Autoregressive process

[francoisd]

Hello,

I am fairly new to EViews and econometrics; I therefore apologize if I sound ignorant. I intend to do a research on the relationship between macroeconomic factors and stock returns. My dependent variable will be the returns on the S&P 500 and my independent variables will be the industrial production, the CRB raw industrial index, the ISM index, retail sales, initial claims, housing starts, CPI core, PPI and oil prices. My research will be somehow based on the Chen, Ross & Roll paper written in the 80s.

My question is the following. I read posts in other sections of the board and I still can not understand what an autoregressive process is? When I add a AR(1) to my regression model, it seems to fit better as the adjusted R-squared jumps by almost 20%. I was therefore wondering if someone could explain in a very simple way (I sometimes have no clue what is explained in other posts as my knownledge on the subject is not advanced enough) what an autoregressive process is and why does adding AR(1) to my model increases the goodness of the fit?

Thank you very much

best regards

[EViews Gareth]

In very simple terms you're just saying that today's error (or randomness, or "shock"), is related to yesterday's error (or randomness or "shock").

If there was a shock that caused the stock market to fall by a lot yesterday, then a large positive AR(1) coefficient would say that the stock market would also fall today.

[startz]

If you are finding large adjusted R-square from adding AR(1) to the explanation of the return on the S&P 500, you should be concerned that you have misspecified something (unless you are using overlapping observations). The S&P 500 is pretty close to white noise.

[francoisd]

Thank you very much Gareth and Startz

However, I feel dumb asking but are overlapping observations simply when the dependent variable is available for every period and the regressors as well?

Here is my equation without AR(1)

INDEX_SP500 = -0.0667205076021*UIC + 2.36212979571*RETAIL + 1.39401734926*PPI - 0.228390336426*OIL_PRICE + 0.111679657083*ISM + 3.44661320396*INDPRO - 0.320943599836*HOUSING_STARTS - 0.202327778446*CRB - 8.97075049799*CPICORE + 0.090202299803

Here is my equation with AR(1)

INDEX_SP500 = -0.0555198212617*UIC + 0.665364225137*RETAIL + 0.0942370231408*PPI - 0.0288186121632*OIL_PRICE + 0.157091847903*ISM - 1.24855689449*INDPRO - 0.0855792798859*HOUSING_STARTS + 0.220367712199*CRB - 1.60104228572*CPICORE + 0.0396127759132 + [AR(1)=0.970158686244]

The difference of adjusted R2 is 20% less without AR(1). However, coefficients just make more sense considering their impact on the S&P500 when I do not use AR(1).

All my series are monthly, with percent change year-to-year from Jan 1993 to Dec 2008. Do you still reckon that I've misspecified something Startz? Furthermore, I was thinking of using lagging the CRB raw industrials index by 6 and 12 periods and perhaps do the same with the industrial production by 1 or 2 periods.

thank you

regards

[startz]

An example of overlapping observations would be using quarterly returns observed each month.

If you'll forgive a strange question, are you quite sure you have the S&P 500 return, as opposed to the level of the S&P 500 index?

[francoisd]

Sorry, I have not made myself clear. You are right, I am using the index values but using year-to-year percent change for monthly data.

Thanks for answering my question on the overlapping variables, I do not think I have overlapping data since all my variables are monthly; the only one I had to adjust was the weekly unemployment claims that I converted into a monthly serie.

Do you find that my equation makes sense?

thank you

[startz]

Sorry, I have not made myself clear. You are right, I am using the index values but using year-to-year percent change for monthly data.

Thanks for answering my question on the overlapping variables, I do not think I have overlapping data since all my variables are monthly; the only one I had to adjust was the weekly unemployment claims that I converted into a monthly serie.

Do you find that my equation makes sense?

thank you

That's a helpful explanation. The issue you have is that several of your variables are nonstationary. Depending on what you're trying to do, that can be a major problem. Perhaps others can usefully chime in here.