PACF and Autoregressive model

[Profet]

Hi, I'm recently studying time series and stocastic processes in order to analyze some financial market data.
I have a problem in understanding how to create and use an autoregressive model to predict future prices based on a specific time series.

I've already done the partial autocorrelation function (PACF) to study the direct correlation between a time series and its lagged values, and I plotted it in a correlogram.

I've read that you can set up an autoregressive process, starting from the partial autocorrelation, using the formula: zt=Φ1zt-1+…+Φ2zt-2+… Φpzt-p +at.

I tried to calculate an AR(1) process function to estimate only the next first value: I found out the Φ value, that should be the linear regression coefficient, and I calculated all the zt values of the time series.

The problem is that the results are very different from the original prices, and they seem to show a different range of data. I don't know how to continue or if I'm doing something wrong. I'll be glad if someone will help me and correct me if something is missing or if there are some errors in my work.

Thanks in advice.

 

[tkhunny]

Really hard to help without seeing the data and understanding your formulation and results. This is particularly unhelpful: "seem to show a different range of data." No useful information in there at all.

Have you estimated the long-term trend?
What do your seasonal components look like?
How large is your known data time horizon?
Do the data suggest and auto-correlation of any kind?

Lots of questions. The arithmetic can be quite tedious. Complete understanding of the problem is required.

 

[Profet]

Thanks for your reply. I know that I might have been generic regarding to my problem but I'm not very expert about this topic.

For my analysis, I detrended my data in order to turn them into stationary price variations (they are more predictable than prices themselves) and consider them without trend and seasonal components.

I have a data history starting from 2010 (more than 200.000 variables); I will attach an image of the PACF and correlogram made in Excel to show you how the correlation looks like. I pointed out the correlation of the Y(t) until its 11 lagged series ( Y(t-11) ), but my focus is only on the second value Y(t-1), in order to understand if there's a significance relation between Y and Y(t-1) and if I can create an autoregressive model AR(1) based on this relation, to estimate the correlation of the next market data.

I hope I explained myself clearly.

 

[tkhunny]

It look's like your prediction uses all previous data with equal weight. Am I reading that wrong? If I am getting it, that can't make much sense. Let's read up a bit on "over-fitting".

 

[Profet]

I haven't predicted anything yet; the graph I posted shows only the correlation between a time series and its past values. My question is about creating an autoregressive process using this data, or in general how do I have to proceed to make it from a given time series.