The test statistic for the Durbin Watson test can range from 0-4 from what I have gathered. Now the lower limit of 0 makes sense considering the test statistic consists of two summations which are both squared and divided by each other; but what gives us our upper limit of 4? Is this limit incorrect? Also, if the upper limit to this test statistic is not 4, than what is it?
Regression Analysis – Understanding the Durbin Watson Test for Detecting Autocorrelation in Time Series
autocorrelationdurbin-watson-testregressiontime series
Related Solutions
For each of the 86 companies , identify an appropriate ARMAX model which should incorporate the effects ( both contemporaneous and lag ) of the two user-suggested predictor variables and any necessary ARIMA structure. Incorporate any needed ( and empirically identifiable ) structure reflecting unspecified deterministic effects via Intervention Detection. Use these empirically identified intervention variables to cleanse the output series and remodel using the cleansed series as an ARMAX model. Now review the results for each of these 86 case studies and conclude about a common model. Estimate the common model both locally ( i.e. for each of the 86 companies ) and then estimate it globally ( all using the cleansed output series). Form an F test according to Gregory Chow http://en.wikipedia.org/wiki/Chow_test to test the null hypothesis of a common set of parameters across the 86 groups. If you reject the hypothesis then carefully examine the individual results ( 86 ) and conclude about which companies DIFFER from which companies. We have recently added this functionality to a new release of AUTOBOX, a piece of software that I am involved with as a developer. We are currently researching a formal way to find out ala Scheffe which companies differ from the others.
AFTER RECEIPT OF DATA:
The complete data enter link description hereset can be found at , I selected the first 3 companies (AA,AAPL,ABT). I selected trading volume (column S) as the dependent and the two predictors tweet (Z) and wiki (V) per the OP's suggestion. This selection can be found at enter link description here. Simple plots of the three dependent series suggest anomalies 
and 
and 
. Since anomalies are present the appropriate regression needs to take into account these effects. Following are the three models ( including any necessary lag structures in the two inputs ) and the appropriate ARIMA structure obtained from an automatic transfer function run using AUTOBOX ( a piece of software I have been developing for the last 42 years )
and 
and 
. We now take the three cleansed series returned from the modelling process and estimate a minimally sufficient common model which in this case would be a comtemporary and 1 lag PDL on tweets and a contemporary PDL on wiki with an ARIMA of (1,0,0)(0,0,0). Estimating this model locally and globally provides insight as to the commonality of coefficients .
with coefficients 
. The test for commonality is easily rejected with an F value of 79 with 3,291 df. Note that the DW statistic is 2.63 from the composite analysis. The summary of coefffici
ents is presented here. The OP poster reflected that the only software he has access to is insufficient to be able to answer this thorny research question.
Best Answer
The limits are both correct.
The DW statistic is, for $e_t$ the residuals of an appropriate regression, \begin{align*} DW&=\frac{\sum_{t=2}^T(e_t-e_{t-1})^2}{\sum_{t=1}^Te_t^2}\\ &=\frac{\sum_{t=2}^T(e_t^2+e_{t-1}^2-2e_{t}e_{t-1})}{\sum_{t=1}^Te_t^2}\\ &=\frac{\sum_{t=2}^Te_t^2}{\sum_{t=1}^Te_t^2}+\frac{\sum_{t=2}^Te_{t-1}^2}{{\sum_{t=1}^Te_t^2}}-2\frac{\sum_{t=2}^Te_{t}e_{t-1}}{\sum_{t=1}^Te_t^2} \end{align*} The first two fractions are obviously between 0 and 1 (both entries are positive, and we sum more positive terms in the denominator). In fact, they will almost always be very close to 1, as the numerators only differ from the denominator by $e_1^2$ and $e_T^2$, respectively, which, for $T$ reasonably large, will be negligible.
The third one can be bound to be between -1 and 1 by the Cauchy-Schwarz inequality: \begin{align*} \left(\sum_{t=2}^Te_{t}e_{t-1}\right)^2&\leq\sum_{t=2}^Te_{t}^2\sum_{t=2}^Te_{t-1}^2\\ &\leq\sum_{t=1}^Te_{t}^2\sum_{t=1}^Te_{t}^2=\left(\sum_{t=1}^Te_{t}^2\right)^2, \end{align*} so that $$ -\sum_{t=1}^Te_{t}^2\leq\sum_{t=2}^Te_{t}e_{t-1}\leq\sum_{t=1}^Te_{t}^2 $$ Somewhat less rigorously, but more intuitively: We have that the DW statistic can approximatively be written as $$ DW\approx 2(1-\hat\rho),$$ where $\hat\rho$ is the estimated $AR(1)$ coefficient. For $\hat\rho\to\pm1$, we see that the statistic tends to the bounds.
That this is not rigorous follows from the fact that $|\hat\rho|$ can be bigger than one. For large $T$ that should not happen very often when the true $\rho$ is less than one in absolute value, as it is required to be by assumption. But it can happen: