Add hamilton filter

[Shunsuke-Hori]

This PR adds "Hamilton filter" from Why You Should Never Use the Hodrick-Prescott Filter

Proposition 4 in the paper shows that the error term v_{t+h} of the regression

y_{t+h} = beta_0 + beta_1 y_{t} + ... + beta_p y{t-p+1} + v_{t+h}

gives cyclical component.

If *arg (p in the paper) is not passed, the true process is assumed to be a random walk. Then, we no longer need to do regression and we just take the difference.

Example:

df['y_c'], df['y_t'] = hamilton_filter(df['y'], 8, 4) # apply to data `y` in pd.dataframe
df['y_c'], df['y_t'] = hamilton_filter(y, 8, 4) # apply to data `y` in np.array

# random walk
df['y_c'], df['y_t'] = hamilton_filter(df['y'], 8) # apply to data `y` in pd.dataframe
df['y_c'], df['y_t'] = hamilton_filter(y, 8) # apply to data `y` in np.array

[jstac]

@Shunsuke-Hori I didn't know you were writing Python code now :-)

This looks good.

Random thought: Will we end up with a few filters? Should we have a subpackage? I guess we can created one later on if others are added...

[coveralls]

Coverage increased (+0.03%) to 95.165% when pulling bacc9c0 on Shunsuke-Hori:add-hamilton-filter into e5e76bd on QuantEcon:master.

[Shunsuke-Hori]

@jstac If more filters are added, we may be better to make it. Al least, I don't have any plan to add more filters now.

Two questions:

• Is there any way to test locally? Would anyone mind telling me how?
• Below is the difference between python and matlab output; python gives larger output for all periods. Is it wierd? too large? If so, does anyone know why?
  

[mmcky]

Hi @Shunsuke-Hori if you are not using windows you can use make test at the base level of QuantEcon.py. Otherwise you can use nose directly using nosetests -v assuming nose is on your path.

[Shunsuke-Hori]

Thank you @mmcky, I can run the test locally now.

It's ready for review.

[Shunsuke-Hori]

Regarding the difference with matlab output, original matlab code is using inv(X'*X)*X'y instead of (X'*X)\X'y. With \, output becomes close.

[mmcky]

@Shunsuke-Hori can you please update the description to the PR to document what this routine does, and any references of how it was implemented etc, a simple example for how it can be used etc. Thanks.

[Shunsuke-Hori]

@mmcky Thank you for pointing it out. It's updated.

[mmcky]

thanks @Shunsuke-Hori this is looking good. I think we can leave it in filter for now and when the time comes to add new filters we may setup a filters sub-module. I have marked this as ready and will allow a day for comments.

[mmcky]

thanks @Shunsuke-Hori for this contribution. Merging now.