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I've asked a few questions here before regarding my thesis. Although I try my best to follow-up on your suggestions, my statistical knowledge is limited but I try my utmost. Adding a predictive model to your thesis is not required (since it isn't taught during the studies) but my thesis coach insists. So I've just let SPSS dictate the best-fitting ARIMA model for my thesis.

Basically, I have taken some internet data (hbVol0LN is number of tweets, hbBullQuality0 is the ratio for postive against negative tweets, etc.) for 100 companies over 103 days. Here, the dependent variable is the return of the stock of each of those 100 companies per day. I already performed an OLS (although it has been pointed out that this is not the ideal model for my research, it is accepted by my coach), but now I believe this ARIMA model should hold the predictive value of the data.

It is very hard to find annotated ARIMA output online, or a paper which describes the output in a way I can understand. Could you perhaps give me some insights of what this output is telling me? Any help at all is greatly appreciated.

If you're having a hard time reading the graph, here's the full-size one: https://i.sstatic.net/H42YP.png

Again, I cannot express how frustrating it is for somebody who has hardly had to do any statistics during his studies, having to produce a predictive model. Therefore, really, any help is appreciated.

enter image description here

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    $\begingroup$ @ttnphns That suggestion is not very helpful. You should consider the fact that Pr0no is having trouble understanding time series model fitting and is a bit panicked. A simple explanation like what I give below seems to me to be more appropriate. $\endgroup$
    – Michael R. Chernick
    Commented Aug 20, 2012 at 21:09
  • $\begingroup$ I don't think so. If the OP would deign to read through "Forecasting option" in Case Studies submenu there, the misunderstanding (showing, in particularly, in comments to your good answer) would probably go away. $\endgroup$
    – ttnphns
    Commented Aug 20, 2012 at 22:05
  • $\begingroup$ @ttnphns My interpretation of MAPE = 170,905 and MaxAPE = 12045,319 (Model Fit table) come from the SPSS tutorial (which I already went through)...but it didn't answer my questions. I'm confused how as to how R-squared can be fairly reasonable at 0.286, while the uncertainty of the prediction (as explained in the SPSS help menu) seems to be, as said, 12045%? I don't understand, since in the example given in the SPSS help files, it's a neat 3%. $\endgroup$
    – Pr0no
    Commented Aug 20, 2012 at 22:12
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    $\begingroup$ @Pr0no, the R-squared is too low for time series modeling. Normally, it would be .70 or higher. So there's no wonder that MAPE is high (MAPE can be >100% which then means that your error, or magnitude of residual, most of the time is greater than the actual value you're predicting). The model (0,0,17) looks unnatural: 17-order MA-parameter! Almost just a noise. Your model is bad and predicts badly. There must be something you are missing when you do input and specifications in the Modeler $\endgroup$
    – ttnphns
    Commented Aug 20, 2012 at 22:49
  • $\begingroup$ R square is far from zero. MA terms of 9 and 17 are unusual but it is not a totally useless model. $\endgroup$
    – Michael R. Chernick
    Commented Aug 20, 2012 at 23:15

2 Answers 2

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My response to your other post How to perform pooled cross-sectional time series analysis? detailed how to deal with panel data. You have been put in a difficult position of having to explain the output of SPSS's expert modeler , which in my opinion is inadequate for your analytical needs. Using all of the data (10,300 observations) http://www.autobox.com/stack/pooled/dataset-irishstat.xls to identify an appropriate XARMAX model leads to model over-specification due to the "false sample size" since the daily readings/observations are not statistically independent of each other . I don't believe that the developers of expert modeler had your data set in mind. Additionally since no outliers (pulses/level shifts/seasonal pulses/local time trends are detected/incorporated i.e. unspecified deterministic structure there are additional uncertainties ( major questions ! ) about the final model.I should mention that I am a developer/writer of AUTOBOX which competes with SPSS, so my comments are not only expert but may be biased, but I hope not.SPSS attempts to conclude about 1) what differencing is appropriate for each series 2) what the delay is between the output and each of the input series 3) what the pdl/adl lag structure is in terms of both fixed and dynamic effects 4) what the appropriate ARIMA structure is ALL without any concern for unspecified deterministic structure. AUTOBOX actually details how the forecast can be decomposed to illustrate the impact of the predictor series. After a review of the model form/coefficients , I conclude that their results are questionable BUT I must reiterate that model identification is best done locally i.e. for each company separately and then tested for consistency across companies before concluding that a global estimate (your coefficents) have any meaning. One more thing the ma7 structure probably reflects a day-of-the-week effect which has been omitted but inadequately proxied.

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The first table is a set of statistics like R-square, mean square error, mean absolute percentage error etc that decribe how well the model fits the data. The acfs and pacfs are presented for the residuals. If the model is reasonable the residuals will look like white noise (independent zero mean random variables) which means that the acf and pacf are theoretically 0 at all non-zero lags. The sample estimates in your case indicate that the residuals do not have significant lagged acfs and pacfs. So that is good for the model.

The model parameter block show which AR and MA terms were fit, the value of their coefficients, the standard error of the estimate, the t statistic for the significance test and the p-values for the test of the null hypothesis that the coefficient is 0. The other covariates that you included in the model are also given with their parameter estimates and p-values. There is one AR term at lag 2 and moving average terms at lag 7, lag 9, and lag 17.

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  • $\begingroup$ Thanks Michael. What I understand is that SPSS only returns one model. This is why in the "Model Fit" table, all values are similar I guess. But I understood that the MAPE (mean absolute percentage error) is a measure of how much the DV varies from the model-predicted level. It therefore provides an indication of the uncertainty in the prediction. As I understand, in my case the uncertainty is 12,000%? That would be laughable (though not funny ;-) $\endgroup$
    – Pr0no
    Commented Aug 20, 2012 at 21:15
  • $\begingroup$ @Pr0no To get a prediction you take the covariates and the lagged observations, multiply them by their coefficients and add them up to predict the value one step into the future. $\endgroup$
    – Michael R. Chernick
    Commented Aug 20, 2012 at 21:20
  • $\begingroup$ So basically from this output you can write a predictive formula like you would write an explainatory formula using OLS output? Also, am I right with the 12,000%? Or else what does it mean? Thanks for your help btw. I'm at my wit's end here :-) $\endgroup$
    – Pr0no
    Commented Aug 20, 2012 at 21:22
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    $\begingroup$ Yes regarding determining the prediction formula. I am not sure where you get the 12% from. Several of the variables in the fit table are informative about how good the fit is . Also the R square of 0.286 means that approximately 29% of the variation in the response is explained by the model. That isn't great but it is still significant. All the coefficients in your model are statistically significant with p-values less than 0.001 except for one which is at 0.039. $\endgroup$
    – Michael R. Chernick
    Commented Aug 20, 2012 at 21:28
  • $\begingroup$ I mean MAPE = 170,905 and MaxAPE = 12045,319 (Model Fit table), both of which were measures of uncertainty of the prediction. At least, that's how I understood it. $\endgroup$
    – Pr0no
    Commented Aug 20, 2012 at 21:35

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