Hi, guys,
it might sound stupid, but could you simply explain how to identify if regresion is Time series or Multiple (from having a short discription of the case and from regresion table)?
Multiple regression means that you have a dependent variable explained by 2 or more independent variables. How can these dependent and independent variables be? You may have time series variables, or cross sectional variables (in cross sectional you have different companies, stocks, etc instead of moments in time of only one company, stock, etc), so you can have a multiple time series regression model, or you can have a multiple cross-sectional regression model.
For example:
GDP(t) = b0 + b1*C(t) + b2*Inv(t) + b3*G(t) + b4*X-M + e(t) … Multiple time series regression
GDP(t) = b0 + b1*GDP(t-1) + b2*GDP(t-2) + e(t) … Autoregressive time series regression, order 2
AA bond spreads from USA market = b0 + b1*(D/E ratio)(i) + b2*(EBITDA)(i) + e(i) … Multiple Cross-sectional regression. Note that (i) means each company from the sample that goes from 1 to n.
So there is no partition between multiple regression and time series, they can be the same, what you must differentiate is times series models vs cross-sectional models.
Any question please ask!. Regards
Perfect, It make sence.
So how then you would “add to the boxes” all time series material? What I see now it is a big mess - AR1, ARCH1, AR2, seasonality, etc. How to make it clear? And what is main diff. among them?
P.S. did you learned that from material only, or have any work experiance?
Well, you know, how could I summarize the whole time-series chapter, it is quite difficult to do. What I can tell is the understanding hidden below the words.
AR(1), AR(2) or even AR§ are just autoregressive models, this means we are trying to explain the present of a time variable with past values of itself. Maybe using only 1 past period is not enough to explain the present, maybe we need 2 past periods (AR2), or maybe even it is not enough with contiguous periods, for example it is necessary to use X(t) = b0 + b1*X(t-1) + b2*X(t-12) + e(t).
But how we know we are correctly modeling (specifying) the X variable using past values of itself? The error terms behavior will guide us. A correctly specified AR model has an error that comply with OLS model assumptions (check them again). So in theory we have some tools to test the error terms behavior. One of them is using error autocorrelations, that is not more than calculating the correlation of the error serie e(t) with itself but 1 period lagged e(t-1). Commonly, using 1 lag is not enough, we need more lags; the important lags we need to check out are those related with seasonality. For example, if we are modeling quarterly sales (1Q 2Q 3Q 4Q sales) it is very likely that 4Q sales were highly correlated with past 4Q sales (the seasonality effect), so it is very likely that if our model didn’t consider the b2*X(t-4) independent variable, our fourth lag error autocorrelation be significant, so this means that our AR(1) model was not correctly specified. To fix this, we add b2*X(t-4) as an independent variable. Summing up, to declare our AR model correclty specified, the error autocorrelations must not be significantly different than zero, this means that t-tests are lower than 2.0 (approx), or p-values higher than alpha (0.05).
Note that when we use AR models we cannot use Durbin-Watson (D-W) statistic, because the independent variables are correlated with the error terms, so its use turns invalid. The exam can display D-W value with AR models, but do not use it for determinating autocorrelation of errors, use the above procedure.
ARCH models, what are those things?, remember its name. ARCH means Autoregressive Conditional Heteroskedasticity, so it is used to check for conditional het. But on what? On the error terms (it is always about the errors…). Conditional heteroskedaticity would mean that the error terms increase or decrease with the increase or decrease of the independent variables; and since in the AR models the error terms are correlated with the independent variables, it is the same to use only errors for test conditional het.
ARCH(1) example
error(t)^2 = b0 + b1*error(t-1)^2 + u(t) … where u(t) is the error term of the error model (crazy right?)
We build this to test the value of b1, if this b1 is statistically different than zero, our AR model had conditional heteroskedasticity, so we must recalculate the initial AR model (already correctly specified first) using robust errors (also known as white-corrected errors) OLS method.
I think this is the travel across the time-series world. Note that understanding this is important, but more important is know how to interpret statistics like T, F, R2, D-W, lag autocorrelation, unit roots, etc.
About your last question, I have a relative good background on econometrics. I learnt how to demostrate formulas, use econometric software and theory explaining exams. I like much more the CFA questions because they are more direct, just that 
Any question please ask! Regards.
Awesome, thank you so much for that post Harrogath! I’m struggling with Time Series, and this is the best explanation I’ve seen so far.
Yes. Perfect. Thanks.
I’m so glad guys to be a help for you all. Thanks!