Predicting Further Values in a Set of Data

[IshaanM8]

Good day to everyone reading this. Thanks for your time.
I've got this question here (more like an research assignment) which requires me to predict further values in a given set of values.
I've attached a picture for a better understanding.
The data is the cases of influenza in a country over the years.
There's values missing in from May, 2019 onwards.
We have to use the previous set of data, come up with a "Prediction model" and use that to predict the values until end of 2019.
The thing is, our teacher is very incompetent, and only told us to use "polynomials from the graphs we make in excel" and use that...
Anyone got any clues/hints on how i could come up with this prediction model? Please ask if you need any of the graphs. 
P.S. I used the polynomial of 6 for the graphing.
I did the graphing monthly, (Jan - December for a year) but I have literally 0 idea what to do, to get a "model" that predicts the cases for the upcoming months

Thanks for any help

[Prometheus]

Do you have to use polynomials? Just by eye it seems like a time series approach like ARIMA would make a better model (there is both seasonality and an upward trend), but maybe your teacher wants you to learn something specific about fitting polynomials. No idea how to do this in excel, but shouldn't be too hard to find a tutorial online somewhere - or have you already made the graph? Check out Runge's phenomena for why high order polynomials are often not a good model choice, although i think there's a more fundamental reason in this case.

[studiot]

That is quite a lot of data to be processing.

What subject and level is this an assignment in?

 

You say you are using polynomial of 6 for graphing.

Why does this mean and why are you using it?

 

You have 12 estimates of a time series analysis showing both continued upward growth in cases and a peak and decline of cases in the middle years.

 

The first thing I would do is to try to plot these as 13 ordinary number v time graphs.

This would give you an envelope within which you can create your model.

There is also the  variation across the months to consider which can be done as a separate exercise.

 

+1 to prometheus who posted whilst I was thing on this and clearly beat me to much the same ideas.

[IshaanM8]

On 5/21/2019 at 6:32 PM, Prometheus said:

Do you have to use polynomials? Just by eye it seems like a time series approach like ARIMA would make a better model (there is both seasonality and an upward trend), but maybe your teacher wants you to learn something specific about fitting polynomials. No idea how to do this in excel, but shouldn't be too hard to find a tutorial online somewhere - or have you already made the graph? Check out Runge's phenomena for why high order polynomials are often not a good model choice, although i think there's a more fundamental reason in this case.

We don't have to use polynomials. There's multiple ways my teacher tells me, but because this is a "problem - solving task" we're to think up of something of our own. Thanks for the tips, I'll definitely check out Runge's Phenomena and ARIMA. 

Cheers!

On 5/21/2019 at 6:38 PM, studiot said:

That is quite a lot of data to be processing.

What subject and level is this an assignment in?

 

You say you are using polynomial of 6 for graphing.

Why does this mean and why are you using it?

 

You have 12 estimates of a time series analysis showing both continued upward growth in cases and a peak and decline of cases in the middle years.

 

The first thing I would do is to try to plot these as 13 ordinary number v time graphs.

This would give you an envelope within which you can create your model.

There is also the  variation across the months to consider which can be done as a separate exercise.

 

+1 to prometheus who posted whilst I was thing on this and clearly beat me to much the same ideas.

This is "Maths Methods" In Australia which is the 2nd hardest subject for "Mathematics"

Currently Year 11 

I'm using the polynomial of 6 because that's the highest available polynomial in excel.

I've plotted them and they're all very similar to each other.

I then got an average of all these data values and got an "Average Year". I'll be using the Equation from that "Average Year" graph as my Model. But is there anything else I can do to "Refine" it and make it even more accurate?