I am trying to use time series analysis for air pollution data (hourly base). The variables included in the model are SO2, NO2, O3, CO and PM10. Also, I have the climatology information like temperature, wind speed and relative humidity. When I use the ARIMA model, the results are not bad as well as I have stationary issue with some pollutants. I read in some papers, if the data are not reaching to stationary level, then Vector Error Corrected Model (VECM) will be a good solution to fit an accurate time series model.
any suggestion or recommendation for this type of modeling?
Regards,
Ahmad
1) You probably will need to transform some of your variables as they are non-negative (wind speed, relative humidity, etc.)
2) To evaluate alternative approaches please let me recommend the following framework:
Conference Paper Data Formats and Visual Tools for Forecast Evaluation in Cyb...
3) More specifically, the best approach to compare alternative methods is to use the AvgRelMAE, especially if you use the transformed scale and then back-transform your forecasts, more details can be found here:
Chapter Forecast Error Measures: Critical Review and Practical Recommendations
4) Yes, you can apply VECM, but compared to simpler alternatives it may not give much improvements. The only way to find out is to apply it to your data and to compare it with simpler approaches. This is sometimes called a 'forecast-value-added' (FVA) analysis (see slide 6 of the presentation below). In order to implement the FVA for your data based on the AvgRelMAE, as earlier recommended, you can use this work describing a step-by-step solution:
Conference Paper Data Formats and Visual Tools for Forecast Evaluation in Cyb...
HTH.
P.S. You can use this guide when implementing the VECM itself:
https://towardsdatascience.com/vector-autoregressions-vector-error-correction-multivariate-model-a69daf6ab618
There you can find some explanations of why we need VECM instead of ARIMAX in certain cases.
You can use VECM analysis in any case where you have time series that are not stationary.
In general, if variables are not stationary then there is a chance that any estimations you have from them are invalid (i.e. spurious).
VECM allows you to test whether your variables are cointegrated = whether their relationship may be estimated despite the fact they are non-stationary.
The ARIMA models as far as I know treat non-stationarity, but they are univariate, that is they concern only one variable at a time.
Since your model is multivariate, that is you examine the relationships between the variables, I believe that VECM is the preferred model.
After determinig the number of cointregation through the test of likelihood ratio, we may use VECM in time series analysis.
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