4

Yes, Hyndman has a brief explanation of the subject here. ARIMAX is a transfer model $$y_t=\frac {\beta(B)} {v(B)} x_t+\frac{\theta(B)}{\phi(B)}z_t$$ where $x_t$ is contemporaneous exogenous variables and $\beta(B)=\beta$ is a simple coefficient matrix. The transfer function approach would have $\beta(B)$ with a set of possibly lagged exogenous variables. A ...


3

This is a classic time series problem and there are lots of papers on it (see Tong JRSSA 1977 for an early discusson). You could transform the series (set lambda = 0.5 for example) and you will get slightly better ARIMA results. But the main problem is that the cycles are of unpredictable length, so any model you produce will struggle to capture the ...


3

To give a general answer on the background and the concept behind series, time series can be used to predict both long term and short term, the problem is what you are trying to predict and how: sometimes time series theory itself will tell you that some series are indeed not predictable, especially in the long term (because their long term moments are not ...


3

I think a good way to do this is via Bayesian Structural Time Series (BSTS). I found out about this approach via these 2 sites (1, 2). I would still be interested in other approaches. Here is the example done with the bsts package in R. I use a time series component and a regression component. The regression component incorporates the prior information. A ...


2

I can suggest a simple approach. Extract the trend, seasonality and noise from the series using any number of available methods. When you forecast, if you're confident in your trend forecast, then use your own expert outlook. Next, you add back the seasonality. The remainder, a noise, can be regressed on exogenous variables if you have forecasts for them. ...


2

Great Question ! "Could I combine my ARIMA forecast with this prior information somehow to form an ensemble forecast?" I have been involved with a commercial time series forecasting package called AUTOBOX and have incorporated delphi-type predictor series where the user provides probabilities of intervals and this is then used to monte-carlo a family of ...


1

This is an interesting problem, I would begin by developing a model including the determinants of signups. Get a general in-sample relationship between those variables and the dependent variable (sign-ups), then, include a shift parameter (here I would use a dummy variable) for the time during the which the marketing campaign was undertaken (at your ...


1

There are several ways to approach this issue ranging from simple heuristics to rigorous econometric models. Among the heuristics is to simply interpolate the values for higher temporal levels down to a more disaggregate periodicity. Many software packages offer automatic methods for doing this. A more rigorous approach for mixed temporality is Ghysels' ...


1

Yes, you can. The DM test only requires the loss differential to be covariance stationary, nothing more. There is nothing special about squared errors or absolute errors or CRPS (in particular, propriety is not even required). See Diebold (2013), "Comparing Predictive Accuracy, Twenty Years Later: A Personal Perspective on the Use and Abuse of Diebold-...


1

From your code, it looks like you may be using random training/validation splits to fit models. This is OK for data sets where each observation is statistically independent, but it's not appropriate for time series analysis. Because there's autocorrelation in time series data, there's a lot of similarity between adjacent time points. If you split the ...


1

Use the observed values as there may be lag structure needed for GDP (X) that may be different than the lag structure need for air traffic passenger data (Y) . You can always subsequently express the change in passenger forecast as a percentage of the previous value as it relates to the change in GDP as it relates to the previous value of GDP . Finally to ...


Only top voted, non community-wiki answers of a minimum length are eligible