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Edit: I would like to refer you to my new and more specific question: Edited: Choice between forecasting models

I'm researching forecasting models. Since I have data that has both a trend and seasionality and is caused by other variables, I would like to describe a model that combines Time Series Models and Causal Models. However, I can't seem to find models that combine those two. What are models for me to look at?

The following models are models that I already described:

  • Moving Average
  • Weighted Moving Average
  • Exponential smoothing
  • Single lineair regression
  • Method of Holt
  • Method of Pegels
  • Seasonal Naïve Method
  • Method of Holt-Winters
  • Multiple Lineair Regression
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  • $\begingroup$ It is important to detect pulses/level shifts/seasonal pulses/local time trends as if untreated your results my be questionable. Parameter constancy is also important to verify along with error variance constancy (not simply Box-Cox) as there effects can be ruinous on your model. For an overview , I wrote autobox.com/cms/index.php/afs-university/intro-to-forecasting/… which might help you understand the opportunities. $\endgroup$
    – IrishStat
    Feb 17, 2016 at 12:33
  • $\begingroup$ If you are looking for causal models with time-varying covariates, I'd recommend taking a look at Marginal Structural Models. See here for one of the standard references in this areas for example: ncbi.nlm.nih.gov/pubmed/10955408 $\endgroup$ Feb 18, 2016 at 4:27
  • $\begingroup$ @StatsStudent Can you elaborate what it means by 'time-varying covariates'? This sounds like non-mainstream technique and interesting. Thanks $\endgroup$ Feb 18, 2016 at 11:52

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You may check regression with ARIMA errors, ARIMAX and transfer function models; they are briefly described in Rob J. Hyndman's blog post "The ARIMAX model muddle". All these models allow for the dependent variable to be a function of its own lags and other variables including seasonal terms (dummies, Fourier terms and the like). Alternatively, seasonality can be included sort of multiplicatively by turning ARIMA into seasonal ARIMA (SARIMA).

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In addition to what Richard Hardy said, we can use unobserved component model (UCM). It allows us to include regressors.

I have also seen people using Random Forest and neural network for forecasting considering other regressors. You can compare the fitted values against actual and test the model accuracy on a holdout sample as well to see which model is performing better.

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