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Math Help - OLS Regression

  1. #1
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    OLS Regression

    Hi Guys,

    I am having some difficulties estimating a univariate equation. I was not able to write down the formula here, so i have uploaded it in the file attached.

    Essentially, in equation (1), the dependent variable is output, and independent variables are an autoregression of the dependent variable and the Termspread and Federal Funds Rate.

    The data is all monthly figures, which is why in equation (2) a scaling constant (c) is used which is equal to 1200. I need to make a forecast h=12 (so 12 months ahead).
    What i have done is substituted, c=1200 and h=12 into equation (2), and ran this under generate on eviews.

    I then ran equation (1) as an OLS regression.

    However my results look very strange, could someone please help me as to what am i supposed to do?

    Thanks in advanced!

    Mark
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  2. #2
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    Re: OLS Regression

    Hey markviduka.

    Its very hard to give advice on a problem where one can not see the data or attempting to put it into context.

    These things will affect the ability to try and model the data and if possible, make forecasts for future values.
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  3. #3
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    Re: OLS Regression

    Thank you for your reply. I have added bellow the literature, and the exact dataset used in the literature. The model can be found on the first page, including an explanation. The results of the forecast are found on page 3.

    Hope this calirifies my question,

    Mark
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  4. #4
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    Re: OLS Regression

    Here are the descriptions of the variables in the excel file:

    • Ggz_spr: the “GZ credit spread,” the average (cross-sectional) credit spread on senior unsecured corporate bonds issued by nonfinancial firms in our sample (in percentage
    points).
    • baa_aaa: the spread between yields on Baa- and Aaa-rated long-term corporate bonds issued by industrial firms (in percentage points).
    • termspr: term spread (3-month Treasury yield less 10-year Treasury yield) (in percentage
    points).
    • ffr_r: real federal funds rate (in percent).
    • empl: private nonfarm payroll employment (thousands of employees).
    • ipm: manufacturing industrial production index (2007=100).
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  5. #5
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    Re: OLS Regression

    With regards to your assumptions, I'm assuming that yoou assume a normally distributed density for the delta's of the logarithms of the prices. This is typically assumed in introductory stochastic pricing mechanisms.

    The thing though that I think you should do before you do anything is to plot your predictor as a function of your response and then on the same plot, plot a mean response curve of the predictor.

    This serves a couple of reasons: firstly you can look at the normality assumption for the residuals and secondly you can use it to see the behaviour of the mean response as well as for selected realizations (i.e. individual trends).

    Have you used R before? Or SAS? You can use excel to do it as well but either way you need to plot the values of the predictor (thing you are predicting) against the response variables for all data points and then do a mean response.

    Based on the mean response and the data trends you then fit a least squares model based on the data and the nature of the problem.

    The information you have given me on financial variables is not helpful for me because I don't understand the assumptions or the interactions that take place. If correlation exists between these variables, then it will be a problem.

    What I might recommend though is that for predictions you look at worse case scenarios. This translates into finding conservative variances for your predicted distributions so that they are high enough to be conservative but not any higher.

    This is the idea behind "fat-tails" in finance and although they are terrible at what they do (handling events like default), the idea is still valuable in a sense.

    You can search the literature and text-books for fat tails and you should look at any theory in probability and statistics regarding getting any kind of conservative estimate for the variance measures given the data.

    Some distributions that deal with fat tails include the Cauchy and t-distributions and if you have skewed distributions, then you will need to look at a variety of distributions like the Weilbull distribution.

    I say the above because markets are rigged and there is always the case of Enrons, WorldComs, and Bear Sterns. Unless you are an insider, the best possible approach is to get an idea of how bad it can get and besides actual confidence intervals, the next thing is the volatility.

    Apart from this I would also look at any assumptions with a really skeptical eye. If you are taking forecasts for things like production indices, then I would be really careful about using them particularly if they came from another source.

    Also if you are looking at treasuries, you will want to look at things like real government debt and how manipulation is used by the rating agencies to keep a rating. It is in the interest of big spenders to have a high rating because the interest is going to be low, but the US is a big spender with massive debt which means that a lower rating makes them pay higher interest.

    Models don't really give you an insight into the human element which is greed and manipulation and if you don't factor these in (and I don't mean though the joke economics model of rational agent theory) then your predictions will probably be off.
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  6. #6
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    Re: OLS Regression

    Thank you very much for your response Chiro.

    I am using a software called Eviews (econometric views). What I am unsure about is how to manipulate this dependent variable (with the scaling constant "c" and forecast horizon "h") as the paper has done to make the forecast (on page 1, right bellow equation (2)).

    I am using a very different data-set though, I am just trying to understand the methadology in the paper.

    I have tried to use the data from the paper to match the results on page 3. For example, to make a 3-month forecast for payroll employment (first top collumn on page 3): we use the OLS regression: Payroll employment = Payroll employment(t-1) + Payroll employment(t-2) +Payroll employment (t-i) + Term Spread + Real FFR.

    The variables term spread and real ffr are taken as given. However, the paper states the changes must be made to the dependent variable Payroll employment such that ∇Y(t+h) = (c/h+1) ln(Y(t+h)/Y(t-1). I have made those changes in the following way for this three month forecast for the equation mentioned in the previous paragraph: ∇Y(t+3) = (1200/3+1) ln(Y(t+3)/Y(t-1). However, after I regress this, the output does not match the results of the paper, not even closely ! Essentially, this is where the confusion lies.. am i doing something wrong in this manipulation of the dependent variable?

    I hope this is a little clearer, please let me know if I can further explain.

    Mark
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  7. #7
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    Re: OLS Regression

    Did you do the same transformation for the right hand side? (There are delta terms on the RHS as well as the LHS)
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  8. #8
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    Re: OLS Regression

    According to the paper the transformation need be done to the dependent variable (which does have Autoregression on itself on the RHS). The remainder of the variable on the RHS do not seem to require a transformation. I just tried to run the transformation for the other variables (term spread and federal funds rate), but once again the results differ significantly to the paper..
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  9. #9
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    Re: OLS Regression

    You have delta terms on both sides: the one on the RHS has an argument involving i. If you haven't transformed all the terms on the RHS you will need to do that first.
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  10. #10
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    Re: OLS Regression

    If I understand correctly, run the transformation ∇Y(t+3) = (1200/3+1) ln(Y(t+3)/Y(t-1) seperately for all thee variables (Y=industrial product, term spread, and real federal funds rate)? Once this is done, carry out the normal regression?
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  11. #11
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    Re: OLS Regression

    There are delta terms on the RHS after the first sigma: you need to calculate those terms as well using the formula.
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  12. #12
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    Re: OLS Regression

    Thank you chiro!
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