We now explore various methods for forecasting (i.e. predicting) the next value(s) in a time series. A **time series** is a sequence of observations y_{1}, …, y* _{n}*. We usually think of the subscripts as representing evenly spaced time intervals (seconds, minutes, months, seasons, years, etc.).

Topics:

- Forecasting Accuracy
- Basic forecasting methods
- Stochastic Process
- Autoregressive Processes
- Moving Average Processes
- Autoregressive Moving Average Processes (ARMA)
- Autoregressive Integrated Moving Average Processes (ARIMA)

For those of you doing financial analysis, the Deriscope website provides access to a wealth of free financial data to Excel.

Hi Charles,

Have you published the time series analysis in a book.

Mohammed,

No I haven’t. I expect to publish the first of a series of books shortly. I plan to publish a book on time series analysis as well, but that won’t happen this year.

Charles

Hi Charles,

Very nice blog.

I was wondering whether you could help me understand lag removal in time series analysis. I am dealing with a time series data that has multiple parameters. I understand that we need to remove lag before any modeling is performed.

Thanks

Adi

Adi,

You can find information about this topic in the various webpages listed on the reference webpage. In particular, you can start by looking at

http://www.real-statistics.com/time-series-analysis/stochastic-processes/stationary-process/

Charles

Hi Charles,

I use your RealStats Add-in for Excel. For school we usa a time-serie analysis book by Rob J Hyndman.

I was comparing the coefficients of RealsStats with the coefficients of ARIMA in RStudio. For RStudio, I use the ‘fpp2’ package by Rob J Hyndman.

With the exact same dataset the coefficients are different.

I was wondered why they are different. Is this because RealStats is using the solver at the background and is estimating the coefficients? Or is it because R uses different algorithms.

Also with models like ARIMA(1,1,1) the coefficients are almost the same as the coefficients in R. But with a model like ARIMA(3,1,3) the coefficients are very different.

Greatings,

John

John,

Thanks for identifying this. The Real Statistics add-in using two approaches for estimating the ARIMA coefficients, one via Solver and another iterative approach. In test examples, the estimates agreed with R.

Can you send me an Excel file with your data and the results you got from R? I will then try to figure what is going one.

Charles