Error correction model in vector r

Question

I need to evaluate the relationship between prices in New York (N) and London (L) using a vector error correction model adapted from Joel Hasbrook. After much research on the Internet, I still have not achieved much success, so I thought that I would ask you experts to see if I could get any direction in this model.

My dataset is a dataframe with date, time, symbol, price.

Refund (r_t) is defined as the logarithmic difference between the price for each 15-minute interval (p (t) -p (t-1)) for both New York and London (equations 1 and 2).

The model uses r_t in New York to simulate 2 return lags in New York and London (equation 3).

He then uses the rt model in London for two lag returns in New York and London (equation 4).

N and L represent New York and London, respectively, somewhere in the model, and t represents time.

r_t^N=∆ log(P_t^N ) r_t^L=∆ log(P_t^L ) r_t^N=α(log(P_(t-1)^N)-log(P_(t-1)^L))+∑_(i=1)to 2(γ_i^(N,N) r_(ti)^N) + ∑_(i=1)to 2(γ_i^(N,L) r_(ti)^L)+ ε_t^N r_t^L=α(log(P_(t-1)^L)-log(P_(t-1)^N))+∑_(i=1)to 2(γ_i^(L,L) r_(ti)^L) + ∑_(i=1)to 2(γ_i^(L,N) r_(ti)^N)+ ε_t^L 

Any help would be soooooo approved. Thank you in advance for your help!

I am new to R and have worked a bit with SAS and time series procedures. I saw a link to using vars (), but the examples I looked do not seem to be applicable, so I'm pretty stuck. I made DW statistics, and there is joint integration.

I just can't figure out how to write code for this ...

Answer 1

You can use the urca package in R to do this: (let's say your mydf data with column LN as stock returns for the London stock market and NY as stock returns for the New York stock market). The following is an example code (not verified):

 install.packages("urca") library(urca) mysample <- mydf[, c("NY", "LN")] myvecm <- ca.jo(mysample, ecdet = "const", type="eigen", K=2, spec="longrun") myvecm.ols <- cajools(myvecm) 

Note. I assume that you have used Johansen co-integration test and eigen statistics; k indicates the delay number, which for your example is 2, ecdet says that cointegration has a constant. See the manual for more details.