I have got two time series data sets for 63 years. I want to fit a trend line to them. Here is what am doing:
- I first estimate a linear (y=a+bt+e) and an exponential model (y=at^b) as the graph shows that the data is rising) but the Durbin Watson is very low (it is 0.8).
- So I check the data for autocorrelation in Eviews using the LM test. There is positive autocorrelation.
- I then include 2 AR terms in my linear and exponential regression models.
- When I get the results of both these models I select the one with the smaller AIC abd BIC criteria. (which is the linear one)
- The Durbin Watson is now 1.8
As I am new to time series regression please let me know if my procedure is correct or whether I am missing something. Also as I am regressing the dependent variable on only time (as the independent variable) is the presence if autocorrelation correct?? Most textbooks refer to independent variable other than time when explaining autocorrelation.
This is my data. Thank you
Area
9357
12690
12321
13283
13784
13921
13981
14105
14300
14899
14840
14795
15111
15270
15442
15170
15357
15474
15648
15868
16478
16972
16658
16799
18377
18660
18934
19047
19201
19543
19596
19630
19865
20237
20458
20631
20879
21168
21299
21258
21219.8
21464.6
21771.6
22210
22556
22362
22554.056
23138.164
23345.748
23598.183
23751.836
23914.204
24119.436
24516.211
24760.722
24992.725
25445.042
25881.998
26210.913
26157.423
26398.806
26309.387
26453.969
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 63 values exhibit a non-constant error process and two distinct trends . See the Tsay article http://onlinelibrary.wiley.com/doi/10.1002/for.3980070102/abstract and here http://docplayer.net/12080848-Outliers-level-shifts-and-variance-changes-in-time-series.html without charge. The equation is here
and final residual plot here 
. The break-point in error variance at period 27 (1975) is clouded by the strong ARIMA structure . The variance of the residuals reduced dramatically at period 27 suggesting Weighted Least Squares. The final Actual/Fit/Forecast graph is here 
. It is interesting (at least to me) that at period 27 (1975) the trend abated while the error variance reduced. Do you have any idea as to what may or may not have happened (permanent effect) starting at 1975. Also interesting is that upon a close look at the variablity in the original series supports the exploratory data analysis done here. Following are the errors (without weighed analysis) suggesting the deterministic reduction at or around period 27 
and 