I obtained ARMA(0,1). Does not this result contadict with effciciency market hypothesis?
I use BIC criterion to select the model. The BIC criterions are as below:
MODEL BIC-model contains intercept BIC-model does not contain intercept ARMA(0,0) -11,936.6 -11,941.2 ARMA(1,0) -11,936.9 -11,941.9 ARMA(0,1) -11,937.1 -11,942.0 ARMA(1,1) -11,929.3 -11,934.2 ARMA(2,0) -11,929.5 -11,934.4 ARMA(0,2) -11,929.3 -11,934.2 ARMA(2,1) -11,921.9 -11,926.5 ARMA(1,2) -11,921.5 -11,926.4 ARMA(2,2) -11,922.7 -11,927.5
According to BIC, I decide MA(1) process. The statistics of MA(1) process are as below:
Coefficient 0.058409111 Standard Error 0.019695617 P-value 0.003021036
I can't explain the obtained result.
I am also confused with the constant term. Even though BIC does not select a model with constant, I suspect the model include a constant term since in long term the price will go up becouse of the inflation rate.
I haven't studied in finance so much. I will be very glad for an explanation. Thanks a lot.