Dear Niematallah,

You can easily use a dummy variable: define value-1 for weekends and value-0 common days. Just please pay attention to interpret coefficient of your dummy variable. For instance in a log-log model, since you do not have dummy variable in a logarithmic form, its coefficient can not consider as elasticity. Please take a look on some related papers to find out how you can cover this issue.

Good luck!

Thank you for you answer

so the only way to do that is to use dummy varaiables?

Perhaps use an approach akin and analogous to research done with respect to trading and retail volatility for such events as Black Mondays, Black Fridays, Cyber Mondays, etc and other "special"/notable days in trading , retail and economic history.

Article Black Friday and Cyber Monday: Understanding consumer intent...

Obviously you are using daily data on electricity consumption. Therefore, you seem to have enough degrees of freedom to set several dummies. Nevertheless, I recommend to look first on a diagram (preferably a circle ("clock") diagram with 7 sectors instead of the usual 12) to get an impression if the data are very different for the week days. You can also look at the average consumption of the week days, which could make it possible to set only one dummy with different values in the first round. Then you can try a regression with unit dummies for other special days and use the results to adjust the data for this effect and again make the first step (to set new weekday dummies) and do a second regression. Of course, one could repeat this procedure several times, but I think that two steps are sufficient.

Dear Nema

A technique other than dummy variables is probit or logit models, setting 1 for the special days, and 0 for the ordinary days. You need to have a look on the literature on these two models.

Several good answers have been posted, especially about using dummy variables for special day effects. If you use a dummy for these, just be careful that each of the "special days" meets some common criteria; for example, including a holiday with with a Saturday might be too much of a stretch.

The second part of your question seems to ask about structural change. If I am mistaken, then ignore the rest of this. If it does, then consider going even further using dummy variables something like this:

• Create a variable that we might call time; it preferably begins with zero for your first observation and increases with each time period. (Using zero makes the intrepretation easier.)
• Create a dummy variable that might be zero before an event and one otherwise.  For example, it might be a date related to the Kyoto Protocol you might wish to testing to see if structural change occurred afterwards in the usage of electricity. Let's call it DKyoto for example.
• Multiply time * DKyoto; let's call this third new variable tmDKyoto
• Including time, DKyoto, and tmDKyoto allows a researcher to test for structural change in the daily demand for electricity because this approach allows both the intercept and the slope (of time) to change (i.e., the coefficients are additive with the originating series.)  Moreover, using the t-Statistic related to each estimated coefficient implicitly allows the researcher to statistically test for this structural change.  We prefer doing it this way instead of running two separate regressions (i.e., one an the data before and another regression after the suspected structural break was thought to occur) and then doing a Chow test.
• As noted previously, you probably have plenty of degrees of freedom. Although you have them does not necessarily mean that you should use them, of course. With that said, you might consider potentially include the special day dummies in the same model. It is a tricky question about using them and multiplying them by tmDKyoto.  This is an already long answer, so let's not go into that discussion unless this gets to the point(s) of your question, especially since you seemed to be seeking a different approach than using dummy variables.

I hope this helps.

Rob

Thank you for your answer

• I have  run chow test for structural changes. And i would like to model the effect of the structural changes and the special days.
• By  "Moreover, using the t-Statistic related to each estimated coefficient implicitly allows the researcher to statistically test for this structural change" what do you mean?
• I have plotted the public holidays and weekends against time to check their pattern in order to decide whether to use one dummy variable for all (if they have similar pattern) or use separate dummies for each. Is this the right way to do that?
• Also, the special day dummies are for the whole period before and after the structural changes, so should they be multiplied by tmDkyoto?

Thank you

Its better to see the histogram of power consumption on special days, excluding special days and including special days. Then the summarize it. If you find a large difference then it would be better to add the special days to one(some) cluster(s). Of course caution is needed here.  That will help in analyzing properly. For example you are only considering say sunday. The number of sundays will be smaller thereby some times show statistically significant which is because of the small size. it is a problem. And if you make many dummies then it will affect the f test.

Hi Niematallah,

I am pleased that my answer might be of some use. May I suggest that you glance at the file that is attached so I can respond to some of your questions.  This must be quick because I need to teach a class in a few minutes. I will write more later about your last two questions.

Notice the estimated coefficients on both DKyoto and tmDKyoto are both above 1.96, which is the critical t for large sample sizes that is almost guaranteed when we are looking at daily data.  The logic goes something like this.  Since both of the t-statistics exceed the critical value, we might be able to reject the null hypothesis of no difference between before and after the Kyoto event.   In other words, we are able to discern the difference in intercept and slope of the two different equations if we run them separately and then conduct a Chow test.  These t-statistics are the basis of these inferences.  

Of course, it is possible that the equation may not have both a change in intercept and slope.  That depends on the situation and a strong case can still be made for rejecting the null hypothesis if the dummy on the intercept is significant.  Changing the slope without changing the intercept is a different issue, and I can go through that if you wish. 

I will address the big dots for weekend observations later.  I need to run to class now.  If anything is unclear, please let me know.

Rob

Hi Mr. Rob

Thank you for your explanation it is extremely helpful.

Based on the attached document the equation before the event is: EU= 1000+0.005(time)+e, isn't it?

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In order to check the significance of the dummy variables for structural changes and when regressing the EU value on the (time) ,Dkyoto and tmDkyoto can I include the other explanatory variables also? For example temperature, and dummies for special days?Please find attached the estimation output  using all the explanatory variables

Devent, time0Devent are the variables to counter for the structural changes. That is Devent is a dummy varaiable that equals 0 for  observations  before the event and equal 1 for observations after, while time0Devent is time multiplied by Devent.

As can be seen the t-statistic for the 2 variables is significant, Does this mean we can reject that there is no difference between before and after the event?

Thank you.

Niema