Is your data hourly averaged? Because in this case, the data is not Gaussian distributed and also not stationary. The ARMA is not a correct description for that. Hence, the data has to be transformed and normalized before to adjust the time series to the ARMA.

Here, yo have a good reference: https://www.academia.edu/6219010/Forecast_of_hourly_average_wind_speed_with_ARMA_models_in_Navarre_Spain

http://www.engr.mun.ca/~tariq/deepa.pdf 

Hi Adrian G,

Thanks for your prompt answer, you are right, the data were recorded hourly. To do the time series stationary, I applied a logistic transformation (after I normalized the data), however, I am not sure how ARMA model works and also, how to find the parameters of this?

Thank you for your references.

Best

Samir

For the parameter estimation you can use RLS (recursive least square). You have it in the Identification Toolbox of Matlab.

To know how an ARMA model works, you can read a textbook about signal processing for electrical engineering courses (for example Proakis, chapter 11).

Yep regression is commonly used ! ARMA specifically  you need to get the model (time series or polynomial ) for regression .

You can download SPSS software which contains different details of ARMA or ARIMA models. In the help menu you can find discover how to manipulate data and the theoretical origin also you can refer to the book  (Time series analysis: forecasting and control)  by Box-Jenkins. Please refer to the following link: -

http://onlinelibrary.wiley.com/book/10.1002/9781118619193

Hello Samir

Here I introduce a very useful MATLAB toolbox. All models including ARMA, ARMAX, ARX, etc. (even spectral and polynomial models) can be easily identified. Its very user friendly and fast. You can compare the results and choose the appropriate one.

======>>>"systemIdentification"

Thanks a lot everyone.

ARIMA processes are a class of stochastic processes used to analyze time series which can be made to be “stationary” by differencing (if necessary), perhaps in conjunction with nonlinear transformations such as logging or deflating (if necessary). A random variable that is a time series is stationary if its statistical properties are all constant over time. An ARIMA model can be viewed as a “filter” that tries to separate the signal from the noise, and the signal is then extrapolated into the future to obtain forecasts. The application of the ARIMA methodology for the study of time series analysis is due to Box and Jenkins.

The general statistical scheme of ARIMA is as follows:

· Step 0: A class of models is formulated assuming certain hypotheses.

· Step 1: A model is identified for the observed data.

· Step 2: The model parameters are estimated.

· Step 3: If the hypotheses of the model are validated, go to Step 4, otherwise go to Step 1 to refine the model.

· Step 4: The model is ready for forecasting.