I need your help and guidance in a paper using ARIMA modeling. I am working on sea surface temperature modeling based on MODIS remote sensing data, ARIMA model has been used with SPSS.
I am new with ARIMA so results are already obtained but unable to define proper methodology and explain results.
Well, I am using raster data averages that are in monthly from Aug 2002 toApril2020 (213 months). I used SPSS for ARIMA the model is (3,1,1) (3,1,1). As I am new with this, I need your help to understand the model equation and meaning of these R-squared, R-squared, RMSE, MAPE, MaxAPE, MAE, MaxA, and Normalized BIC in model fitting.
I need to know model equation how to write this and SPSS based results interpretation. Though I have model results already.
Your help will be much appreciated. Would you like to help me with this?
There is a difference between ARIMA (p, d, q) and SARIMA (p, d, q) (P, D, Q) or SARIMA (P, D, Q) models in time series. ARIMA means Autoregressive Integrated Moving Avergare, while SARIMA means Seasonal Autoregressive Integrated Moving Average. ARIMA is fitted to non-seasonal data, while SARIMA is fitted to seasonal data. The "p" and "q" represent the order of the non-seaonal autoregressive and moving average process, while "d" is the order of the non-seasonal difference. "P" and "Q" represent the order of the seasonal autoregressive and moving average process, while "D" represent the order of the seasonal difference.
The model (3,1,1) (3,1,1) is the expression for the multiplicative SARIMA (p, d, q) (P, D, Q) model, (Box and Jenkins 1976). If you are fitting ARIMA to a series, it is expressed as ARIMA (p, d, q) with the order (3, 1, 1), not (3, 1, 1) (3, 1, 1) as expressed in your write up. The (3, 1, 1) means the orders of the autoregressive component is "3", moving average is "1" and difference is "1". That is ACF spikes at lag1, PACF spikes at lag 3 after the first order difference (d=1).
The result of your Time Series model (3,1,1)(3,1,1) is SARIMA which means Seasonal AutoRegressive Integrated Moving Average. The data used is a seasonal data, that is why you have seasonal component in your ARIMA model. The first component (3,1,1) is the none seasonal component while the later (3,1,1) is the seasonal component.
Morning Imran AHMED Khan ,
Please see the attached papers that I have attached. The two are my research articles that I have published. Hope they will help you with your answers.
Regards,
Katleho Makatjane (Dr)
Thank you so much.
Would you Plz write (3,1,1)(3,1,1) model equation.
It will save my life.
Regards
Apparently, the model you described was found by a stepwise search when you have different alternative model specifications. SPSS gave you the one with the best AICc or BIC (please check the SPSS documentation). As you mentioned, to evaluate your model you can use R-squared, R-squared, RMSE, MAPE, MaxAPE, MAE, MaxA, and Normalized BIC. But these metrics are usually difficult to interpret and do not reflect forecasting performance for practical purposes.
You need rolling-origin out-of-sample evaluation to obtain a better picture of forecasting performance. Let me recommend our chapter: Chapter Forecast Error Measures: Critical Review and Practical Recommendations
You can use this forecast evaluation framework with step-by-step instructions (originally developed for many series, but can be adapted for 1 time series as well):
Conference Paper Data Formats and Visual Tools for Forecast Evaluation in Cyb...
Basically, you can use SPSS to generate out-of-sample forecasts and then store them in the TSTS and FTS format described in the above paper. Then it's easy to calculate out-of-sample error metrics (such as out-of-sample MAE or MSE / RelMAE or RelMSE) and in any programming environment.
Regards,
Andrey Davydenko
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