A few thoughts:

1. Can you not just use a goodness-of-fit test? Choose a distribution and compare both samples. Or use a qqplot. You may want to do this with returns (i.e. changes) instead of the original series, since this is often easier to model. There are also relative distribution functions (see, for instance, the reldist package).
2. You could look at whether the two series are cointegrated (use the Johansen test). This is available in the urca package (and related book).
3. There many multivariate time series models such as VAR that could be applied to model the dependencies (see the vars package).
4. You could trying using a copula, which is used for dependence modeling, and is available in the copula package.

A few thoughts:

1. Can you not just use a goodness-of-fit test? Choose a distribution and compare both samples. Or use a qqplot. You may want to do this with returns (i.e. changes) instead of the original series, since this is often easier to model. There are also relative distribution functions (see, for instance, the reldist package).
2. You could look at whether the two series are cointegrated (use the Johansen test). This is available in the urca package (and related book).
3. There many multivariate time series models such as VAR that could be applied to model the dependencies (see the vars package).
4. You could trying using a copula, which is used for dependence modeling, and is available in the copula package.

If the noise is serious concern, then try using a filter on the data before analyzing it.

A few thoughts:

1. Can you not just use a goodness-of-fit test? Choose a distribution and compare both samples. Or use a qqplot. Possible do this with returns instead of the original series.
2. You could look at whether the two series are cointegrated.

A few thoughts:

1. Can you not just use a goodness-of-fit test? Choose a distribution and compare both samples. Or use a qqplot. You may want to do this with returns (i.e. changes) instead of the original series, since this is often easier to model. There are also relative distribution functions (see, for instance, the reldist package).
2. You could look at whether the two series are cointegrated (use the Johansen test). This is available in the urca package (and related book).
3. There many multivariate time series models such as VAR that could be applied to model the dependencies (see the vars package).
4. You could trying using a copula, which is used for dependence modeling, and is available in the copula package.