# Time Series-Regression analysis- Monthly Revenue instead of Quarterly revenue

I am studying Time series with Regression analysis.

I have data that has seasonality and trend. I am using Dummy variables for seasonality- In this case I am using quarters.

I selected Quarter 1, Quarter 2 and Quarter 3 and obtained the following model:

$Revenue= \beta_0+\beta_1{X_{1t}}+\beta_2({X_{S1,t}})+\beta_3({X_{S2,t}}) + \beta_4({X_{S3,t1t}})$

Or equivalently:

$Revenue= \beta_0+\beta_1{X_{1t}}+\beta_2(Qrt1)+\beta_3(Qrt2) + \beta_4(Qrt3)$

However if instead of having the quarterly revenue I have available the monthly revenue how should I analyse this time series?

I am confused regarding this question. I do not understand what is suppose to do, if I have the monthly revenue, I think instead of:

$revenue= \beta_0+\beta_1{X_{1t}}+\beta_2({X_{S1,t}})+\beta_3({X_{S2,t}}) + \beta_4({X_{S3,t1t}})$, I should have

$revenue=\beta_0+\beta_1(Jan)+\beta_2(Feb)+\beta_3(March)+\beta_4(April)+\beta_5(May)+\beta_6(JUn)+\beta_7(July)+\beta_8(Aug)+\beta_9(Setp)+\beta_10(Oct)+\beta_11(Nov)$

But I am not really sure what is meant by this question.

Can anyone help me on this?

Thanks

I edited the question to add the following information:

I have the following data:

The question is: If I have available Monthly revenue, how should I analise the time series?

• Is this an assignment for school? If so, can you post the actual question itself? If not, what is the end goal here? What are you trying to find? At the beginning of this question, you say you have seasonal data...but you actually have monthly data. Please clarify and I'll do my best to help you out – Sarah W Mar 19 '17 at 0:20
• Hi, I edited my post and add the information I have. I would like to understand what is suppose to do in this case. I was reading about this on the internet and I found something called cubic spline interpolation, which converts quarterly data to monthly data but I am not sure if I really need to do this. Thanks – user290335 Mar 19 '17 at 0:35
• Ghysels MIDAS (MIxed DAta Sampling) model is designed for use with data of mixed temporal frequencies. Check it out. – Mike Hunter Mar 19 '17 at 0:52

If you have monthly revenue data and the goal is to determine the regression coefficients for quarterly revenue, then you would have to categorize each month into the appropriate quarter. For example - if the 1st quarter is defined as October/November/December, then the revenue for these months should be grouped into the variable Qrt1. However, not all companies define their quarters/seasons the same...so make sure you're defining them correctly.

In this data set there is no monthly data. Based on this table, the quarterly data cannot be converted into monthly data. If you have monthly data, then you can easily convert it into quarterly/seasonal data by creating a new categorical variable and then assigning the months accordingly.

If you're trying to compare two different data sets, then they need to be in the same format. In other words, you can't compare regression coefficients for quarterly data to regression coefficients for monthly data. As for the cubic spline...again, it depends on the question. There isn't much data here to work with so I wouldn't recommend it (rule of thumb is 10 per variable but again, it seems like there's info missing in the question).

I hope this answers your question. If my answer is unclear or isn't what you need, let me know.

• So, based on what you said I should discard the idea of converting the quarterly data that I have into monthly data. However I still do not understand what Am I suppose to answer for the question: 'If monthly revenue were available how I would analyse this time series?' I am not omitting any information, this is the real question :) . Thank you very much for your help – user290335 Mar 19 '17 at 0:53
• Yes, I would. There isn't a lot of data to work with here plus cublic spline is VERY complicated (after all, we need results PLUS interpretability...I don't know who your audience is). If monthly revenue were available AND what you want to find out is the seasonal effect on revenue, then you would need to convert your monthly data into quarterly/seasonal data. How you 'should' analyze your data is completely dependent on your goal. Get me? – Sarah W Mar 19 '17 at 0:56
• Yes I understood, I think that this question is not very clear, I will do what you just said because it makes sense to me. Thank you once again for your help. – user290335 Mar 19 '17 at 0:59
• Wow - I would have a serious conversation with your professor about the clarity of this question. 'Should' is a moral question....it's completely subjective and will change depending on the goal of the project. – Sarah W Mar 19 '17 at 1:01
• You are right! Unfortunately is what we have :) – user290335 Mar 19 '17 at 1:03